Nonlinear positron acoustic solitary waves
International Nuclear Information System (INIS)
Tribeche, Mouloud; Aoutou, Kamel; Younsi, Smain; Amour, Rabia
2009-01-01
The problem of nonlinear positron acoustic solitary waves involving the dynamics of mobile cold positrons is addressed. A theoretical work is presented to show their existence and possible realization in a simple four-component plasma model. The results should be useful for the understanding of the localized structures that may occur in space and laboratory plasmas as new sources of cold positrons are now well developed.
Solitary waves on nonlinear elastic rods. I
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1984-01-01
Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction betwe...... nonlinearity. The balance between dispersion and nonlinearity in the equation is investigated.......Acoustic waves on elastic rods with circular cross section are governed by improved Boussinesq equations when transverse motion and nonlinearity in the elastic medium are taken into account. Solitary wave solutions to these equations have been found. The present paper treats the interaction between...... the solitary waves numerically. It is demonstrated that the waves behave almost like solitons in agreement with the fact that the improved Boussinesq equations are nearly integrable. Thus three conservation theorems can be derived from the equations. A new subsonic quasibreather is found in the case of a cubic...
Solitary waves on nonlinear elastic rods. II
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Christiansen, Peter Leth; Lomdahl, P. S.
1987-01-01
In continuation of an earlier study of propagation of solitary waves on nonlinear elastic rods, numerical investigations of blowup, reflection, and fission at continuous and discontinuous variation of the cross section for the rod and reflection at the end of the rod are presented. The results ar...... are compared with predictions of conservation theorems for energy and momentum....
Periodic and solitary wave solutions of cubic–quintic nonlinear ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 86; Issue 6. Periodic and solitary wave solutions of cubic–quintic nonlinear reaction-diffusion equation with variable convection coefficients. BHARDWAJ S B SINGH RAM MEHAR SHARMA KUSHAL MISHRA S C. Regular Volume 86 Issue 6 June 2016 pp 1253-1258 ...
Nonlinear electrostatic solitary waves in electron-positron plasmas
Lazarus, I. J.; Bharuthram, R.; Moolla, S.; Singh, S. V.; Lakhina, G. S.
2016-02-01
The generation of nonlinear electrostatic solitary waves (ESWs) is explored in a magnetized four component two-temperature electron-positron plasma. Fluid theory is used to derive a set of nonlinear equations for the ESWs, which propagate obliquely to an external magnetic field. The electric field structures are examined for various plasma parameters and are shown to yield sinusoidal, sawtooth and bipolar waveforms. It is found that an increase in the densities of the electrons and positrons strengthen the nonlinearity while the periodicity and nonlinearity of the wave increases as the cool-to-hot temperature ratio increases. Our results could be useful in understanding nonlinear propagation of waves in astrophysical environments and related laboratory experiments.
Current structure of strongly nonlinear interfacial solitary waves
Semin, Sergey; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim; Churaev, Egor
2015-04-01
The characteristics of highly nonlinear solitary internal waves (solitons) in two-layer flow are computed within the fully nonlinear Navier-Stokes equations with use of numerical model of the Massachusetts Institute of Technology (MITgcm). The verification and adaptation of the model is based on the data from laboratory experiments [Carr & Davies, 2006]. The present paper also compares the results of our calculations with the computations performed in the framework of the fully nonlinear Bergen Ocean Model [Thiem et al, 2011]. The comparison of the computed soliton parameters with the predictions of the weakly nonlinear theory based on the Gardner equation is given. The occurrence of reverse flow in the bottom layer directly behind the soliton is confirmed in numerical simulations. The trajectories of Lagrangian particles in the internal soliton on the surface, on the interface and near the bottom are computed. The results demonstrated completely different trajectories at different depths of the model area. Thus, in the surface layer is observed the largest displacement of Lagrangian particles, which can be more than two and a half times larger than the characteristic width of the soliton. Located at the initial moment along the middle pycnocline fluid particles move along the elongated vertical loop at a distance of not more than one third of the width of the solitary wave. In the bottom layer of the fluid moves in the opposite direction of propagation of the internal wave, but under the influence of the reverse flow, when the bulk of the velocity field of the soliton ceases to influence the trajectory, it moves in the opposite direction. The magnitude of displacement of fluid particles in the bottom layer is not more than the half-width of the solitary wave. 1. Carr, M., and Davies, P.A. The motion of an internal solitary wave of depression over a fixed bottom boundary in a shallow, two-layer fluid. Phys. Fluids, 2006, vol. 18, No. 1, 1 - 10. 2. Thiem, O., Carr
On the interaction of small-scale linear waves with nonlinear solitary waves
Xu, Chengzhu; Stastna, Marek
2017-04-01
In the study of environmental and geophysical fluid flows, linear wave theory is well developed and its application has been considered for phenomena of various length and time scales. However, due to the nonlinear nature of fluid flows, in many cases results predicted by linear theory do not agree with observations. One of such cases is internal wave dynamics. While small-amplitude wave motion may be approximated by linear theory, large amplitude waves tend to be solitary-like. In some cases, when the wave is highly nonlinear, even weakly nonlinear theories fail to predict the wave properties correctly. We study the interaction of small-scale linear waves with nonlinear solitary waves using highly accurate pseudo spectral simulations that begin with a fully nonlinear solitary wave and a train of small-amplitude waves initialized from linear waves. The solitary wave then interacts with the linear waves through either an overtaking collision or a head-on collision. During the collision, there is a net energy transfer from the linear wave train to the solitary wave, resulting in an increase in the kinetic energy carried by the solitary wave and a phase shift of the solitary wave with respect to a freely propagating solitary wave. At the same time the linear waves are greatly reduced in amplitude. The percentage of energy transferred depends primarily on the wavelength of the linear waves. We found that after one full collision cycle, the longest waves may retain as much as 90% of the kinetic energy they had initially, while the shortest waves lose almost all of their initial energy. We also found that a head-on collision is more efficient in destroying the linear waves than an overtaking collision. On the other hand, the initial amplitude of the linear waves has very little impact on the percentage of energy that can be transferred to the solitary wave. Because of the nonlinearity of the solitary wave, these results provide us some insight into wave-mean flow
Exact solitary and periodic wave solutions for a generalized nonlinear Schroedinger equation
International Nuclear Information System (INIS)
Sun Chengfeng; Gao Hongjun
2009-01-01
The generalized nonlinear Schroedinger equation (GNLS) iu t + u xx + β | u | 2 u + γ | u | 4 u + iα (| u | 2 u) x + iτ(| u | 2 ) x u = 0 is studied. Using the bifurcation of travelling waves of this equation, some exact solitary wave solutions were obtained in [Wang W, Sun J,Chen G, Bifurcation, Exact solutions and nonsmooth behavior of solitary waves in the generalized nonlinear Schroedinger equation. Int J Bifucat Chaos 2005:3295-305.]. In this paper, more explicit exact solitary wave solutions and some new smooth periodic wave solutions are obtained.
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Using direct algebraic method,exact solitary wave solutions are performed for a class of third order nonlinear dispersive disipative partial differential equations. These solutions are obtained under certain conditions for the relationship between the coefficients of the equation. The exact solitary waves of this class are rational functions of real exponentials of kink-type solutions.
Energy Technology Data Exchange (ETDEWEB)
Arevalo, Edward, E-mail: arevalo@temf.tu-darmstadt.d [Technische Universitaet Darmstadt, Institut fuer Theorie elektromagnetischer Felder, TEMF, Schlossgartenstr. 8, D-64289 Darmstadt (Germany)
2009-09-21
The effect of instability on the propagation of solitary waves along one-dimensional discrete nonlinear Schroedinger equation with cubic nonlinearity is revisited. A self-contained quasicontinuum approximation is developed to derive closed-form expressions for small-amplitude solitary waves. The notion that the existence of nonlinear solitary waves in discrete systems is a signature of the modulation instability is used. With the help of this notion we conjecture that instability effects on moving solitons can be qualitative estimated from the analytical solutions. Results from numerical simulations are presented to support this conjecture.
International Nuclear Information System (INIS)
Tian Lixin; Yin Jiuli
2004-01-01
In this paper, we introduce the fully nonlinear generalized Camassa-Holm equation C(m,n,p) and by using four direct ansatzs, we obtain abundant solutions: compactons (solutions with the absence of infinite wings), solitary patterns solutions having infinite slopes or cups, solitary waves and singular periodic wave solutions and obtain kink compacton solutions and nonsymmetry compacton solutions. We also study other forms of fully nonlinear generalized Camassa-Holm equation, and their compacton solutions are governed by linear equations
Identification and determination of solitary wave structures in nonlinear wave propagation
International Nuclear Information System (INIS)
Newman, W.I.; Campbell, D.K.; Hyman, J.M.
1991-01-01
Nonlinear wave phenomena are characterized by the appearance of ''solitary wave coherent structures'' traveling at speeds determined by their amplitudes and morphologies. Assuming that these structures are briefly noninteracting, we propose a method for the identification of the number of independent features and their respective speeds. Using data generated from an exact two-soliton solution to the Korteweg-de-Vries equation, we test the method and discuss its strengths and limitations. 41 refs., 2 figs
Periodic and solitary wave solutions of cubic–quintic nonlinear ...
Indian Academy of Sciences (India)
Hence, most of the real nonlinear physical equations possess variable ... evolution of the system with time and second term represents the convective flux term. The ... Travelling wave solutions of nonlinear reaction-diffusion equations are.
Nonlinear Wave Propagation and Solitary Wave Formation in Two-Dimensional Heterogeneous Media
Luna, Manuel
2011-05-01
Solitary wave formation is a well studied nonlinear phenomenon arising in propagation of dispersive nonlinear waves under suitable conditions. In non-homogeneous materials, dispersion may happen due to effective reflections between the material interfaces. This dispersion has been used along with nonlinearities to find solitary wave formation using the one-dimensional p-system. These solitary waves are called stegotons. The main goal in this work is to find two-dimensional stegoton formation. To do so we consider the nonlinear two-dimensional p-system with variable coefficients and solve it using finite volume methods. The second goal is to obtain effective equations that describe the macroscopic behavior of the variable coefficient system by a constant coefficient one. This is done through a homogenization process based on multiple-scale asymptotic expansions. We compare the solution of the effective equations with the finite volume results and find a good agreement. Finally, we study some stability properties of the homogenized equations and find they and one-dimensional versions of them are unstable in general.
Ma, Li-Yuan; Ji, Jia-Liang; Xu, Zong-Wei; Zhu, Zuo-Nong
2018-03-01
We study a nonintegrable discrete nonlinear Schrödinger (dNLS) equation with the term of nonlinear nearest-neighbor interaction occurred in nonlinear optical waveguide arrays. By using discrete Fourier transformation, we obtain numerical approximations of stationary and travelling solitary wave solutions of the nonintegrable dNLS equation. The analysis of stability of stationary solitary waves is performed. It is shown that the nonlinear nearest-neighbor interaction term has great influence on the form of solitary wave. The shape of solitary wave is important in the electric field propagating. If we neglect the nonlinear nearest-neighbor interaction term, much important information in the electric field propagating may be missed. Our numerical simulation also demonstrates the difference of chaos phenomenon between the nonintegrable dNLS equation with nonlinear nearest-neighbor interaction and another nonintegrable dNLS equation without the term. Project supported by the National Natural Science Foundation of China (Grant Nos. 11671255 and 11701510), the Ministry of Economy and Competitiveness of Spain (Grant No. MTM2016-80276-P (AEI/FEDER, EU)), and the China Postdoctoral Science Foundation (Grant No. 2017M621964).
Combined solitary-wave solution for coupled higher-order nonlinear Schroedinger equations
International Nuclear Information System (INIS)
Tian Jinping; Tian Huiping; Li Zhonghao; Zhou Guosheng
2004-01-01
Coupled nonlinear Schroedinger equations model several interesting physical phenomena. We used a trigonometric function transform method based on a homogeneous balance to solve the coupled higher-order nonlinear Schroedinger equations. We obtained four pairs of exact solitary-wave solutions including a dark and a bright-soliton pair, a bright- and a dark-soliton pair, a bright- and a bright-soliton pair, and the last pair, a combined bright-dark-soliton pair
Energy Technology Data Exchange (ETDEWEB)
Emadi, E.; Zahed, H. [Physics Department, Faculty of Science, Sahand University of Technology, 51335–1996 Tabriz (Iran, Islamic Republic of)
2016-08-15
The behavior of linear and nonlinear dust ion acoustic (DIA) solitary waves in an unmagnetized quantum dusty plasma, including inertialess electrons and positrons, ions, and mobile negative dust grains, are studied. Reductive perturbation and Sagdeev pseudopotential methods are employed for small and large amplitude DIA solitary waves, respectively. A minimum value of the Mach number obtained for the existence of solitary waves using the analytical expression of the Sagdeev potential. It is observed that the variation on the values of the plasma parameters such as different values of Mach number M, ion to electron Fermi temperature ratio σ, and quantum diffraction parameter H can lead to the creation of compressive solitary waves.
Rani, Monika; Bhatti, Harbax S.; Singh, Vikramjeet
2017-11-01
In optical communication, the behavior of the ultrashort pulses of optical solitons can be described through nonlinear Schrodinger equation. This partial differential equation is widely used to contemplate a number of physically important phenomena, including optical shock waves, laser and plasma physics, quantum mechanics, elastic media, etc. The exact analytical solution of (1+n)-dimensional higher order nonlinear Schrodinger equation by He's variational iteration method has been presented. Our proposed solutions are very helpful in studying the solitary wave phenomena and ensure rapid convergent series and avoid round off errors. Different examples with graphical representations have been given to justify the capability of the method.
Energy Technology Data Exchange (ETDEWEB)
Han, Jiu-Ning, E-mail: hanjiuning@126.com; He, Yong-Lin; Luo, Jun-Hua; Nan, Ya-Gong; Han, Zhen-Hai; Dong, Guang-Xing [College of Physics and Electromechanical Engineering, Hexi University, Zhangye 734000 (China); Duan, Wen-Shan [College of Physics and Electronic Engineering, Northwest Normal University, Lanzhou 730070 (China); Li, Jun-Xiu [College of Civil Engineering, Hexi University, Zhangye 734000 (China)
2014-01-15
With the consideration of the superthermal electron distribution, we present a theoretical investigation about the nonlinear propagation of electron-acoustic solitary and shock waves in a dissipative, nonplanar non-Maxwellian plasma comprised of cold electrons, superthermal hot electrons, and stationary ions. The reductive perturbation technique is used to obtain a modified Korteweg-de Vries Burgers equation for nonlinear waves in this plasma. We discuss the effects of various plasma parameters on the time evolution of nonplanar solitary waves, the profile of shock waves, and the nonlinear structure induced by the collision between planar solitary waves. It is found that these parameters have significant effects on the properties of nonlinear waves and collision-induced nonlinear structure.
Solitary waves under the competition of linear and nonlinear periodic potentials
International Nuclear Information System (INIS)
Rapti, Z; Kevrekidis, P G; Konotop, V V; Jones, C K R T
2007-01-01
In this paper, we study the competition of the linear and nonlinear lattices and its effects on the stability and dynamics of bright solitary waves. We consider both lattices in a perturbative framework, whereby the technique of Hamiltonian perturbation theory can be used to obtain information about the existence of solutions, and the same approach, as well as eigenvalue count considerations, can be used to obtain detailed conditions about their linear stability. We find that the analytical results are in very good agreement with our numerical findings and can also be used to predict features of the dynamical evolution of such solutions. A particularly interesting result of these considerations is the existence of a tunable cancellation effect between the linear and nonlinear lattices that allows for increased mobility of the solitary wave
Solitary wave solutions to nonlinear evolution equations in ...
Indian Academy of Sciences (India)
1Computer Engineering Technique Department, Al-Rafidain University College, Baghdad, ... applied to extract solutions are tan–cot method and functional variable approaches. ... Consider the nonlinear partial differential equation in the form.
New method for rekindling the nonlinear solitary waves in Maxwellian complex space plasma
Das, G. C.; Sarma, Ridip
2018-04-01
Our interest is to study the nonlinear wave phenomena in complex plasma constituents with Maxwellian electrons and ions. The main reason for this consideration is to exhibit the effects of dust charge fluctuations on acoustic modes evaluated by the use of a new method. A special method (G'/G) has been developed to yield the coherent features of nonlinear waves augmented through the derivation of a Korteweg-de Vries equation and found successfully the different nature of solitons recognized in space plasmas. Evolutions have shown with the input of appropriate typical plasma parameters to support our theoretical observations in space plasmas. All conclusions are in good accordance with the actual occurrences and could be of interest to further the investigations in experiments and satellite observations in space. In this paper, we present not only the model that exhibited nonlinear solitary wave propagation but also a new mathematical method to the execution.
Solitary wave solutions of two-dimensional nonlinear Kadomtsev ...
Indian Academy of Sciences (India)
Aly R Seadawy
2017-09-13
Sep 13, 2017 ... We considered the two-dimensional DASWs in colli- sionless, unmagnetized cold plasma consisting of dust fluid, ions and electrons. The dynamics of DASWs is governed by the normalized fluid equations of nonlin- ear continuity (1), nonlinear motion of system (2) and. (3) and linear Poisson equation (4) as.
International Nuclear Information System (INIS)
Li Jin-Yuan; Fang Nian-Qiao; Yuan Xiao-Bo; Zhang Ji; Xue Yu-Long; Wang Xue-Mu
2016-01-01
In the past few decades, the (1+1)-dimensional nonlinear Schrödinger (NLS) equation had been derived for envelope Rossby solitary waves in a line by employing the perturbation expansion method. But, with the development of theory, we note that the (1+1)-dimensional model cannot reflect the evolution of envelope Rossby solitary waves in a plane. In this paper, by constructing a new (2+1)-dimensional multiscale transform, we derive the (2+1)-dimensional dissipation nonlinear Schrödinger equation (DNLS) to describe envelope Rossby solitary waves under the influence of dissipation which propagate in a plane. Especially, the previous researches about envelope Rossby solitary waves were established in the zonal area and could not be applied directly to the spherical earth, while we adopt the plane polar coordinate and overcome the problem. By theoretical analyses, the conservation laws of (2+1)-dimensional envelope Rossby solitary waves as well as their variation under the influence of dissipation are studied. Finally, the one-soliton and two-soliton solutions of the (2+1)-dimensional NLS equation are obtained with the Hirota method. Based on these solutions, by virtue of the chirp concept from fiber soliton communication, the chirp effect of envelope Rossby solitary waves is discussed, and the related impact factors of the chirp effect are given. (paper)
Fusion an annihilation of solitary waves for a (2+1)-dimensional nonlinear system
Energy Technology Data Exchange (ETDEWEB)
Qiang, Ji-Ye [Nanjing Agricultural Univ. (China). Agronomy College; Lishui Univ., Zhejiang (China). College of Mathematics and Physics; Yunnan Agricultural Univ., Kunming (China). Tobacco College; Ma, Song-Hua; Ren, Qing-Bao [Lishui Univ., Zhejiang (China). College of Mathematics and Physics; Wang, Shao-Hua [Nanjing Agricultural Univ. (China). Agronomy College
2010-12-15
In this paper, a new projective equation is used to obtain the variable separation solutions with two arbitrary functions of the (2+1)-dimensional Broek-Kaup system (BKK). Based on the derived solitary wave solutions and by selecting appropriate functions, some novel localized excitations such as fusion and annihilation of solitary waves are investigated. (orig.)
Diffractons: Solitary Waves Created by Diffraction in Periodic Media
Ketcheson, David I.; Quezada de Luna, Manuel
2015-01-01
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. These solitary waves depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation
Multi-component optical solitary waves
DEFF Research Database (Denmark)
Kivshar, Y. S.; Sukhorukov, A. A.; Ostrovskaya, E. A.
2000-01-01
We discuss several novel types of multi-component (temporal and spatial) envelope solitary waves that appear in fiber and waveguide nonlinear optics. In particular, we describe multi-channel solitary waves in bit-parallel-wavelength fiber transmission systems for highperformance computer networks......, multi-color parametric spatial solitary waves due to cascaded nonlinearities of quadratic materials, and quasiperiodic envelope solitons due to quasi-phase-matching in Fibonacci optical superlattices. (C) 2000 Elsevier Science B.V. All rights reserved....
Sultana, S.; Schlickeiser, R.
2018-05-01
Fully nonlinear features of heavy ion-acoustic solitary waves (HIASWs) have been investigated in an astrophysical degenerate relativistic quantum plasma (ADRQP) containing relativistically degenerate electrons and non-relativistically degenerate light ion species, and non-degenerate heavy ion species. The pseudo-energy balance equation is derived from the fluid dynamical equations by adopting the well-known Sagdeev-potential approach, and the properties of arbitrary amplitude HIASWs are examined. The small amplitude limit for the propagation of HIASWs is also recovered. The basic features (width, amplitude, polarity, critical Mach number, speed, etc.) of HIASWs are found to be significantly modified by the relativistic effect of the electron species, and also by the variation of the number density of electron, light ion, and heavy ion species. The basic properties of HIASWs, that may propagated in some realistic astrophysical plasma systems (e.g., in white dwarfs), are briefly discussed.
International Nuclear Information System (INIS)
Sabry, R.; Shukla, P. K.; Moslem, W. M.
2009-01-01
Properties of fully nonlinear ion-acoustic solitary waves in a plasma with positive-negative ions and nonthermal electrons are investigated. For this purpose, the hydrodynamic equations for the positive-negative ions, nonthermal electron density distribution, and the Poisson equation are used to derive the energy integral equation with a new Sagdeev potential. The latter is analyzed to examine the existence regions of the solitary pulses. It is found that the solitary excitations strongly depend on the mass and density ratios of the positive and negative ions as well as the nonthermal electron parameter. Numerical solution of the energy integral equation clears that both positive and negative potentials exist together. It is found that faster solitary pulses are taller and narrower. Furthermore, increasing the electron nonthermality parameter (negative-to-positive ions density ratio) decreases (increases) the localized excitation amplitude but increases (decreases) the pulse width. The present model is used to investigate the solitary excitations in the (H + ,O 2 - ) and (H + ,H - ) plasmas, where they are presented in the D- and F-regions of the Earth's ionosphere. This investigation should be helpful in understanding the salient features of the fully nonlinear ion-acoustic solitary waves in space and in laboratory plasmas where two distinct groups of ions and non-Boltzmann distributed electrons are present.
Grimshaw, RHJ
2007-01-01
After the initial observation by John Scott Russell of a solitary wave in a canal, his insightful laboratory experiments and the subsequent theoretical work of Boussinesq, Rayleigh and Korteweg and de Vries, interest in solitary waves in fluids lapsed until the mid 1960's with the seminal paper of Zabusky and Kruskal describing the discovery of the soliton. This was followed by the rapid development of the theory of solitons and integrable systems. At the same time came the realization that solitary waves occur naturally in many physical systems, and play a fundamental role in many circumstances. The aim of this text is to describe the role that soliton theory plays in fluids in several contexts. After an historical introduction, the book is divided five chapters covering the basic theory of the Korteweg-de Vries equation, and the subsequent application to free-surface solitary waves in water to internal solitary waves in the coastal ocean and the atmospheric boundary layer, solitary waves in rotating flows, ...
Sakaguchi, Hidetsugu; Ishibashi, Kazuya
2018-06-01
We study self-propelled particles by direct numerical simulation of the nonlinear Kramers equation for self-propelled particles. In our previous paper, we studied self-propelled particles with velocity variables in one dimension. In this paper, we consider another model in which each particle exhibits directional motion. The movement direction is expressed with a variable ϕ. We show that one-dimensional solitary wave states appear in direct numerical simulations of the nonlinear Kramers equation in one- and two-dimensional systems, which is a generalization of our previous result. Furthermore, we find two-dimensionally localized states in the case that each self-propelled particle exhibits rotational motion. The center of mass of the two-dimensionally localized state exhibits circular motion, which implies collective rotating motion. Finally, we consider a simple one-dimensional model equation to qualitatively understand the formation of the solitary wave state.
Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru
2018-01-01
This paper addresses the coupled nonlinear Schrödinger equation (CNLSE) in monomode step-index in optical fibers which describes the nonlinear modulations of two monochromatic waves, whose group velocities are almost equal. A class of dark, bright, dark-bright and dark-singular optical solitary wave solutions of the model are constructed using the complex envelope function ansatz. Singular solitary waves are also retrieved as bye products of the in integration scheme. This naturally lead to some constraint conditions placed on the solitary wave parameters which must hold for the solitary waves to exist. The modulation instability (MI) analysis of the model is studied based on the standard linear-stability analysis. Numerical simulation and physical interpretations of the obtained results are demonstrated. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the CNLSE.
On solitary surface waves in cold plasmas
International Nuclear Information System (INIS)
Vladimirov, S.V.; Yu, M.Y.; Stenflo, L.
1993-01-01
A new type of nonlinear electromagnetic solitary surface waves propagating along the boundary of a cold plasma is discussed. These waves are described by a novel nonlinear evolution equation, obtained when the nonlinear surface currents at the boundary are taken into consideration. (Author)
International Nuclear Information System (INIS)
Zahran, M.A.; El-Shewy, E.K.
2008-01-01
The nonlinear properties of solitary wave structures are reported in an unmagnetized collisionless plasma comprising of cold relativistic electron fluid, Maxwellian hot electrons, relativistic electron beam, and stationary ions. The Korteweg--de Vries (KdV) equation has been derived using a reductive perturbation theory. As the wave amplitude increases, the width and velocity of the soliton deviate from the prediction of the KdV equation i.e. the breakdown of the KdV approximation. On the other hand, to overcome this weakness we extend our analysis to obtain the KdV equation with fifth-order dispersion term. The solution of the resulting equation has been obtained
Exact solitary waves of the Fisher equation
International Nuclear Information System (INIS)
Kudryashov, Nikolai A.
2005-01-01
New method is presented to search exact solutions of nonlinear differential equations. This approach is used to look for exact solutions of the Fisher equation. New exact solitary waves of the Fisher equation are given
Ahmad, S.; Ahmad, A.; Bacha, B. A.; Khan, A. A.; Abdul Jabar, M. S.
2017-12-01
Surface Plasmon Polaritons (SPPs) are theoretically investigated at the interface of a dielectric metal and gold. The output pulse from the dielectric is used as the input pulse for the generation of SPPs. The SPPs show soliton-like behavior at the interface. The solitary form of a SPP is maintained under the effects of Kerr nonlinearity, Doppler broadening and Fresnel dragging whereas its phase shift is significantly modified. A 0.3radian phase shift is calculated in the presence of both Kerr nonlinearity and Fresnel dragging in the absence of plasma motion. The phase shift is enhanced to 60radian due to the combined effect of Doppler broadening, Kerr nonlinearity and Fresnel dragging. The results may have significant applications in nano-photonics, optical tweezers, photovoltaic devices, plasmonster and sensing technology.
Directory of Open Access Journals (Sweden)
Yunlong Shi
2014-01-01
Full Text Available We solve the so-called dissipative nonlinear Schrödinger equation by means of multiple scales analysis and perturbation method to describe envelope solitary Rossby waves with dissipation effect in stratified fluids. By analyzing the evolution of amplitude of envelope solitary Rossby waves, it is found that the shear of basic flow, Brunt-Vaisala frequency, and β effect are important factors to form the envelope solitary Rossby waves. By employing trial function method, the asymptotic solution of dissipative nonlinear Schrödinger equation is derived. Based on the solution, the effect of dissipation on the evolution of envelope solitary Rossby wave is also discussed. The results show that the dissipation causes a slow decrease of amplitude of envelope solitary Rossby waves and a slow increase of width, while it has no effect on the propagation velocity. That is quite different from the KdV-type solitary waves. It is notable that dissipation has certain influence on the carrier frequency.
Is DNA a nonlinear dynamical system where solitary conformational ...
Indian Academy of Sciences (India)
Unknown
DNA is considered as a nonlinear dynamical system in which solitary conformational waves can be excited. The ... nonlinear differential equations and their soliton-like solu- .... structure and dynamics can be added till the most accurate.
Two-color walking Peregrine solitary waves.
Baronio, Fabio; Chen, Shihua; Mihalache, Dumitru
2017-09-15
We study the extreme localization of light, evolving upon a non-zero background, in two-color parametric wave interaction in nonlinear quadratic media. We report the existence of quadratic Peregrine solitary waves, in the presence of significant group-velocity mismatch between the waves (or Poynting vector beam walk-off), in the regime of cascading second-harmonic generation. This finding opens a novel path for the experimental demonstration of extreme rogue waves in ultrafast quadratic nonlinear optics.
Solitary waves for a coupled nonlinear Schrodinger system with dispersion management
Directory of Open Access Journals (Sweden)
Panayotis Panayotaros
2010-08-01
Full Text Available We consider a system of coupled nonlinear Schrodinger equations with periodically varying dispersion coefficient that arises in the context of fiber-optics communication. We use Lions's Concentration Compactness principle to show the existence of standing waves with prescribed L^2 norm in an averaged equation that approximates the coupled system. We also use the Mountain Pass Lemma to prove the existence of standing waves with prescribed frequencies.
Solitary heat waves in nonlinear lattices with squared on-site potential
Indian Academy of Sciences (India)
A model Hamiltonian is proposed for heat conduction in a nonlinear lattice with squared on-site potential using the second quantized operators and averaging the same using a suitable wave function, equations are derived in discrete form for the field amplitude and the properties of heat transfer are examined theoretically.
Solitary heat waves in nonlinear lattices with squared on-site potential
Indian Academy of Sciences (India)
Abstract. A model Hamiltonian is proposed for heat conduction in a nonlinear lattice with squared on-site potential using the second quantized operators and averaging the same using a suitable wave function, equations are derived in discrete form for the field amplitude and the prop- erties of heat transfer are examined ...
Ambipolarons: Solitary wave solutions for the radial electric field in a plasma
International Nuclear Information System (INIS)
Hastings, D.E.; Hazeltine, R.D.; Morrison, P.J.
1986-01-01
The ambipolar radial electric field in a nonaxisymmetric plasma can be described by a nonlinear diffusion equation. This equation is shown to possess solitary wave solutions. A model nonlinear diffusion equation with a cubic nonlinearity is studied. An explicit analytic step-like form for the solitary wave is found. It is shown that the solitary wave solutions are linearly stable against all but translational perturbations. Collisions of these solitary waves are studied and three possible final states are found: two diverging solitary waves, two stationary solitary waves, or two converging solitary waves leading to annihilation
On exact solitary wave solutions of the nonlinear Schroedinger equation with a source
International Nuclear Information System (INIS)
Raju, T Solomon; Kumar, C Nagaraja; Panigrahi, Prasanta K
2005-01-01
We use a fractional transformation to connect the travelling wave solutions of the nonlinear Schroedinger equation (NLSE), phase locked with a source, to the elliptic equations satisfying, f-Prime ± af ± λf 3 = 0. The solutions are necessarily of rational form, containing both trigonometric and hyperbolic types as special cases. Bright and dark solitons, as well as singular solitons, are obtained in a suitable range of parameter values. (letter to the editor)
Solitary drift waves in the presence of magnetic shear
International Nuclear Information System (INIS)
Meiss, J.D.; Horton, W.
1982-07-01
The two-component fluid equations describing electron drift and ion acoustic waves in a nonuniform magnetized plasma are shown to possess nonlinear two-dimensional solitary wave solutions. In the presence of magnetic shear, radiative shear damping is exponentially small in L/sub s//L/sub n/ for solitary drift waves, in contrast to linear waves
Lu, Dianchen; Seadawy, A. R.; Arshad, M.; Wang, Jun
In this paper, new exact solitary wave, soliton and elliptic function solutions are constructed in various forms of three dimensional nonlinear partial differential equations (PDEs) in mathematical physics by utilizing modified extended direct algebraic method. Soliton solutions in different forms such as bell and anti-bell periodic, dark soliton, bright soliton, bright and dark solitary wave in periodic form etc are obtained, which have large applications in different branches of physics and other areas of applied sciences. The obtained solutions are also presented graphically. Furthermore, many other nonlinear evolution equations arising in mathematical physics and engineering can also be solved by this powerful, reliable and capable method. The nonlinear three dimensional extended Zakharov-Kuznetsov dynamica equation and (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsov equation are selected to show the reliability and effectiveness of the current method.
Interaction dynamics of electrostatic solitary waves
Directory of Open Access Journals (Sweden)
V. L. Krasovsky
1999-01-01
Full Text Available Interaction of nonlinear electrostatic pulses associated with electron phase density holes moving in a collisionless plasma is studied. An elementary event of the interaction is analyzed on the basis of the energy balance in the system consisting of two electrostatic solitary waves. It is established that an intrinsic property of the system is a specific irreversibility caused by a nonadiabatic modification of the internal structure of the holes and their effective heating in the process of the interaction. This dynamical irreversibility is closely connected with phase mixing of the trapped electrons comprising the holes and oscillating in the varying self-consistent potential wells. As a consequence of the irreversibility, the "collisions" of the solitary waves should be treated as "inelastic" ones. This explains the general tendency to the merging of the phase density holes frequently observed in numerical simulation and to corresponding coupling of the solitary waves.
Rogue waves in nonlinear science
International Nuclear Information System (INIS)
Yan Zhenya
2012-01-01
Rogue waves, as a special type of solitary waves, play an important role in nonlinear optics, Bose-Einstein condensates, ocean, atmosphere, and even finance. In this report, we mainly review on the history of the rogue wave phenomenon and recent development of rogue wave solutions in some nonlinear physical models arising in the fields of nonlinear science.
Traveling solitary wave solutions to evolution equations with nonlinear terms of any order
International Nuclear Information System (INIS)
Feng Zhaosheng
2003-01-01
Many physical phenomena in one- or higher-dimensional space can be described by nonlinear evolution equations, which can be reduced to ordinary differential equations such as the Lienard equation. Thus, to study those ordinary differential equations is of significance not only in mathematics itself, but also in physics. In this paper, a kind of explicit exact solutions to the Lienard equation is obtained. The applications of the solutions to the nonlinear RR-equation and the compound KdV-type equation are presented, which extend the results obtained in the previous literature
Dust acoustic solitary and shock waves in strongly coupled dusty ...
Indian Academy of Sciences (India)
between nonlinear and dispersion effects can result in the formation of symmetrical solitary waves. Also shock ... et al have studied the effect of nonadiabatic dust charge variation on the nonlinear dust acoustic wave with ..... Figure 5 presents the border between oscillatory- and monotonic-type shock waves as functions of ...
Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method
International Nuclear Information System (INIS)
Ebaid, A.
2007-01-01
Based on the Exp-function method, exact solutions for some nonlinear evolution equations are obtained. The KdV equation, Burgers' equation and the combined KdV-mKdV equation are chosen to illustrate the effectiveness of the method
Bulk solitary waves in elastic solids
Samsonov, A. M.; Dreiden, G. V.; Semenova, I. V.; Shvartz, A. G.
2015-10-01
A short and object oriented conspectus of bulk solitary wave theory, numerical simulations and real experiments in condensed matter is given. Upon a brief description of the soliton history and development we focus on bulk solitary waves of strain, also known as waves of density and, sometimes, as elastic and/or acoustic solitons. We consider the problem of nonlinear bulk wave generation and detection in basic structural elements, rods, plates and shells, that are exhaustively studied and widely used in physics and engineering. However, it is mostly valid for linear elasticity, whereas dynamic nonlinear theory of these elements is still far from being completed. In order to show how the nonlinear waves can be used in various applications, we studied the solitary elastic wave propagation along lengthy wave guides, and remarkably small attenuation of elastic solitons was proven in physical experiments. Both theory and generation for strain soliton in a shell, however, remained unsolved problems until recently, and we consider in more details the nonlinear bulk wave propagation in a shell. We studied an axially symmetric deformation of an infinite nonlinearly elastic cylindrical shell without torsion. The problem for bulk longitudinal waves is shown to be reducible to the one equation, if a relation between transversal displacement and the longitudinal strain is found. It is found that both the 1+1D and even the 1+2D problems for long travelling waves in nonlinear solids can be reduced to the Weierstrass equation for elliptic functions, which provide the solitary wave solutions as appropriate limits. We show that the accuracy in the boundary conditions on free lateral surfaces is of crucial importance for solution, derive the only equation for longitudinal nonlinear strain wave and show, that the equation has, amongst others, a bidirectional solitary wave solution, which lead us to successful physical experiments. We observed first the compression solitary wave in the
Partial Differential Equations and Solitary Waves Theory
Wazwaz, Abdul-Majid
2009-01-01
"Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II w...
Solitary waves and homoclinic orbits
International Nuclear Information System (INIS)
Balmforth, N.J.
1994-03-01
The notion that fluid motion often organizes itself into coherent structures has increasingly permeated modern fluid dynamics. Such localized objects appear in laminar flows and persist in turbulent states; from the water on windows on rainy days, to the circulations in planetary atmospheres. This review concerns solitary waves in fluids. More specifically, it centres around the mathematical description of solitary waves in a single spatial dimension. Moreover, it concentrates on strongly dissipative dynamics, rather than integrable systems like the KdV equation. One-dimensional solitary waves, or pulses and fronts as they are also called, are the simplest kinds of coherent structure (at least from a geometrical point of view). Nevertheless, their dynamics can be rich and complicated. In some circumstances this leads to the formation of spatio-temporal chaos in the systems giving birth to the solitary waves, and understanding that phenomenon is one of the major goals in the theory outlined in this review. Unfortunately, such a goal is far from achieved to date, and the author assess its current status and incompleteness
Analytical study of dissipative solitary waves
Energy Technology Data Exchange (ETDEWEB)
Dini, Fatemeh [Department of Physics, Amirkabir University of Technology, Tehran (Iran, Islamic Republic of); Emamzadeh, Mehdi Molaie [Department of Physics, Amirkabir University of Technology, Tehran (Iran, Islamic Republic of); Khorasani, Sina [School of Electrical Engineering, Sharif University of Technology, PO Box 11365-363, Tehran (Iran, Islamic Republic of); Bobin, Jean Louis [Universite Pierre et Marie Curie, Paris (France); Amrollahi, Reza [Department of Physics, Amirkabir University of Technology, Tehran (Iran, Islamic Republic of); Sodagar, Majid [School of Electrical Engineering, Sharif University of Technology, PO Box 11365-363, Tehran (Iran, Islamic Republic of); Khoshnegar, Milad [School of Electrical Engineering, Sharif University of Technology, PO Box 11365-363, Tehran (Iran, Islamic Republic of)
2008-02-15
In this paper, the analytical solution to a new class of nonlinear solitons is presented with cubic nonlinearity, subject to a dissipation term arising as a result of a first-order derivative with respect to time, in the weakly nonlinear regime. Exact solutions are found using the combination of the perturbation and Green's function methods up to the third order. We present an example and discuss the asymptotic behavior of the Green's function. The dissipative solitary equation is also studied in the phase space in the non-dissipative and dissipative forms. Bounded and unbounded solutions of this equation are characterized, yielding an energy conversation law for non-dissipative waves. Applications of the model include weakly nonlinear solutions of terahertz Josephson plasma waves in layered superconductors and ablative Rayleigh-Taylor instability.
Microtubules: A network for solitary waves
Directory of Open Access Journals (Sweden)
Zdravković Slobodan
2017-01-01
Full Text Available In the present paper we deal with nonlinear dynamics of microtubules. The structure and role of microtubules in cells are explained as well as one of models explaining their dynamics. Solutions of the crucial nonlinear differential equation depend on used mathematical methods. Two commonly used procedures, continuum and semi-discrete approximations, are explained. These solutions are solitary waves usually called as kink solitons, breathers and bell-type solitons. [Project of the Serbian Ministry of Education, Science and Technological Development, Grant no. III45010
The lifecycle of axisymmetric internal solitary waves
Directory of Open Access Journals (Sweden)
J. M. McMillan
2010-09-01
Full Text Available The generation and evolution of solitary waves by intrusive gravity currents in an approximate two-layer fluid with equal upper- and lower-layer depths is examined in a cylindrical geometry by way of theory and numerical simulations. The study is limited to vertically symmetric cases in which the density of the intruding fluid is equal to the average density of the ambient. We show that even though the head height of the intrusion decreases, it propagates at a constant speed well beyond 3 lock radii. This is because the strong stratification at the interface supports the formation of a mode-2 solitary wave that surrounds the intrusion head and carries it outwards at a constant speed. The wave and intrusion propagate faster than a linear long wave; therefore, there is strong supporting evidence that the wave is indeed nonlinear. Rectilinear Korteweg-de Vries theory is extended to allow the wave amplitude to decay as r^{-p} with p=½ and the theory is compared to the observed waves to demonstrate that the width of the wave scales with its amplitude. After propagating beyond 7 lock radii the intrusion runs out of fluid. Thereafter, the wave continues to spread radially at a constant speed, however, the amplitude decreases sufficiently so that linear dispersion dominates and the amplitude decays with distance as r^{-1}.
Diffractons: Solitary Waves Created by Diffraction in Periodic Media
Ketcheson, David I.
2015-03-31
A new class of solitary waves arises in the solution of nonlinear wave equations with constant impedance and no dispersive terms. These solitary waves depend on a balance between nonlinearity and a dispersion-like effect due to spatial variation in the sound speed of the medium. A high-order homogenized model confirms this effective dispersive behavior, and its solutions agree well with those obtained by direct simulation of the variable-coefficient system. These waves are observed to be long-time stable, globally attracting solutions that arise in general as solutions to nonlinear wave problems with periodically varying sound speed. They share some properties with known classes of solitary waves but possess important differences as well.
Impact induced solitary wave propagation through a woodpile structure
International Nuclear Information System (INIS)
Kore, R; Waychal, A; Yadav, P; Shelke, A; Agarwal, S; Sahoo, N; Uddin, Ahsan
2016-01-01
In this paper, we investigate solitary wave propagation through a one-dimensional woodpile structure excited by low and high velocity impact. Woodpile structures are a sub-class of granular metamaterial, which supports propagation of nonlinear waves. Hertz contact law governs the behavior of the solitary wave propagation through the granular media. Towards an experimental study, a woodpile structure was fabricated by orthogonally stacking cylindrical rods. A shock tube facility has been developed to launch an impactor on the woodpile structure at a velocity of 30 m s −1 . Embedded granular chain sensors were fabricated to study the behavior of the solitary wave. The impact induced stress wave is studied to investigate solitary wave parameters, i.e. contact force, contact time, and solitary wave velocity. With the aid of the experimental setup, numerical simulations, and a theoretical solution based on the long wavelength approximation, formation of the solitary wave in the woodpile structure is validated to a reasonable degree of accuracy. The nondispersive and compact supported solitary waves traveling at sonic wave velocity offer unique properties that could be leveraged for application in nondestructive testing and structural health monitoring. (paper)
Surf similarity and solitary wave runup
DEFF Research Database (Denmark)
Fuhrman, David R.; Madsen, Per A.
2008-01-01
The notion of surf similarity in the runup of solitary waves is revisited. We show that the surf similarity parameter for solitary waves may be effectively reduced to the beach slope divided by the offshore wave height to depth ratio. This clarifies its physical interpretation relative to a previ...... functional dependence on their respective surf similarity parameters. Important equivalencies in the runup of sinusoidal and solitary waves are thus revealed.......The notion of surf similarity in the runup of solitary waves is revisited. We show that the surf similarity parameter for solitary waves may be effectively reduced to the beach slope divided by the offshore wave height to depth ratio. This clarifies its physical interpretation relative...... to a previous parameterization, which was not given in an explicit form. Good coherency with experimental (breaking) runup data is preserved with this simpler parameter. A recasting of analytical (nonbreaking) runup expressions for sinusoidal and solitary waves additionally shows that they contain identical...
Localization and solitary waves in solid mechanics
Champneys, A R; Thompson, J M T
1999-01-01
This book is a collection of recent reprints and new material on fundamentally nonlinear problems in structural systems which demonstrate localized responses to continuous inputs. It has two intended audiences. For mathematicians and physicists it should provide useful new insights into a classical yet rapidly developing area of application of the rich subject of dynamical systems theory. For workers in structural and solid mechanics it introduces a new methodology for dealing with structural localization and the related topic of the generation of solitary waves. Applications range from classi
Electromagnetic solitary waves in magnetized plasmas
International Nuclear Information System (INIS)
Hazeltine, R.D.; Holm, D.D.; Morrison, P.J.
1985-03-01
A Hamiltonian formulation, in terms of noncanonical Poisson bracket, is presented for a nonlinear fluid system that includes reduced magnetohydrodynamics and the Hasegawa-Mima equation as limiting cases. The single-helicity and axisymmetric versions possess three nonlinear Casimir invariants, from which a generalized potential can be constructed. Variation of the generalized potential yields a description of exact nonlinear stationary states. The new equilibria, allowing for plasma flow as well as partial electron adiabaticity, are distinct from those found in conventional magnetohydrodynamic theory. They differ from electrostatic stationary states in containing plasma current and magnetic field excitation. One class of steady-state solutions is shown to provide a simple electromagnetic generalization of drift-solitary waves
Solitary wave solution to a singularly perturbed generalized Gardner ...
Indian Academy of Sciences (India)
2017-03-24
Mar 24, 2017 ... Abstract. This paper is concerned with the existence of travelling wave solutions to a singularly perturbed gen- eralized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the ...
Nonlinear surface Alfven waves
International Nuclear Information System (INIS)
Cramer, N.F.
1991-01-01
The problem of nonlinear surface Alfven waves propagating on an interface between a plasma and a vacuum is discussed, with dispersion provided by the finite-frequency effect, i.e. the finite ratio of the frequency to the ion-cyclotron frequency. A set of simplified nonlinear wave equations is derived using the method of stretched co-ordinates, and another approach uses the generation of a second-harmonic wave and its interaction with the first harmonic to obtain a nonlinear dispersion relation. A nonlinear Schroedinger equation is then derived, and soliton solutions found that propagate as solitary pulses in directions close to parallel and antiparallel to the background magnetic field. (author)
Conservative numerical methods for solitary wave interactions
Energy Technology Data Exchange (ETDEWEB)
Duran, A; Lopez-Marcos, M A [Departamento de Matematica Aplicada y Computacion, Facultad de Ciencias, Universidad de Valladolid, Paseo del Prado de la Magdalena s/n, 47005 Valladolid (Spain)
2003-07-18
The purpose of this paper is to show the advantages that represent the use of numerical methods that preserve invariant quantities in the study of solitary wave interactions for the regularized long wave equation. It is shown that the so-called conservative methods are more appropriate to study the phenomenon and provide a dynamic point of view that allows us to estimate the changes in the parameters of the solitary waves after the collision.
Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen
2018-06-01
In this research, we study new two techniques that called the extended simple equation method and the novel (G‧/G) -expansion method. The extended simple equation method depend on the auxiliary equation (dϕ/dξ = α + λϕ + μϕ2) which has three ways for solving depends on the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (α = 0) this auxiliary equation reduces to Bernoulli equation and when (α ≠ 0, λ ≠ 0, μ ≠ 0) we the general solutions of this auxiliary equation while the novel (G‧/G) -expansion method depends also on similar auxiliary equation (G‧/G)‧ = μ + λ(G‧/G) + (v - 1)(G‧/G) 2 which depend also on the value of (λ2 - 4 (v - 1) μ) and the specific condition on the parameters as follow: When (λ = 0) this auxiliary equation reduces to Riccati equation, when (μ = 0) this auxiliary equation reduces to Bernoulli equation and when (λ2 ≠ 4 (v - 1) μ) we the general solutions of this auxiliary equation. This show how both of these auxiliary equation are special cases of Riccati equation. We apply these methods on two dimensional nonlinear Kadomtsev-Petviashvili Burgers equation in quantum plasma and three-dimensional nonlinear modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma. We obtain the exact traveling wave solutions of these important models and under special condition on the parameters, we get solitary traveling wave solutions. All calculations in this study have been established and verified back with the aid of the Maple package program. The executed method is powerful, effective and straightforward for solving nonlinear partial differential equations to obtain more and new solutions.
Numerical Simulation of Cylindrical Solitary Waves in Periodic Media
Quezada de Luna, Manuel; Ketcheson, David I.
2013-01-01
We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient first-order hyperbolic system. We present direct numerical simulations of this multiscale problem, focused on the propagation of a single localized perturbation in media with strongly varying impedance. For the conditions studied, we find little evidence of shock formation. Instead, solutions consist primarily of solitary waves. These solitary waves are observed to be stable over long times and to interact in a manner approximately like solitons. The system considered has no dispersive terms; these solitary waves arise due to the material heterogeneity, which leads to strong reflections and effective dispersion.
Numerical Simulation of Cylindrical Solitary Waves in Periodic Media
Quezada de Luna, Manuel
2013-07-14
We study the behavior of nonlinear waves in a two-dimensional medium with density and stress relation that vary periodically in space. Efficient approximate Riemann solvers are developed for the corresponding variable-coefficient first-order hyperbolic system. We present direct numerical simulations of this multiscale problem, focused on the propagation of a single localized perturbation in media with strongly varying impedance. For the conditions studied, we find little evidence of shock formation. Instead, solutions consist primarily of solitary waves. These solitary waves are observed to be stable over long times and to interact in a manner approximately like solitons. The system considered has no dispersive terms; these solitary waves arise due to the material heterogeneity, which leads to strong reflections and effective dispersion.
Solitary wave and periodic wave solutions for the thermally forced gravity waves in atmosphere
International Nuclear Information System (INIS)
Li Ziliang
2008-01-01
By introducing a new transformation, a new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system, which extends Fan's direct algebraic method to the case when r > 4. The solutions of a first-order nonlinear ordinary differential equation with a higher degree nonlinear term and Fan's direct algebraic method of obtaining exact solutions to nonlinear partial differential equations are applied to the combined KdV-mKdV-GKdV equation, which is derived from a simple incompressible non-hydrostatic Boussinesq equation with the influence of thermal forcing and is applied to investigate internal gravity waves in the atmosphere. As a result, by taking advantage of the new first-order nonlinear ordinary differential equation with a fifth-degree nonlinear term and an eighth-degree nonlinear term, periodic wave solutions associated with the Jacobin elliptic function and the bell and kink profile solitary wave solutions are obtained under the effect of thermal forcing. Most importantly, the mechanism of propagation and generation of the periodic waves and the solitary waves is analysed in detail according to the values of the heating parameter, which show that the effect of heating in atmosphere helps to excite westerly or easterly propagating periodic internal gravity waves and internal solitary waves in atmosphere, which are affected by the local excitation structures in atmosphere. In addition, as an illustrative sample, the properties of the solitary wave solution and Jacobin periodic solution are shown by some figures under the consideration of heating interaction
Exact solitary waves of the Korteveg - de Vries - Burgers equation
Kudryashov, N. A.
2004-01-01
New approach is presented to search exact solutions of nonlinear differential equations. This method is used to look for exact solutions of the Korteveg -- de Vries -- Burgers equation. New exact solitary waves of the Korteveg -- de Vries -- Burgers equation are found.
Nonlinear waves in solar plasmas - a review
International Nuclear Information System (INIS)
Ballai, I
2006-01-01
Nonlinearity is a direct consequence of large scale dynamics in the solar plasmas. When nonlinear steepening of waves is balanced by dispersion, solitary waves are generated. In the vicinity of resonances, waves can steepen into nonlinear waves influencing the efficiency of energy deposition. Here we review recent theoretical breakthroughs that have lead to a greater understanding of many aspects of nonlinear waves arising in homogeneous and inhomogeneous solar plasmas
Statistical Thermodynamic Approach to Vibrational Solitary Waves in Acetanilide
Vasconcellos, Áurea R.; Mesquita, Marcus V.; Luzzi, Roberto
1998-03-01
We analyze the behavior of the macroscopic thermodynamic state of polymers, centering on acetanilide. The nonlinear equations of evolution for the populations and the statistically averaged field amplitudes of CO-stretching modes are derived. The existence of excitations of the solitary wave type is evidenced. The infrared spectrum is calculated and compared with the experimental data of Careri et al. [Phys. Rev. Lett. 51, 104 (1983)], resulting in a good agreement. We also consider the situation of a nonthermally highly excited sample, predicting the occurrence of a large increase in the lifetime of the solitary wave excitation.
Polarized seismic and solitary waves run-up at the sea bed
Energy Technology Data Exchange (ETDEWEB)
Dennis, L. C.C.; Zainal, A. A.; Faisal, S. Y. [Universiti Teknologi PETRONAS, 31750 Tronoh, Perak (Malaysia); Universiti Teknologi Malaysia, 81310 Johor Bahru (Malaysia)
2012-09-26
The polarization effects in hydrodynamics are studied. Hydrodynamic equation for the nonlinear wave is used along with the polarized solitary waves and seismic waves act as initial waves. The model is then solved by Fourier spectral and Runge-Kutta 4 methods, and the surface plot is drawn. The output demonstrates the inundation behaviors. Consequently, the polarized seismic waves along with the polarized solitary waves tend to generate dissimilar inundation which is more disastrous.
Existence of solitary waves in dipolar quantum gases
Antonelli, Paolo; Sparber, Christof
2011-01-01
We study a nonlinear Schrdinger equation arising in the mean field description of dipolar quantum gases. Under the assumption of sufficiently strong dipolar interactions, the existence of standing waves, and hence solitons, is proved together with some of their properties. This gives a rigorous argument for the possible existence of solitary waves in BoseEinstein condensates, which originate solely due to the dipolar interaction between the particles. © 2010 Elsevier B.V. All rights reserved.
Existence of solitary waves in dipolar quantum gases
Antonelli, Paolo
2011-02-01
We study a nonlinear Schrdinger equation arising in the mean field description of dipolar quantum gases. Under the assumption of sufficiently strong dipolar interactions, the existence of standing waves, and hence solitons, is proved together with some of their properties. This gives a rigorous argument for the possible existence of solitary waves in BoseEinstein condensates, which originate solely due to the dipolar interaction between the particles. © 2010 Elsevier B.V. All rights reserved.
CFD Analysis of Water Solitary Wave Reflection
Directory of Open Access Journals (Sweden)
K. Smida
2011-12-01
Full Text Available A new numerical wave generation method is used to investigate the head-on collision of two solitary waves. The reflection at vertical wall of a solitary wave is also presented. The originality of this model, based on the Navier-Stokes equations, is the specification of an internal inlet velocity, defined as a source line within the computational domain for the generation of these non linear waves. This model was successfully implemented in the PHOENICS (Parabolic Hyperbolic Or Elliptic Numerical Integration Code Series code. The collision of two counter-propagating solitary waves is similar to the interaction of a soliton with a vertical wall. This wave generation method allows the saving of considerable time for this collision process since the counter-propagating wave is generated directly without reflection at vertical wall. For the collision of two solitary waves, numerical results show that the run-up phenomenon can be well explained, the solution of the maximum wave run-up is almost equal to experimental measurement. The simulated wave profiles during the collision are in good agreement with experimental results. For the reflection at vertical wall, the spatial profiles of the wave at fixed instants show that this problem is equivalent to the collision process.
Solitary wave dynamics in time-dependent potentials
International Nuclear Information System (INIS)
Abou Salem, Walid K.
2008-01-01
The long time dynamics of solitary wave solutions of the nonlinear Schroedinger equation in time-dependent external potentials is rigorously studied. To set the stage, the well-posedness of the Cauchy problem for a generalized nonautonomous nonlinear Schroedinger equation with time-dependent nonlinearities and potential is established. Afterward, the dynamics of NLS solitary waves in time-dependent potentials is studied. It is shown that in the space-adiabatic regime where the external potential varies slowly in space compared to the size of the soliton, the dynamics of the center of the soliton is described by Hamilton's equations, plus terms due to radiation damping. Finally, two physical applications are discussed: the first is adiabatic transportation of solitons and the second is the Mathieu instability of trapped solitons due to time-periodic perturbations
Controlling of the electromagnetic solitary waves generation in the wake of a two-color laser
Pan, K. Q.; Li, S. W.; Guo, L.; Yang, D.; Li, Z. C.; Zheng, C. Y.; Jiang, S. E.; Zhang, B. H.; He, X. T.
2018-05-01
Electromagnetic solitary waves generated by a two-color laser interaction with an underdense plasma are investigated. It is shown that, when the former wave packet of the two-color laser is intense enough, it will excite nonlinear wakefields and generate electron density cavities. The latter wave packets will beat with the nonlinear wakefield and generate both high-frequency and low-frequency components. When the peak density of the cavities exceeds the critical density of the low-frequency component, this part of the electromagnetic field will be trapped to generate electromagnetic solitary waves. By changing the laser and plasma parameters, we can control the wakefield generation, which will also control the generation of the solitary waves. One-dimensional particle-in-cell simulations are performed to prove the controlling of the solitary waves. The simulation results also show that solitary waves generated by higher laser intensities will become moving solitary waves. The two-dimensional particle-in-cell also shows the generation of the solitary waves. In the two-dimensional case, solitary waves are distributed in the transverse directions because of the filamentation instability.
Solitary Wave Interactions in Granular Media
Institute of Scientific and Technical Information of China (English)
WEN Zhen-Ying; WANG Shun-Jin; ZHANG Xiu-Ming; LI Lei
2007-01-01
We numerically study the interactions of solitary waves in granular media, by considering a chain of beads, which repel upon contact via the Hertz-type potential, V ∝δn, with 5/2 ≤n≤3 and δ≥0,δbeing the bead-bead overlap. There are two collision types of solitary waves, overtaking collision and head-on collision, in the chain of beads. Our quantitative results show that after collision the large solitary wave gains energy and the small one loses energy for overtaking type while the large one loses energy, and the small one gains energy for head-on type. The scattering effects decrease with n for overtaking collision whereas increase with n for head-on collision.
Propagation of three-dimensional electron-acoustic solitary waves
International Nuclear Information System (INIS)
Shalaby, M.; El-Sherif, L. S.; El-Labany, S. K.; Sabry, R.
2011-01-01
Theoretical investigation is carried out for understanding the properties of three-dimensional electron-acoustic waves propagating in magnetized plasma whose constituents are cold magnetized electron fluid, hot electrons obeying nonthermal distribution, and stationary ions. For this purpose, the hydrodynamic equations for the cold magnetized electron fluid, nonthermal electron density distribution, and the Poisson equation are used to derive the corresponding nonlinear evolution equation, Zkharov-Kuznetsov (ZK) equation, in the small- but finite- amplitude regime. The ZK equation is solved analytically and it is found that it supports both solitary and blow-up solutions. It is found that rarefactive electron-acoustic solitary waves strongly depend on the density and temperature ratios of the hot-to-cold electron species as well as the nonthermal electron parameter. Furthermore, there is a critical value for the nonthermal electron parameter, which decides whether the electron-acoustic solitary wave's amplitude is decreased or increased by changing various plasma parameters. Importantly, the change of the propagation angles leads to miss the balance between the nonlinearity and dispersion; hence, the localized pulses convert to explosive/blow-up pulses. The relevance of this study to the nonlinear electron-acoustic structures in the dayside auroral zone in the light of Viking satellite observations is discussed.
International Nuclear Information System (INIS)
Singh, Kh.I.; Das, G.C.
1993-01-01
Soliton propagations are studied in a relativistic multicomponent ion-beam plasma through the derivation of Korteweg-deVries (K-dV) and modified K-dV (mK-dV) equations. A generalization of the mK-dV equation involving higher order nonlinearities gives a transitive link between the K-dV and mK-dV equations for isothermal plasma, and the validity of this generalized equation throughout the whole range of negative ion concentrations is investigated through the derivation of Sagdeev potential. Parallel discussion of various K-dV solitons enlightening the experimental implications is also made. (author). 22 refs
Spatial Dynamics Methods for Solitary Waves on a Ferrofluid Jet
Groves, M. D.; Nilsson, D. V.
2018-04-01
This paper presents existence theories for several families of axisymmetric solitary waves on the surface of an otherwise cylindrical ferrofluid jet surrounding a stationary metal rod. The ferrofluid, which is governed by a general (nonlinear) magnetisation law, is subject to an azimuthal magnetic field generated by an electric current flowing along the rod. The ferrohydrodynamic problem for axisymmetric travelling waves is formulated as an infinite-dimensional Hamiltonian system in which the axial direction is the time-like variable. A centre-manifold reduction technique is employed to reduce the system to a locally equivalent Hamiltonian system with a finite number of degrees of freedom, and homoclinic solutions to the reduced system, which correspond to solitary waves, are detected by dynamical-systems methods.
On the solitary wave paradigm for tsunamis
DEFF Research Database (Denmark)
Madsen, Per A.; Fuhrman, David R.; Schäffer, Hemming Andreas
2008-01-01
Since the 1970s, solitary waves have commonly been used to model tsunamis especially in experimental and mathematical studies. Unfortunately, the link to geophysical scales is not well established, and in this work we question the geophysical relevance of this paradigm. In part 1, we simulate...
Modulated Langmuir waves and nonlinear Landau damping
International Nuclear Information System (INIS)
Yajima, Nobuo; Oikawa, Masayuki; Satsuma, Junkichi; Namba, Chusei.
1975-01-01
The nonlinear Schroedinger euqation with an integral term, iusub(t)+P/2.usub(xx)+Q/u/ 2 u+RP∫sub(-infinity)sup(infinity)[/u(x',t)/ 2 /(x-x')]dx'u=0, which describes modulated Langmuir waves with the nonlinear Landau damping effect, is solved by numerical calculations. Especially, the effects of nonlinear Landau damping on solitary wave solutions are studied. For both cases, PQ>0 and PQ<0, the results show that the solitary waves deform in an asymmetric way changing its velocity. (auth.)
The effect of shear stress on solitary waves in arteries.
Demiray, H
1997-09-01
In the present work, we study the propagation of solitary waves in a prestressed thick walled elastic tube filled with an incompressible inviscid fluid. In order to include the geometric dispersion in the analysis the wall inertia and shear deformation effects are taken into account for the inner pressure-cross-sectional area relation. Using the reductive perturbation technique, the propagation of weakly non-linear waves in the long-wave approximation is examined. It is shown that, contrary to thin tube theories, the present approach makes it possible to have solitary waves even for a Mooney-Rivlin (M-R) material. Due to dependence of the coefficients of the governing Korteweg-deVries equation on initial deformation, the solution profile changes with inner pressure and the axial stretch. The variation of wave profiles for a class of elastic materials are depicted in graphic forms. As might be seen from these illustrations, with increasing thickness ratio, the profile of solitary wave is steepened for a M-R material but it is broadened for biological tissue.
Effect of finite ion-temperature on ion-acoustic solitary waves in an inhomogeneous plasma
International Nuclear Information System (INIS)
Shivamoggi, B.K.
1981-01-01
The propagation of weakly nonlinear ion-acoustic waves in an inhomogeneous plasma is studied taking into account the effect of finite ion temperature. It is found that, whereas both the amplitude and the velocity of propagation decrease as the ion-acoustic solitary wave propagates into regions of higher density, the effect of a finite ion temperature is to reduce the amplitude but enhance the velocity of propagation of the solitary wave. (author)
Negative ion sound solitary waves revisited
Cairns, R. A.; Cairns
2013-12-01
Some years ago, a group including the present author and Padma Shukla showed that a suitable non-thermal electron distribution allows the formation of ion sound solitary waves with either positive or negative density perturbations, whereas with Maxwellian electrons only a positive density perturbation is possible. The present paper discusses the qualitative features of this distribution allowing the negative waves and shared with suitable two-temperature distributions.
Frustrated Brownian Motion of Nonlocal Solitary Waves
International Nuclear Information System (INIS)
Folli, V.; Conti, C.
2010-01-01
We investigate the evolution of solitary waves in a nonlocal medium in the presence of disorder. By using a perturbational approach, we show that an increasing degree of nonlocality may largely hamper the Brownian motion of self-trapped wave packets. The result is valid for any kind of nonlocality and in the presence of nonparaxial effects. Analytical predictions are compared with numerical simulations based on stochastic partial differential equations.
Electro-acoustic solitary waves in dusty plasmas
International Nuclear Information System (INIS)
Mamun, A.A.; Sayed, F.
2005-10-01
present a rigorous theoretical investigation of electro- acoustic [particularly, dust-ion acoustic (DIA) and dust-acoustic (DA)] solitary waves in dusty plasmas. We employ the reductive perturbation method for small but finite amplitude solitary waves as well as the pseudo-potential approach for arbitrary amplitude ones. We also analyze the effects of non-planar geometry and dust charge fluctuations on both DIA and DA solitary waves, the effect of finite ion-temperature on DIA solitary waves, and the effects of dust-fluid temperature and non-isothermal ion distributions on DA solitary waves. It has been reported that these effects do not only significantly modify the basic features of DIA or DA solitary waves, but also introduce some important new features. The basic features and the underlying physics of DIA and DA solitary waves, which are relevant to space and laboratory dusty plasmas, are briefly discussed. (author)
Directory of Open Access Journals (Sweden)
S. S. Ghosh
2004-01-01
Full Text Available The presence of dynamic, large amplitude solitary waves in the auroral regions of space is well known. Since their velocities are of the order of the ion acoustic speed, they may well be considered as being generated from the nonlinear evolution of ion acoustic waves. However, they do not show the expected width-amplitude correlation for K-dV solitons. Recent POLAR observations have actually revealed that the low altitude rarefactive ion acoustic solitary waves are associated with an increase in the width with increasing amplitude. This indicates that a weakly nonlinear theory is not appropriate to describe the solitary structures in the auroral regions. In the present work, a fully nonlinear analysis based on Sagdeev pseudopotential technique has been adopted for both parallel and oblique propagation of rarefactive solitary waves in a two electron temperature multi-ion plasma. The large amplitude solutions have consistently shown an increase in the width with increasing amplitude. The width-amplitude variation profile of obliquely propagating rarefactive solitary waves in a magnetized plasma have been compared with the recent POLAR observations. The width-amplitude variation pattern is found to fit well with the analytical results. It indicates that a fully nonlinear theory of ion acoustic solitary waves may well explain the observed anomalous width variations of large amplitude structures in the auroral region.
Hossen, Md. Belal; Roshid, Harun-Or; Ali, M. Zulfikar
2018-05-01
Under inquisition in this paper is a (2 + 1)-dimensional Breaking Soliton equation, which can describe various nonlinear scenarios in fluid dynamics. Using the Bell polynomials, some proficient auxiliary functions are offered to apparently construct its bilinear form and corresponding soliton solutions which are different from the previous literatures. Moreover, a direct method is used to construct its rogue wave and solitary wave solutions using particular auxiliary function with the assist of bilinear formalism. Finally, the interactions between solitary waves and rogue waves are offered with a complete derivation. These results enhance the variety of the dynamics of higher dimensional nonlinear wave fields related to mathematical physics and engineering.
Compact solitary waves in linearly elastic chains with non-smooth on-site potential
Energy Technology Data Exchange (ETDEWEB)
Gaeta, Giuseppe [Dipartimento di Matematica, Universita di Milano, Via Saldini 50, 20133 Milan (Italy); Gramchev, Todor [Dipartimento di Matematica e Informatica, Universita di Cagliari, Via Ospedale 72, 09124 Cagliari (Italy); Walcher, Sebastian [Lehrstuhl A Mathematik, RWTH Aachen, 52056 Aachen (Germany)
2007-04-27
It was recently observed by Saccomandi and Sgura that one-dimensional chains with nonlinear elastic interaction and regular on-site potential can support compact solitary waves, i.e. travelling solitary waves with strictly compact support. In this paper, we show that the same applies to chains with linear elastic interaction and an on-site potential which is continuous but non-smooth at minima. Some different features arise; in particular, the speed of compact solitary waves is not uniquely fixed by the equation. We also discuss several generalizations of our findings.
Self-similarity of solitary waves on inertia-dominated falling liquid films.
Denner, Fabian; Pradas, Marc; Charogiannis, Alexandros; Markides, Christos N; van Wachem, Berend G M; Kalliadasis, Serafim
2016-03-01
We propose consistent scaling of solitary waves on inertia-dominated falling liquid films, which accurately accounts for the driving physical mechanisms and leads to a self-similar characterization of solitary waves. Direct numerical simulations of the entire two-phase system are conducted using a state-of-the-art finite volume framework for interfacial flows in an open domain that was previously validated against experimental film-flow data with excellent agreement. We present a detailed analysis of the wave shape and the dispersion of solitary waves on 34 different water films with Reynolds numbers Re=20-120 and surface tension coefficients σ=0.0512-0.072 N m(-1) on substrates with inclination angles β=19°-90°. Following a detailed analysis of these cases we formulate a consistent characterization of the shape and dispersion of solitary waves, based on a newly proposed scaling derived from the Nusselt flat film solution, that unveils a self-similarity as well as the driving mechanism of solitary waves on gravity-driven liquid films. Our results demonstrate that the shape of solitary waves, i.e., height and asymmetry of the wave, is predominantly influenced by the balance of inertia and surface tension. Furthermore, we find that the dispersion of solitary waves on the inertia-dominated falling liquid films considered in this study is governed by nonlinear effects and only driven by inertia, with surface tension and gravity having a negligible influence.
Numerical simulation of solitary waves on deep water with constant vorticity
Dosaev, A. S.; Shishina, M. I.; Troitskaya, Yu I.
2018-01-01
Characteristics of solitary deep water waves on a flow with constant vorticity are investigated by numerical simulation within the framework of fully nonlinear equations of motion (Euler equations) using the method of surface-tracking conformal coordinates. To ensure that solutions observed are stable, soliton formation as a result of disintegration of an initial pulse-like disturbance is modeled. Evidence is obtained that solitary waves with height above a certain threshold are unstable.
Solitary wave and periodic wave solutions for Burgers, Fisher ...
Indian Academy of Sciences (India)
Home; Journals; Pramana – Journal of Physics; Volume 85; Issue 1. Solitary wave and periodic wave solutions for Burgers, Fisher, Huxley and combined forms of these equations by the (′/)-expansion method. Jalil Manafian Mehrdad Lakestani. Volume 85 Issue 1 July 2015 pp 31-52 ...
International Nuclear Information System (INIS)
Ma, Yi-Rong; Qi, Xin; Sun, Jian-An; Duan, Wen-Shan; Yang, Lei
2013-01-01
Dust negative ion acoustic solitary waves in a magnetized multi-ion dusty plasma containing hot isothermal electron, ions (light positive ions and heavy negative ions) and extremely massive charge fluctuating dust grains are investigated by employing the reductive perturbation method. How the dust size distribution affect the height and the thickness of the nonlinear solitary wave are given. It is noted that the characteristic of the solitary waves are different with the different dust size distribution. The magnitude of the external magnetic field also affects the solitary wave form
Soliton wave-speed management: Slowing, stopping, or reversing a solitary wave
Baines, Luke W. S.; Van Gorder, Robert A.
2018-06-01
While dispersion management is a well-known tool to control soliton properties such as shape or amplitude, far less effort has been directed toward the theoretical control of the soliton wave speed. However, recent experiments concerning the stopping or slowing of light demonstrate that the control of the soliton wave speed is of experimental interest. Motivated by these and other studies, we propose a management approach for modifying the wave speed of a soliton (or of other nonlinear wave solutions, such as periodic cnoidal waves) under the nonlinear Schrödinger equation. Making use of this approach, we are able to slow, stop, or even reverse a solitary wave, and we give several examples to bright solitons, dark solitons, and periodic wave trains, to demonstrate the method. An extension of the approach to spatially heterogeneous media, for which the wave may propagate differently at different spatial locations, is also discussed.
Interaction for solitary waves in coasting charged particle beams
Energy Technology Data Exchange (ETDEWEB)
Liu, Shi-Wei; Hong, Xue-Ren; Shi, Yu-Ren; Duan, Wen-shan, E-mail: duanws@nwnu.edu.cn [College of Physics and Electronic Engineering and Joint Laboratory of Atomic an Molecular Physics of NWNU and IMPCAS, Northwest Normal University, Lanzhou 730070 (China); Qi, Xin; Yang, Lei, E-mail: lyang@impcas.ac.cn [Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000 (China); Han, Jiu-Ning [College of Physics and Electromechanical Engineering, Hexi University, Zhangye 734000 (China)
2014-03-15
By using the extended Poincare-Lighthill-Kuo perturbation method, the collision of solitary waves in a coasting charged particle beams is studied. The results show that the system admits a solution with two solitary waves, which move in opposite directions and can be described by two Korteweg-deVries equation in small-amplitude limit. The collision of two solitary waves is elastic, and after the interaction they preserve their original properties. Then the weak phase shift in traveling direction of collision between two solitary waves is derived explicitly.
Stability properties of solitary waves for fractional KdV and BBM equations
Angulo Pava, Jaime
2018-03-01
This paper sheds new light on the stability properties of solitary wave solutions associated with Korteweg-de Vries-type models when the dispersion is very low. Using a compact, analytic approach and asymptotic perturbation theory, we establish sufficient conditions for the existence of exponentially growing solutions to the linearized problem and so a criterium of spectral instability of solitary waves is obtained for both models. Moreover, the nonlinear stability and spectral instability of the ground state solutions for both models is obtained for some specific regimen of parameters. Via a Lyapunov strategy and a variational analysis, we obtain the stability of the blow-up of solitary waves for the critical fractional KdV equation. The arguments presented in this investigation show promise for use in the study of the instability of traveling wave solutions of other nonlinear evolution equations.
Ion-acoustic solitary waves near double layers
International Nuclear Information System (INIS)
Kuehl, H.H.; Imen, K.
1985-01-01
The possibility of ion-acoustic solitary-wave solutions in the uniform plasma on the high-potential side of double layer is investigated. Based on a fluid model of the double layer, it is found that both compressive and rarefactive solitary waves are allowed. Curves are presented which show the regions in parameter space in which these solutions exist
Compressive and rarefactive solitary waves in nonthermal two-component plasmas
International Nuclear Information System (INIS)
Verheest, Frank; Hellberg, Manfred A.
2010-01-01
Using a Sagdeev pseudopotential formalism where nonlinear structures are stationary in a comoving frame, large ion-acoustic solitary waves and double layers have been studied in plasmas with positive ions and nonthermal electrons. The velocity range of positive, compressive solitary waves is limited by the ion density reaching infinite compression, whereas negative, rarefactive solitary waves and double layers can exist when the electron nonthermality exceeds a certain minimum. There are even regions of coexistence, the limits of which can be elucidated by considering the properties of the special Sagdeev pseudopotential at the acoustic speed. In particular, when the compositional parameters and Mach numbers admit only compressive or rarefactive solitary structures, these have to be superacoustic, their amplitude vanishing at the acoustic speed. When both compressive and rarefactive modes can occur, one of them is Korteweg-de Vries (KdV)-like, the other having a non-KdV character, with a finite amplitude at the acoustic speed.
Scattering of quantized solitary waves in the cubic Schrodinger equation
International Nuclear Information System (INIS)
Dolan, L.
1976-01-01
The quantum mechanics for N particles interacting via a delta-function potential in one space dimension and one time dimension is known. The second-quantized description of this system has for its Euler-Lagrange equations of motion the cubic Schrodinger equation. This nonlinear differential equation supports solitary wave solutions. A quantization of these solitons reproduces the weak-coupling limit to the known quantum mechanics. The phase shift for two-body scattering and the energy of the N-body bound state is derived in this approximation. The nonlinear Schrodinger equation is contrasted with the sine-Gordon theory in respect to the ideas which the classical solutions play in the description of the quantum states
The solitary electromagnetic waves in the graphene superlattice
International Nuclear Information System (INIS)
Kryuchkov, Sergey V.; Kukhar', Egor I.
2013-01-01
d’Alembert equation written for the electromagnetic waves propagating in the graphene superlattice is analyzed. The possibility of the propagation of the solitary electromagnetic waves in the graphene superlattice is discussed. The amplitude and the width of the electromagnetic pulse are calculated. The drag current induced by such wave across the superlattice axis is investigated. The numerical estimate of the charge dragged by the solitary wave is made.
Low-frequency electromagnetic solitary and shock waves in an inhomogeneous dusty magnetoplasma
International Nuclear Information System (INIS)
Shukla, P.K.
2003-01-01
It is shown that the nonlinear dynamics of one-dimensional Shukla mode [Phys. Lett. A 316, 238 (2003)] is governed by a modified Kortweg-de Vries-Burgers equation. The latter admits stationary solutions in the form of either a solitary wave or a monotonic/oscillatory shock. The present nonlinear waves may help to understand the salient features of localized density and magnetic field structures in molecular dusty clouds as well as in low-temperature laboratory dusty plasma discharges
International Nuclear Information System (INIS)
Zhang Zaiyun; Liu Zhenhai; Miao Xiujin; Chen Yuezhong
2011-01-01
In this Letter, we investigate the perturbed nonlinear Schroedinger's equation (NLSE) with Kerr law nonlinearity. All explicit expressions of the bounded traveling wave solutions for the equation are obtained by using the bifurcation method and qualitative theory of dynamical systems. These solutions contain bell-shaped solitary wave solutions, kink-shaped solitary wave solutions and Jacobi elliptic function periodic solutions. Moreover, we point out the region which these periodic wave solutions lie in. We present the relation between the bounded traveling wave solution and the energy level h. We find that these periodic wave solutions tend to the corresponding solitary wave solutions as h increases or decreases. Finally, for some special selections of the energy level h, it is shown that the exact periodic solutions evolute into solitary wave solution.
Evolution Of Nonlinear Waves in Compressing Plasma
International Nuclear Information System (INIS)
Schmit, P.F.; Dodin, I.Y.; Fisch, N.J.
2011-01-01
Through particle-in-cell simulations, the evolution of nonlinear plasma waves is examined in one-dimensional collisionless plasma undergoing mechanical compression. Unlike linear waves, whose wavelength decreases proportionally to the system length L(t), nonlinear waves, such as solitary electron holes, conserve their characteristic size Δ during slow compression. This leads to a substantially stronger adiabatic amplification as well as rapid collisionless damping when L approaches Δ. On the other hand, cessation of compression halts the wave evolution, yielding a stable mode.
Evolution Of Nonlinear Waves in Compressing Plasma
Energy Technology Data Exchange (ETDEWEB)
P.F. Schmit, I.Y. Dodin, and N.J. Fisch
2011-05-27
Through particle-in-cell simulations, the evolution of nonlinear plasma waves is examined in one-dimensional collisionless plasma undergoing mechanical compression. Unlike linear waves, whose wavelength decreases proportionally to the system length L(t), nonlinear waves, such as solitary electron holes, conserve their characteristic size {Delta} during slow compression. This leads to a substantially stronger adiabatic amplification as well as rapid collisionless damping when L approaches {Delta}. On the other hand, cessation of compression halts the wave evolution, yielding a stable mode.
Spike-like solitary waves in incompressible boundary layers driven by a travelling wave.
Feng, Peihua; Zhang, Jiazhong; Wang, Wei
2016-06-01
Nonlinear waves produced in an incompressible boundary layer driven by a travelling wave are investigated, with damping considered as well. As one of the typical nonlinear waves, the spike-like wave is governed by the driven-damped Benjamin-Ono equation. The wave field enters a completely irregular state beyond a critical time, increasing the amplitude of the driving wave continuously. On the other hand, the number of spikes of solitary waves increases through multiplication of the wave pattern. The wave energy grows in a sequence of sharp steps, and hysteresis loops are found in the system. The wave energy jumps to different levels with multiplication of the wave, which is described by winding number bifurcation of phase trajectories. Also, the phenomenon of multiplication and hysteresis steps is found when varying the speed of driving wave as well. Moreover, the nature of the change of wave pattern and its energy is the stability loss of the wave caused by saddle-node bifurcation.
Solitary Langmuir waves in two-electron temperature plasma
Prudkikh, V. V.; Prudkikh
2014-06-01
Nonlinear interaction of Langmuir and ion-acoustic waves in two-electron temperature plasma is investigated. New integrable wave interaction regime was discovered, this regime corresponds to the Langmuir soliton with three-hump amplitude, propagating with a speed close to the ion-sound speed in the conditions of strong non-isothermality of electronic components. It was discovered that besides the known analytical solution in the form of one- and two-hump waves, there exists a range of solutions in the form of solitary waves, which in the form of envelope has multi-peak structure and differs from the standard profiles described by hyperbolic functions. In case of fixed plasma parameters, different group velocities correspond to the waves with different number of peaks. It is found that the Langmuir wave package contains both even and uneven numbers of oscillations. Low-frequency potential here has uneven number of peaks. Interrelation of obtained and known earlier results are also discussed.
Ion acoustic solitary waves in a dusty plasma obliquely propagating to an external magnetic field
International Nuclear Information System (INIS)
Choi, Cheong Rim; Ryu, Chang-Mo; Lee, Nam C.; Lee, D.-Y.
2005-01-01
The nonlinear ion acoustic solitary wave in a magnetized dusty plasma, obliquely propagating to the embedding external magnetic field, is revisited. It is found that when the charge density of dust particles is high, the Sagdeev potential needs to be expanded up to δn 4 near n=1. In this case, it is shown that there could exist rarefactive ion acoustic solitary waves as well as the kink-type double layer solutions, in addition to the conventional hump-type ones found in the δn 3 expansion. The amplitude variations of ion acoustic solitary waves in a magnetized dusty plasma are also examined with respect to the change of the dust charge density and the wave directional angle
Influence of ionization on reflection of solitary waves in a magnetized plasma
International Nuclear Information System (INIS)
Jyoti,; Malik, Hitendra K.; Kumar, Ravinder; Dahiya, Raj P.
2013-01-01
The reflection of nonlinear solitary waves is studied in a nonuniform, magnetized plasma diffusing from an ionization source along the magnetic field lines. Contribution of the ionization term is included in the continuity equation. The behavior of solitary waves is governed by modified form of Korteweg–de Vries equation (called mKdV equation). In order to investigate the reflection of solitary waves, the mKdV equations for the right and left going waves are derived, and solved by finding new transformations coupled at the point of reflection, for obtaining the expression of reflection coefficient. Contrary to the case of usual inhomogeneous plasma, the present analysis shows that a combination of usual sech 2 structure and tanh structure (called the tail of soliton) arises due to the influence of ionization term. Interestingly, this tailing structure disappears after the reflection of the soliton and hence, the soliton is downshifted prominently
Landau damping of dust acoustic solitary waves in nonthermal plasmas
Ghai, Yashika; Saini, N. S.; Eliasson, B.
2018-01-01
Dust acoustic (DA) solitary and shock structures have been investigated under the influence of Landau damping in a dusty plasma containing two temperature nonthermal ions. Motivated by the observations of Geotail spacecraft that reported two-temperature ion population in the Earth's magnetosphere, we have investigated the effect of resonant wave-particle interactions on DA nonlinear structures. The Korteweg-de Vries (KdV) equation with an additional Landau damping term is derived and its analytical solution is presented. The solution has the form of a soliton whose amplitude decreases with time. Further, we have illustrated the influence of Landau damping and nonthermality of the ions on DA shock structures by a numerical solution of the Landau damping modified KdV equation. The study of the time evolution of shock waves suggests that an initial shock-like pulse forms an oscillatory shock at later times due to the balance of nonlinearity, dispersion, and dissipation due to Landau damping. The findings of the present investigation may be useful in understanding the properties of nonlinear structures in the presence of Landau damping in dusty plasmas containing two temperature ions obeying nonthermal distribution such as in the Earth's magnetotail.
Shoaling internal solitary waves of depression over gentle slopes
Rivera, Gustavo; Diamessis, Peter
2017-11-01
The shoaling of an internal solitary wave (ISW) of depression over gentle slopes is explored through fully nonlinear and non-hydrostatic simulations using a high resolution/accuracy deformed spectral multidomain penalty method. During shoaling, the wave does not disintegrate as in the case of steeper slope but, instead, maintains its symmetric shape. At the core of the wave, an unstable region forms, characterized by the entrapment of heavier-over-light fluid. The formation of this convective instability is attributed to the vertical stretching by the ISW of the near-surface vorticity layer associated with the baroclinic background current. According to recent field observations in the South China Sea, the unstable region drives localized turbulent mixing within the wave, estimated to be up to four times larger than that in the open ocean, in the form of a recirculating trapped core. In this talk, emphasis is placed on the structure of the unstable region and the persistence of a possible recirculating core using simulations which capture 2D wave propagation combined with 3D representation of the transition to turbulence. As such, a preliminary understanding of the underlying fluid mechanics and the potential broader oceanic significance of ISWs with trapped cores is offered. Financial support gratefully acknowledged to NSF OCE Grant 1634257.
Rotating solitary wave at the wall of a cylindrical container
Amaouche, Mustapha; Ait Abderrahmane, Hamid; Vatistas, Georgios H.
2013-01-01
This paper deals with the theoretical modeling of a rotating solitary surface wave that was observed during water drainage from a cylindrical reservoir, when shallow water conditions were reached. It represents an improvement of our previous study
International Nuclear Information System (INIS)
Han, Jiu-Ning; Luo, Jun-Hua; Sun, Gui-Hua; Liu, Zhen-Lai; Ge, Su-Hong; Wang, Xin-Xing; Li, Jun-Xiu
2014-01-01
The nonlinear dynamics of nonplanar (cylindrical and spherical) electron-acoustic solitary wave structures in an unmagnetized, collisionless plasma composed of stationary ions, cold fluid electrons and hot q-nonextensive distributed electrons are theoretically studied. We discuss the effects of the nonplanar geometry, nonextensivity of hot electrons and ‘hot’ to ‘cold’ electron number density ratio on the time evolution characters of cylindrical and spherical solitary waves. Moreover, the effects of plasma parameters on the nonlinear structure induced by the interaction between two planar solitary waves are also investigated. It is found that these plasma parameters have significant influences on the properties of the above-mentioned nonlinear structures. Our theoretical study may be useful to understand the nonlinear features of electron-acoustic wave structures in astrophysical plasma systems. (paper)
Directory of Open Access Journals (Sweden)
Qicheng Meng
2016-04-01
Full Text Available A third-order KdV solution to the internal solitary wave is derived by a new method based on the weakly nonlinear assumptions in a rigid-lid two-layer system. The solution corrects an error by Mirie and Su (1984. A two-dimensional numerical wave tank has been established with the help of the open source CFD library OpenFOAM and the third-party software waves2Foam. Various analytical solutions, including the first-order to third-order KdV solutions, the eKdV solution and the MCC solution, have been used to initialise the flow fields in the CFD simulations of internal solitary waves. Two groups including 11 numerical cases have been carried out. In the same group, the initial wave amplitudes are the same but the implemented analytical solutions are different. The simulated wave profiles at different moments have been presented. The relative errors in terms of the wave amplitude between the last time step and the initial input have been analysed quantitatively. It is found that the third-order KdV solution results in the most stable internal solitary wave in the numerical wave tank for both small-amplitude and finite-amplitude cases. The finding is significant for the further simulations involving internal solitary waves.
International Nuclear Information System (INIS)
Wang Qi; Li Biao; Zhang Hongqing; Chen Yong
2005-01-01
Taking the (2+1)-dimensional Broer-Kaup-Kupershmidt system as a simple example, some families of rational form solitary wave solutions, triangular periodic wave solutions, and rational wave solutions are constructed by using the Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.
Solitary wave and periodic wave solutions for Burgers, Fisher ...
Indian Academy of Sciences (India)
The generalized (G′/G)-expansion method; Burgers equation; Fisher's equation; ... the travelling wave solutions plays an important role in nonlinear sciences. ... Burgers, Fisher, Huxley equations and combined forms of these equations will ...
Numerical Simulations of Upstream Propagating Solitary Waves and Wave Breaking In A Stratified Fjord
Stastna, M.; Peltier, W. R.
In this talk we will discuss ongoing numerical modeling of the flow of a stratified fluid over large scale topography motivated by observations in Knight Inlet, a fjord in British Columbia, Canada. After briefly surveying the work done on the topic in the past we will discuss our latest set of simulations in which we have observed the gener- ation and breaking of three different types of nonlinear internal waves in the lee of the sill topography. The first type of wave observed is a large lee wave in the weakly strat- ified main portion of the water column, The second is an upward propagating internal wave forced by topography that breaks in the strong, near-surface pycnocline. The third is a train of upstream propagating solitary waves that, in certain circumstances, form as breaking waves consisting of a nearly solitary wave envelope and a highly unsteady core near the surface. Time premitting, we will comment on the implications of these results for our long term goal of quantifying tidally driven mixing in Knight Inlet.
Propagation of sech2-type solitary waves in higher-order KdV-type systems
International Nuclear Information System (INIS)
Ilison, O.; Salupere, A.
2005-01-01
Wave propagation in microstructured media is essentially influenced by nonlinear and dispersive effects. The simplest model governing these effects results in the Korteweg-de Vries (KdV) equation. In the present paper a KdV-type evolution equation, including the third- and fifth-order dispersive and the fourth-order nonlinear terms, is used for modelling the wave propagation in microstructured solids like martensitic-austenitic alloys. The model equation is solved numerically under localised initial conditions. Possible solution types are defined and discussed. The existence of a threshold is established. Below the threshold, the relatively small solitary waves decay in time. However, if the amplitude exceeds a certain threshold, i.e., the critical value, then such a solitary wave can propagate with nearly a constant speed and amplitude and consequently conserve the energy
New theory of the Great Red Spot from solitary waves in the Jovian atmosphere
International Nuclear Information System (INIS)
Maxworthy, T.; Redekopp, L.G.
1976-01-01
It is stated that the nature of the Great Red Spot on Jupiter is a persistent problem. It is considered here that 'solitary' waves on a horizontally sheared zonal flow in a rotating stratified atmosphere would explain many of the known GRS characteristics and also other features that have been observed on Jupiter. 'Solitary' waves are isolated permanent waves in which non-linear steepening balances dispersive spreading effects, and they can arise from arbitrary distrurbances and interact non-linearly without changing their shape. The only memory of such an interaction is a finite spatial phase shift between the fast- and the pre-interaction trajectories; the interaction looks like a rapid acceleration of one wave through another. The matter is here treated mathematically. A number of examples similar to Jupiter's GRS are mentioned in the discussion. (U.K.)
Forced solitary Rossby waves under the influence of slowly varying topography with time
International Nuclear Information System (INIS)
Yang Hong-Wei; Yin Bao-Shu; Yang De-Zhou; Xu Zhen-Hua
2011-01-01
By using a weakly nonlinear and perturbation method, the generalized inhomogeneous Korteweg—de Vries (KdV)—Burgers equation is derived, which governs the evolution of the amplitude of Rossby waves under the influence of dissipation and slowly varying topography with time. The analysis indicates that dissipation and slowly varying topography with time are important factors in causing variation in the mass and energy of solitary waves. (general)
Self-trapping of scalar and vector dipole solitary waves in Kerr media
International Nuclear Information System (INIS)
Zhong Weiping; Belic, Milivoj R.; Assanto, Gaetano; Malomed, Boris A.; Huang Tingwen
2011-01-01
We report solutions for expanding dipole-type optical solitary waves in two-dimensional Kerr media with the self-focusing nonlinearity, using exact analytical (Hirota) and numerical methods. Such localized beams carry intrinsic vorticity and exhibit symmetric shapes for both scalar and vector solitary modes. When vector beams are close to the scalar limit, simulations demonstrate their stability over propagation distances exceeding 50 diffraction lengths. In fact, the continuous expansion helps the vortical beams avoid the instability against the splitting, collapse, or decay, making them 'convectively stable' patterns.
Seadawy, A. R.; El-Rashidy, K.
2018-03-01
The Kadomtsev-Petviashvili (KP) and modified KP equations are two of the most universal models in nonlinear wave theory, which arises as a reduction of system with quadratic nonlinearity which admit weakly dispersive waves. The generalized extended tanh method and the F-expansion method are used to derive exact solitary waves solutions of KP and modified KP equations. The region of solutions are displayed graphically.
Orbital stability of solitary waves for Kundu equation
Zhang, Weiguo; Qin, Yinghao; Zhao, Yan; Guo, Boling
In this paper, we consider the Kundu equation which is not a standard Hamiltonian system. The abstract orbital stability theory proposed by Grillakis et al. (1987, 1990) cannot be applied directly to study orbital stability of solitary waves for this equation. Motivated by the idea of Guo and Wu (1995), we construct three invariants of motion and use detailed spectral analysis to obtain orbital stability of solitary waves for Kundu equation. Since Kundu equation is more complex than the derivative Schrödinger equation, we utilize some techniques to overcome some difficulties in this paper. It should be pointed out that the results obtained in this paper are more general than those obtained by Guo and Wu (1995). We present a sufficient condition under which solitary waves are orbitally stable for 2c+sυ1995) only considered the case 2c+sυ>0. We obtain the results on orbital stability of solitary waves for the derivative Schrödinger equation given by Colin and Ohta (2006) as a corollary in this paper. Furthermore, we obtain orbital stability of solitary waves for Chen-Lee-Lin equation and Gerdjikov-Ivanov equation, respectively.
Solitary ionizing surface waves on low-temperature plasmas
International Nuclear Information System (INIS)
Vladimirov, S.V.; Yu, M.Y.
1993-01-01
It is demonstrated that at the boundary of semi-infinite low-temperature plasma new types of localized ionizing surface wave structures can propagate. The solitary waves are described by an evolution equation similar to the KdV equation, but the solutions differ considerably from that of the latter
Obliquely propagating large amplitude solitary waves in charge neutral plasmas
Directory of Open Access Journals (Sweden)
F. Verheest
2007-01-01
Full Text Available This paper deals in a consistent way with the implications, for the existence of large amplitude stationary structures in general plasmas, of assuming strict charge neutrality between electrons and ions. With the limit of pair plasmas in mind, electron inertia is retained. Combining in a fluid dynamic treatment the conservation of mass, momentum and energy with strict charge neutrality has indicated that nonlinear solitary waves (as e.g. oscillitons cannot exist in electron-ion plasmas, at no angle of propagation with respect to the static magnetic field. Specifically for oblique propagation, the proof has turned out to be more involved than for parallel or perpendicular modes. The only exception is pair plasmas that are able to support large charge neutral solitons, owing to the high degree of symmetry naturally inherent in such plasmas. The nonexistence, in particular, of oscillitons is attributed to the breakdown of the plasma approximation in dealing with Poisson's law, rather than to relativistic effects. It is hoped that future space observations will allow to discriminate between oscillitons and large wave packets, by focusing on the time variability (or not of the phase, since the amplitude or envelope graphs look very similar.
Relativistic solitary waves modulating long laser pulses in plasmas
International Nuclear Information System (INIS)
Sanchez-Arriaga, G; Siminos, E; Lefebvre, E
2011-01-01
This paper discusses the existence of solitary electromagnetic waves trapped in a self-generated Langmuir wave and embedded in an infinitely long circularly polarized electromagnetic wave propagating through a plasma. From a mathematical point of view they are exact solutions of the one-dimensional relativistic cold fluid plasma model with nonvanishing boundary conditions. Under the assumption of travelling wave solutions with velocity V and vector potential frequency ω, the fluid model is reduced to a Hamiltonian system. The solitary waves are homoclinic (grey solitons) or heteroclinic (dark solitons) orbits to fixed points. Using a dynamical systems description of the Hamiltonian system and a spectral method, we identify a large variety of solitary waves, including asymmetric ones, discuss their disappearance for certain parameter values and classify them according to (i) grey or dark character, (ii) the number of humps of the vector potential envelope and (iii) their symmetries. The solutions come in continuous families in the parametric V-ω plane and extend up to velocities that approach the speed of light. The stability of certain types of grey solitary waves is investigated with the aid of particle-in-cell simulations that demonstrate their propagation for a few tens of the inverse of the plasma frequency.
Energy Technology Data Exchange (ETDEWEB)
Singh, S. V., E-mail: satyavir@iigs.iigm.res.in; Lakhina, G. S., E-mail: lakhina@iigs.iigm.res.in [Indian Institute of Geomagnetism, New Panvel (W), Navi Mumbai (India); University of the Western Cape, Belville (South Africa); Devanandhan, S., E-mail: devanandhan@gmail.com [Indian Institute of Geomagnetism, New Panvel (W), Navi Mumbai (India); Bharuthram, R., E-mail: rbharuthram@uwc.ac.za [University of the Western Cape, Belville (South Africa)
2016-08-15
A theoretical investigation is carried out to study the obliquely propagating electron acoustic solitary waves having nonthermal hot electrons, cold and beam electrons, and ions in a magnetized plasma. We have employed reductive perturbation theory to derive the Korteweg-de-Vries-Zakharov-Kuznetsov (KdV-ZK) equation describing the nonlinear evolution of these waves. The two-dimensional plane wave solution of KdV-ZK equation is analyzed to study the effects of nonthermal and beam electrons on the characteristics of the solitons. Theoretical results predict negative potential solitary structures. We emphasize that the inclusion of finite temperature effects reduces the soliton amplitudes and the width of the solitons increases by an increase in the obliquity of the wave propagation. The numerical analysis is presented for the parameters corresponding to the observations of “burst a” event by Viking satellite on the auroral field lines.
Observation of large-amplitude ion acoustic solitary waves in a plasma
International Nuclear Information System (INIS)
Nakamura, Yoshiharu
1987-01-01
Propagation of nonlinear ion acoustic waves in a multi-component plasma with negative ions is investigated in a double-plasma device. When the density of negative ions is larger than a critical value, a broad negative pulse evolves to rarefactive solitons, and a positive pulse whose amplitude is less than a certain threshold value becomes a subsonic wave train. In the same plasma, a positive pulse whose amplitude is larger than the threshold develops into a solitary wave. The critical amplitude is measured as a function of the density of negative ions and compared with predictions of the pseudo-potential method. The energy distribution of electrons in the solitary wave is also measured. (author)
Effect of Different Size Dust Grains on the Properties of Solitary Waves in Space Environments
International Nuclear Information System (INIS)
Elwakil, S.A.; Zahran, M.A.; El-Shewy, E.K.; Abdelwahed, H.G.
2009-01-01
Propagation of nonlinear dust-acoustic (DA) waves in an unmagnetized collisionless dusty plasma consisting of dust grains obey power law dust size distribution and nonthermal ions are investigated. For nonlinear DA waves, a reductive perturbation method was employed to obtain a Korteweg-de Vries (KdV) equation for the first-order potential. The effects of a dust size distribution, dust radius and the non-thermal distribution of ions on the soliton amplitude, width and energy of electrostatic solitary structures are presented
Li, Tatsien
2017-01-01
This book focuses on nonlinear wave equations, which are of considerable significance from both physical and theoretical perspectives. It also presents complete results on the lower bound estimates of lifespan (including the global existence), which are established for classical solutions to the Cauchy problem of nonlinear wave equations with small initial data in all possible space dimensions and with all possible integer powers of nonlinear terms. Further, the book proposes the global iteration method, which offers a unified and straightforward approach for treating these kinds of problems. Purely based on the properties of solut ions to the corresponding linear problems, the method simply applies the contraction mapping principle.
Electron-acoustic solitary waves in the Earth's inner magnetosphere
Dillard, C. S.; Vasko, I. Y.; Mozer, F. S.; Agapitov, O. V.; Bonnell, J. W.
2018-02-01
The broadband electrostatic turbulence observed in the inner magnetosphere is produced by large-amplitude electrostatic solitary waves of generally two types. The solitary waves with symmetric bipolar parallel (magnetic field-aligned) electric field are electron phase space holes. The solitary waves with highly asymmetric bipolar parallel electric field have been recently shown to correspond to the electron-acoustic plasma mode (existing due to two-temperature electron population). Through theoretical and numerical analysis of hydrodynamic and modified Korteweg-de Vries equations, we demonstrate that the asymmetric solitary waves appear due to the steepening of initially quasi-monochromatic electron-acoustic perturbation arrested at some moment by collisionless dissipation (Landau damping). The typical steepening time is found to be from a few to tens of milliseconds. The steepening of the electron-acoustic waves has not been reproduced in self-consistent kinetic simulations yet, and factors controlling the formation of steepened electron-acoustic waves, rather than electron phase space holes, remain unclear.
Coherent structures in wave boundary layers. Part 2. Solitary motion
DEFF Research Database (Denmark)
Sumer, B. Mutlu; Jensen, Palle Martin; Sørensen, Lone B.
2010-01-01
This study continues the investigation of wave boundary layers reported by Carstensen, Sumer & Fredsøe (J. Fluid Mech., 2010, part 1 of this paper). The present paper summarizes the results of an experimental investigation of turbulent solitary wave boundary layers, simulated by solitary motion...... the boundary-layer flow experiences a regular array of vortex tubes near the bed over a short period of time during the deceleration stage; and (iii) transitional regime characterized with turbulent spots, revealed by single/multiple, or, sometimes, quite dense spikes in the bed shear stress traces...
International Nuclear Information System (INIS)
Zhang, Shan; Hong, Xue-Ren; Wang, Hong-Yu; Xie, Bai-Song
2011-01-01
Nonparaxial and nonlinear propagation of a short intense laser beam in a parabolic plasma channel is analyzed by means of the variational method and nonlinear dynamics. The beam propagation properties are classified by five kinds of behaviors. In particularly, the electromagnetic solitary wave for finite pulse laser is found beside the other four propagation cases including beam periodically oscillating with defocussing and focusing amplitude, constant spot size, beam catastrophic focusing. It is also found that the laser pulse can be allowed to propagate in the plasma channel only when a certain relation for laser parameters and plasma channel parameters is satisfied. For the solitary wave, it may provide an effective way to obtain ultra-short laser pulse.
Single-peak solitary wave solutions for the variant Boussinesq ...
Indian Academy of Sciences (India)
ear dispersive waves in shallow water. This equation has attracted a lot of attention ... which is a model for water waves (a = 0), where u(x, t) is the velocity, H(x, t) is the total depth and the subscripts denote partial ... cusped solitary wave solutions of the osmosis K(2, 2) equation. Zhang and Chen [6] obtained new types of ...
Obliquely Incident Solitary Wave onto a Vertical Wall
Yeh, Harry
2012-10-01
When a solitary wave impinges obliquely onto a reflective vertical wall, it can take the formation of a Mach reflection (a geometrically similar reflection from acoustics). The mathematical theory predicts that the wave at the reflection can amplify not twice, but as high as four times the incident wave amplitude. Nevertheless, this theoretical four-fold amplification has not been verified by numerical or laboratory experiments. We discuss the discrepancies between the theory and the experiments; then, improve the theory with higher-order corrections. The modified theory results in substantial improvement and is now in good agreement with the numerical as well as our laboratory results. Our laboratory experiments indicate that the wave amplitude along the reflective wall can reach 0.91 times the quiescent water depth, which is higher than the maximum of a freely propagating solitary wave. Hence, this maximum runup 0.91 h would be possible even if the amplitude of the incident solitary wave were as small as 0.24 h. This wave behavior could provide an explanation for local variability of tsunami runup as well as for sneaker waves.
Solitary electron density waves in a magnetized, plasma-loaded waveguide
International Nuclear Information System (INIS)
Lynov, J.-P.
1980-08-01
Investigations of two different types of nonlinear, solitary electron density waves in a magnetized, plasma-loaded waveguide are presented. One of the wavetypes is a localized, compressional pulse identified as a Trivelpiece-Gould soliton. The modification of this soliton by the resonant electrons is studied theoretically, by direct numerical solution of the model equation, experimentally, and by numerical simulation of the experiment. The other wave is a localized, rarefactive pulse called an electron hole. It is a positive pulse consisting of a large number of trapped electrons and is a purely kinetic phenomenon. A simple waterbag model for the electron hole is derived and compared with the results from the experiment and the numerical simulation. Finally, interactions between the solitary waves are investigated. (Auth.)
Directory of Open Access Journals (Sweden)
Baojun Zhao
2018-01-01
Full Text Available Envelope gravity solitary waves are an important research hot spot in the field of solitary wave. And the weakly nonlinear model equations system is a part of the research of envelope gravity solitary waves. Because of the lack of technology and theory, previous studies tried hard to reduce the variable numbers and constructed the two-dimensional model in barotropic atmosphere and could only describe the propagation feature in a direction. But for the propagation of envelope gravity solitary waves in real ocean ridges and atmospheric mountains, the three-dimensional model is more appropriate. Meanwhile, the baroclinic problem of atmosphere is also an inevitable topic. In the paper, the three-dimensional coupled nonlinear Schrödinger (CNLS equations are presented to describe the evolution of envelope gravity solitary waves in baroclinic atmosphere, which are derived from the basic dynamic equations by employing perturbation and multiscale methods. The model overcomes two disadvantages: (1 baroclinic problem and (2 propagation path problem. Then, based on trial function method, we deduce the solution of the CNLS equations. Finally, modulational instability of wave trains is also discussed.
Quantum ion-acoustic solitary waves in weak relativistic plasma
Indian Academy of Sciences (India)
Abstract. Small amplitude quantum ion-acoustic solitary waves are studied in an unmagnetized two- species relativistic quantum plasma system, comprised of electrons and ions. The one-dimensional quantum hydrodynamic model (QHD) is used to obtain a deformed Korteweg–de Vries (dKdV) equation by reductive ...
Exact solitary ion acoustic waves in a magnetoplasma
International Nuclear Information System (INIS)
Ray, D.
1979-01-01
Solitary ion acoustic waves in a magnetoplasma have been studied by Shukla and Yu [J. Math. Phys. 19, 2506 (1978)]. A more rigorous study confirms the conditions that Shukla and Yu said would be necessary for humps. However, it is shown that a density cavity is also possible in the limiting case
Flow and sediment transport induced by a plunging solitary wave
DEFF Research Database (Denmark)
Sumer, B. Mutlu; Sen, M.Berke; Karagali, Ioanna
2011-01-01
Two parallel experiments involving the evolution and runup of plunging solitary waves on a sloping bed were conducted: (1) a rigid-bed experiment, allowing direct (hot film) measurements of bed shear stresses, and (2) a sediment-bed experiment, allowing for the measurement of pore-water pressures...
A relativistic solitary wave in electron positron plasma
International Nuclear Information System (INIS)
Berezhiani, V.I.; Skarka, V.; Mahajan, S.
1993-09-01
The relativistic solitary wave propagation is studied in cold electron-positron plasma embedded in an external arbitrary strong magnetic field. The exact, analytical soliton-like solution corresponding to a localized, purely electromagnetic pulse with arbitrary big amplitude is found. (author). 7 refs, 1 fig
Solitary wave exchange potential and nucleon-nucleon interaction
International Nuclear Information System (INIS)
Prema, K.; Raghavan, S.S.; Sekhar Raghavan
1986-11-01
Nucleon-nucleon interaction is studied using a phenomenological potential model called solitary wave exchange potential model. It is shown that this simple model reproduces the singlet and triplet scattering data and the deuteron parameters reasonably well. (author). 6 refs, 2 figs, 1 tab
Nonlinear elastic waves in materials
Rushchitsky, Jeremiah J
2014-01-01
The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professional...
Akbar, M Ali; Hj Mohd Ali, Norhashidah
2014-01-01
The exp(-Ф(η))-expansion method is an ascending method for obtaining exact and solitary wave solutions for nonlinear evolution equations. In this article, we implement the exp(-Ф(η))-expansion method to build solitary wave solutions to the fourth order Boussinesq equation. The procedure is simple, direct and useful with the help of computer algebra. By using this method, we obtain solitary wave solutions in terms of the hyperbolic functions, the trigonometric functions and elementary functions. The results show that the exp(-Ф(η))-expansion method is straightforward and effective mathematical tool for the treatment of nonlinear evolution equations in mathematical physics and engineering. 35C07; 35C08; 35P99.
Solitary wave evolution in a magnetized inhomogeneous plasma under the effect of ionization
International Nuclear Information System (INIS)
Jyoti; Malik, Hitendra K.
2011-01-01
A modified form of Korteweg-deVries (KdV) equation appropriate to nonlinear ion acoustic solitary waves in an inhomogeneous plasma is derived in the presence of an external magnetic field and constant ionization in the plasma. This equation differs from usual version of the KdV equation because of the inclusion of two terms arising due to ionization and density gradient present in the plasma. In this plasma, only the compressive solitary waves are found to propagate corresponding to the fast and slow modes. The amplitude of the solitary wave increases with an enhancement in the ionization for the fast mode as well as for the slow mode. The effect of magnetic field is to enhance the width of the solitary structure. The amplitude is found to increase (decrease) with an enhancement in charge number of the ions for the fast (slow) mode. The tailing structure becomes more (less) prominent with the rise in ion drift velocity for the case of fast (slow) mode.
Three-dimensional stability of solitary kinetic Alfven waves and ion-acoustic waves
International Nuclear Information System (INIS)
Ghosh, G.; Das, K.P.
1994-01-01
Starting from a set of equations that lead to a linear dispersion relation coupling kinetic Alfven waves and ion-acoustic waves, three-dimensional KdV equations are derived for these waves. These equations are then used to investigate the three-dimensional stability of solitary kinetic Alfven waves and ion-acoustic waves by the small-k perturbation expansion method of Rowlands and Infeld. For kinetic Alfven waves it is found that there is instability if the direction of the plane-wave perturbation lies inside a cone, and the growth rate of the instability attains a maximum when the direction of the perturbation lies in the plane containing the external magnetic field and the direction of propagation of the solitary wave. For ion-acoustic waves the growth rate of instability attains a maximum when the direction of the perturbation lies in a plane perpendicular to the direction of propagation of the solitary wave. (Author)
Ship-induced solitary Riemann waves of depression in Venice Lagoon
International Nuclear Information System (INIS)
Parnell, Kevin E.; Soomere, Tarmo; Zaggia, Luca; Rodin, Artem; Lorenzetti, Giuliano; Rapaglia, John; Scarpa, Gian Marco
2015-01-01
We demonstrate that ships of moderate size, sailing at low depth Froude numbers (0.37–0.5) in a navigation channel surrounded by shallow banks, produce depressions with depths up to 2.5 m. These depressions (Bernoulli wakes) propagate as long-living strongly nonlinear solitary Riemann waves of depression substantial distances into Venice Lagoon. They gradually become strongly asymmetric with the rear of the depression becoming extremely steep, similar to a bore. As they are dynamically similar, air pressure fluctuations moving over variable-depth coastal areas could generate meteorological tsunamis with a leading depression wave followed by a devastating bore-like feature. - Highlights: • Unprecedently deep long-living ship-induced waves of depression detected. • Such waves are generated in channels with side banks under low Froude numbers. • The propagation of these waves is replicated using Riemann waves. • Long-living waves of depression form bore-like features at rear slope
Ship-induced solitary Riemann waves of depression in Venice Lagoon
Energy Technology Data Exchange (ETDEWEB)
Parnell, Kevin E. [College of Marine and Environmental Sciences and Centre for Tropical Environmental and Sustainability Sciences, James Cook University, Queensland 4811 (Australia); Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Soomere, Tarmo, E-mail: soomere@cs.ioc.ee [Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Estonian Academy of Sciences, Kohtu 6, 10130 Tallinn (Estonia); Zaggia, Luca [Institute of Marine Sciences, National Research Council, Castello 2737/F, 30122 Venice (Italy); Rodin, Artem [Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn (Estonia); Lorenzetti, Giuliano [Institute of Marine Sciences, National Research Council, Castello 2737/F, 30122 Venice (Italy); Rapaglia, John [Sacred Heart University Department of Biology, 5151 Park Avenue, Fairfield, CT 06825 (United States); Scarpa, Gian Marco [Università Ca' Foscari, Dorsoduro 3246, 30123 Venice (Italy)
2015-03-06
We demonstrate that ships of moderate size, sailing at low depth Froude numbers (0.37–0.5) in a navigation channel surrounded by shallow banks, produce depressions with depths up to 2.5 m. These depressions (Bernoulli wakes) propagate as long-living strongly nonlinear solitary Riemann waves of depression substantial distances into Venice Lagoon. They gradually become strongly asymmetric with the rear of the depression becoming extremely steep, similar to a bore. As they are dynamically similar, air pressure fluctuations moving over variable-depth coastal areas could generate meteorological tsunamis with a leading depression wave followed by a devastating bore-like feature. - Highlights: • Unprecedently deep long-living ship-induced waves of depression detected. • Such waves are generated in channels with side banks under low Froude numbers. • The propagation of these waves is replicated using Riemann waves. • Long-living waves of depression form bore-like features at rear slope.
Algebraic method for constructing singular steady solitary waves: a case study
Clamond, Didier; Dutykh, Denys; Galligo, André
2016-07-01
This article describes the use of algebraic methods in a phase plane analysis of ordinary differential equations. The method is illustrated by the study of capillary-gravity steady surface waves propagating in shallow water. We consider the (fully nonlinear, weakly dispersive) Serre-Green-Naghdi equation with surface tension, because it provides a tractable model that, at the same time, is not too simple, so interest in the method can be emphasized. In particular, we analyse a special class of solutions, the solitary waves, which play an important role in many fields of physics. In capillary-gravity regime, there are two kinds of localized infinitely smooth travelling wave solutions-solitary waves of elevation and of depression. However, if we allow the solitary waves to have an angular point, then the `zoology' of solutions becomes much richer, and the main goal of this study is to provide a complete classification of such singular localized solutions using the methods of the effective algebraic geometry.
International Nuclear Information System (INIS)
Roy Choudhury, S.
2007-01-01
The Ostrovsky equation is an important canonical model for the unidirectional propagation of weakly nonlinear long surface and internal waves in a rotating, inviscid and incompressible fluid. Limited functional analytic results exist for the occurrence of one family of solitary-wave solutions of this equation, as well as their approach to the well-known solitons of the famous Korteweg-de Vries equation in the limit as the rotation becomes vanishingly small. Since solitary-wave solutions often play a central role in the long-time evolution of an initial disturbance, we consider such solutions here (via the normal form approach) within the framework of reversible systems theory. Besides confirming the existence of the known family of solitary waves and its reduction to the KdV limit, we find a second family of multihumped (or N-pulse) solutions, as well as a continuum of delocalized solitary waves (or homoclinics to small-amplitude periodic orbits). On isolated curves in the relevant parameter region, the delocalized waves reduce to genuine embedded solitons. The second and third families of solutions occur in regions of parameter space distinct from the known solitary-wave solutions and are thus entirely new. Directions for future work are also mentioned
Nonlinear acoustic waves in nonthermal plasmas with negative and positive dust
International Nuclear Information System (INIS)
Verheest, Frank
2009-01-01
Using a Sagdeev pseudopotential formalism where nonlinear structures are stationary in a co-moving frame, large dust-acoustic solitary waves and double layers have been studied in plasmas with negative and positive cold dust, in the presence of nonthermal electrons and ions. This has been done in a systematic way, to delimit the compositional parameter space in which such modes can be found. The existence domain of negative/positive solitary waves is limited by infinite compression of the negative/positive dust or by the occurrence of negative/positive double layers. These double layers require a sufficient nonthermality of the electrons/ions and the presence of enough positive/negative dust. There are parameter ranges where both negative and positive solitary structures coexist, sometimes both of the solitary wave type, sometimes one a solitary wave and the other a double layer. Typical Sagdeev pseudopotentials and solitary wave profiles have been presented.
International Nuclear Information System (INIS)
Yusufoglu, E.; Bekir, A.; Alp, M.
2008-01-01
In this paper, we establish exact solutions for nonlinear evolution equations. The sine-cosine method is used to construct periodic and solitary wave solutions of the Kawahara and modified Kawahara equations. These solutions may be important of significance for the explanation of some practical physical problems
Electron acoustic solitary waves in unmagnetized two electron population dense plasmas
International Nuclear Information System (INIS)
Mahmood, S.; Masood, W.
2008-01-01
The electron acoustic solitary waves are studied in unmagnetized two population electron quantum plasmas. The quantum hydrodynamic model is employed with the Sagdeev potential approach to describe the arbitrary amplitude electron acoustic waves in a two electron population dense Fermi plasma. It is found that hot electron density hump structures are formed in the subsonic region in such type of quantum plasmas. The wave amplitude as well as the width of the soliton are increased with the increase of percentage presence of cold (thinly populated) electrons in a multicomponent quantum plasma. It is found that an increase in quantum diffraction parameter broadens the nonlinear structure. Furthermore, the amplitude of the nonlinear electron acoustic wave is found to increase with the decrease in Mach number. The numerical results are also presented to understand the formation of solitons in two electron population Fermi plasmas.
2015-09-30
Interaction of Surface Gravity Waves with Nonlinear Internal Gravity Waves Lian Shen St. Anthony Falls Laboratory and Department of Mechanical...on studying surface gravity wave evolution and spectrum in the presence of surface currents caused by strongly nonlinear internal solitary waves...interaction of surface and internal gravity waves in the South China Sea. We will seek answers to the following questions: 1) How does the wind-wave
Danehkar, A.
2018-06-01
Suprathermal electrons and inertial drifting electrons, so called electron beam, are crucial to the nonlinear dynamics of electrostatic solitary waves observed in several astrophysical plasmas. In this paper, the propagation of electron-acoustic solitary waves (EAWs) is investigated in a collisionless, unmagnetized plasma consisting of cool inertial background electrons, hot suprathermal electrons (modeled by a κ-type distribution), and stationary ions. The plasma is penetrated by a cool electron beam component. A linear dispersion relation is derived to describe small-amplitude wave structures that shows a weak dependence of the phase speed on the electron beam velocity and density. A (Sagdeev-type) pseudopotential approach is employed to obtain the existence domain of large-amplitude solitary waves, and investigate how their nonlinear structures depend on the kinematic and physical properties of the electron beam and the suprathermality (described by κ) of the hot electrons. The results indicate that the electron beam can largely alter the EAWs, but can only produce negative polarity solitary waves in this model. While the electron beam co-propagates with the solitary waves, the soliton existence domain (Mach number range) becomes narrower (nearly down to nil) with increasing the beam speed and the beam-to-hot electron temperature ratio, and decreasing the beam-to-cool electron density ratio in high suprathermality (low κ). It is found that the electric potential amplitude largely declines with increasing the beam speed and the beam-to-cool electron density ratio for co-propagating solitary waves, but is slightly decreased by raising the beam-to-hot electron temperature ratio.
On the generation and evolution of internal solitary waves in the southern Red Sea
Guo, Daquan
2015-04-01
Satellite observations recently revealed the existence of trains of internal solitary waves in the southern Red Sea between 16.0°N and 16.5°N, propagating from the centre of the domain toward the continental shelf [Da silva et al., 2012]. Given the relatively weak tidal velocity in this area and their generation in the central of the domain, Da Silva suggested three possible mechanisms behind the generation of the waves, namely Resonance and disintegration of interfacial tides, Generation of interfacial tides by impinging, remotely generated internal tidal beams and for geometrically focused and amplified internal tidal beams. Tide analysis based on tide stations data and barotropic tide model in the Red Sea shows that tide is indeed very weak in the centre part of the Red Sea, but it is relatively strong in the northern and southern parts (reaching up to 66 cm/s). Together with extreme steep slopes along the deep trench, it provides favourable conditions for the generation of internal solitary in the southern Red Sea. To investigate the generation mechanisms and study the evolution of the internal waves in the off-shelf region of the southern Red Sea we have implemented a 2-D, high-resolution and non-hydrostatic configuration of the MIT general circulation model (MITgcm). Our simulations reproduce well that the generation process of the internal solitary waves. Analysis of the model\\'s output suggests that the interaction between the topography and tidal flow with the nonlinear effect is the main mechanism behind the generation of the internal solitary waves. Sensitivity experiments suggest that neither tidal beam nor the resonance effect of the topography is important factor in this process.
2016-01-01
This volume brings together four lecture courses on modern aspects of water waves. The intention, through the lectures, is to present quite a range of mathematical ideas, primarily to show what is possible and what, currently, is of particular interest. Water waves of large amplitude can only be fully understood in terms of nonlinear effects, linear theory being not adequate for their description. Taking advantage of insights from physical observation, experimental evidence and numerical simulations, classical and modern mathematical approaches can be used to gain insight into their dynamics. The book presents several avenues and offers a wide range of material of current interest. Due to the interdisciplinary nature of the subject, the book should be of interest to mathematicians (pure and applied), physicists and engineers. The lectures provide a useful source for those who want to begin to investigate how mathematics can be used to improve our understanding of water wave phenomena. In addition, some of the...
Rotating solitary wave at the wall of a cylindrical container
Amaouche, Mustapha
2013-04-30
This paper deals with the theoretical modeling of a rotating solitary surface wave that was observed during water drainage from a cylindrical reservoir, when shallow water conditions were reached. It represents an improvement of our previous study, where the radial flow perturbation was neglected. This assumption led to the classical planar Korteweg–de Vries equation for the wall wave profile, which did not account for the rotational character of the base flow. The present formulation is based on a less restricting condition and consequently corrects the last shortcoming. Now the influence of the background flow appears in the wave characteristics. The theory provides a better physical depiction of the unique experiment by predicting fairly well the wave profile at least in the first half of its lifetime and estimating the speed of the observed wave with good accuracy.
Oblique non-neutral solitary Alfven modes in weakly nonlinear pair plasmas
International Nuclear Information System (INIS)
Verheest, Frank; Lakhina, G S
2005-01-01
The equal charge-to-mass ratio for both species in pair plasmas induces a decoupling of the linear eigenmodes between waves that are charge neutral or non-neutral, also at oblique propagation with respect to a static magnetic field. While the charge-neutral linear modes have been studied in greater detail, including their weakly and strongly nonlinear counterparts, the non-neutral mode has received less attention. Here the nonlinear evolution of a solitary non-neutral mode at oblique propagation is investigated in an electron-positron plasma. Employing the framework of reductive perturbation analysis, a modified Korteweg-de Vries equation (with cubic nonlinearity) for the lowest-order wave magnetic field is obtained. In the linear approximation, the non-neutral mode has its magnetic component orthogonal to the plane spanned by the directions of wave propagation and of the static magnetic field. The linear polarization is not maintained at higher orders. The results may be relevant to the microstructure in pulsar radiation or to the subpulses
Some new exact solitary wave solutions of the van der Waals model arising in nature
Bibi, Sadaf; Ahmed, Naveed; Khan, Umar; Mohyud-Din, Syed Tauseef
2018-06-01
This work proposes two well-known methods, namely, Exponential rational function method (ERFM) and Generalized Kudryashov method (GKM) to seek new exact solutions of the van der Waals normal form for the fluidized granular matter, linked with natural phenomena and industrial applications. New soliton solutions such as kink, periodic and solitary wave solutions are established coupled with 2D and 3D graphical patterns for clarity of physical features. Our comparison reveals that the said methods excel several existing methods. The worked-out solutions show that the suggested methods are simple and reliable as compared to many other approaches which tackle nonlinear equations stemming from applied sciences.
Semi-analytic variable charge solitary waves involving dust phase-space vortices (holes)
Energy Technology Data Exchange (ETDEWEB)
Tribeche, Mouloud; Younsi, Smain; Amour, Rabia; Aoutou, Kamel [Plasma Physics Group, Faculty of Sciences-Physics, Theoretical Physics Laboratory, University of Bab-Ezzouar, USTHB BP 32, El Alia, Algiers 16111 (Algeria)], E-mail: mtribeche@usthb.dz
2009-09-15
A semi-analytic model for highly nonlinear solitary waves involving dust phase-space vortices (holes) is outlined. The variable dust charge is expressed in terms of the Lambert function and we take advantage of this transcendental function to investigate the localized structures that may occur in a dusty plasma with variable charge trapped dust particles. Our results which complement the previously published work on this problem (Schamel et al 2001 Phys. Plasmas 8 671) should be of basic interest for experiments that involve the trapping of dust particles in ultra-low-frequency dust acoustic modes.
Semi-analytic variable charge solitary waves involving dust phase-space vortices (holes)
International Nuclear Information System (INIS)
Tribeche, Mouloud; Younsi, Smain; Amour, Rabia; Aoutou, Kamel
2009-01-01
A semi-analytic model for highly nonlinear solitary waves involving dust phase-space vortices (holes) is outlined. The variable dust charge is expressed in terms of the Lambert function and we take advantage of this transcendental function to investigate the localized structures that may occur in a dusty plasma with variable charge trapped dust particles. Our results which complement the previously published work on this problem (Schamel et al 2001 Phys. Plasmas 8 671) should be of basic interest for experiments that involve the trapping of dust particles in ultra-low-frequency dust acoustic modes.
Stability of negative solitary waves for an integrable modified Camassa-Holm equation
International Nuclear Information System (INIS)
Yin Jiuli; Tian Lixin; Fan Xinghua
2010-01-01
In this paper, we prove that the modified Camassa-Holm equation is Painleve integrable. We also study the orbital stability problem of negative solitary waves for this integrable equation. It is shown that the negative solitary waves are stable for arbitrary wave speed of propagation.
Large amplitude solitary waves in a multicomponent plasma with negative ions
International Nuclear Information System (INIS)
Nakamura, Y.; Tsukabayashi, I.; Ludwig, G.O.; Ferreira, J.L.
1987-09-01
When the concentration of negative ions is larger than a critical value, a small compressive pulse evolves into a subsonic wave train and a large pulse develops into a solitary wave. The threshold amplitude and velocity of the solitary waves are measured and compared with predictions using the pseudopotential method. (author) [pt
Dynamical barrier for the formation of solitary waves in discrete lattices
International Nuclear Information System (INIS)
Kevrekidis, P.G.; Espinola-Rocha, J.A.; Drossinos, Y.; Stefanov, A.
2008-01-01
We consider the problem of the existence of a dynamical barrier of 'mass' that needs to be excited on a lattice site to lead to the formation and subsequent persistence of localized modes for a nonlinear Schroedinger lattice. We contrast the existence of a dynamical barrier with its absence in the static theory of localized modes in one spatial dimension. We suggest an energetic criterion that provides a sufficient, but not necessary, condition on the amplitude of a single-site initial condition required to form a solitary wave. We show that this effect is not one-dimensional by considering its two-dimensional analog. The existence of a sufficient condition for the excitation of localized modes in the non-integrable, discrete, nonlinear Schroedinger equation is compared to the dynamics of excitations in the integrable, both discrete and continuum, version of the nonlinear Schroedinger equation
Dynamical barrier for the formation of solitary waves in discrete lattices
Energy Technology Data Exchange (ETDEWEB)
Kevrekidis, P.G. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003 (United States)], E-mail: kevrekid@math.umass.edu; Espinola-Rocha, J.A. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003 (United States); Drossinos, Y. [European Commission, Joint Research Centre, I-21020 Ispra (Vatican City State, Holy See,) (Italy); School of Mechanical and Systems Engineering, University of Newcastle upon Tyne, Newcastle upon Tyne NE1 7RU (United Kingdom); Stefanov, A. [Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd., Lawrence, KS 66045-7523 (United States)
2008-03-24
We consider the problem of the existence of a dynamical barrier of 'mass' that needs to be excited on a lattice site to lead to the formation and subsequent persistence of localized modes for a nonlinear Schroedinger lattice. We contrast the existence of a dynamical barrier with its absence in the static theory of localized modes in one spatial dimension. We suggest an energetic criterion that provides a sufficient, but not necessary, condition on the amplitude of a single-site initial condition required to form a solitary wave. We show that this effect is not one-dimensional by considering its two-dimensional analog. The existence of a sufficient condition for the excitation of localized modes in the non-integrable, discrete, nonlinear Schroedinger equation is compared to the dynamics of excitations in the integrable, both discrete and continuum, version of the nonlinear Schroedinger equation.
Dust acoustic solitary waves and double layers in a dusty plasma with two-temperature trapped ions
International Nuclear Information System (INIS)
El-Labany, S.K.; El-Taibany, W.F.; Mamun, A.A.; Moslem, Waleed M.
2004-01-01
The combined effects of trapped ion distribution, two-ion-temperature, dust charge fluctuation, and dust fluid temperature are incorporated in the study of nonlinear dust acoustic waves in an unmagnetized dusty plasma. It is found that, owing to the departure from the Boltzmann ion distribution to the trapped ion distribution, the dynamics of small but finite amplitude dust acoustic waves is governed by a modified Korteweg-de Vries equation. The latter admits a stationary dust acoustic solitary wave solution, which has stronger nonlinearity, smaller amplitude, wider width, and higher propagation velocity than that involving adiabatic ions. The effect of two-ion-temperature is found to provide the possibility for the coexistence of rarefactive and compressive dust acoustic solitary structures and double layers. Although the dust fluid temperature increases the amplitude of the small but finite amplitude solitary waves, the dust charge fluctuation does the opposite effect. The present investigation should help us to understand the salient features of the nonlinear dust acoustic waves that have been observed in a recent numerical simulation study
Collaborative Research: Dynamics of Electrostatic Solitary Waves on Current Layers
Energy Technology Data Exchange (ETDEWEB)
Pickett, Jolene S.
2012-10-31
The research carried out under the subject grant has provided insight into the generation of Electrostatic Solitary Waves (ESWs), which are nonlinear structures observed in space plasma data. These ESWs, appearing as pulses in the electric field time series data, represent the presence of several hundred meters to kilometer size positive potential structures, similar to champagne bubbles, where the electrons have been depleted, and which travel along Earth's magnetic field lines. The laboratory experiments carried out at the UCLA LAPD under the grant allowed us the opportunity to change various plasma and field conditions within the plasma device, and experiment with injection of suprathermal electron beams, in order to create ESWs. This then allowed us to determine the most likely method of generation of the ESWs. By comparing the properties of the ESWs observed in the LAPD to those observed in space and the plasma and field conditions under which those ESWs were observed in both locations, we were able to evaluate various ESW generation mechanisms. The findings of the laboratory experiments are that ESWs are generated through a lower hybrid instability. The ESWs observed in Earth's auroral current regions have similar characteristics to those generated by the laboratory when referenced to basic plasma and field characteristics, leading us to the conclusion that the lower hybrid drift instability is certainly a possibility for generation of the ESWs, at least in the auroral (northern/southern lights) regions. Due to space instrumentation insufficiencies and the limitations on telemetry, and thus poor time resolution, it is not possible to determine absolutely what generates these bubbles in space, but the laboratory experiments and supporting simulations have helped us to further our understanding of the processes under which they are generated. The public benefits from the findings of this research because the research is focused on current layers
Periodic waves in nonlinear metamaterials
International Nuclear Information System (INIS)
Liu, Wen-Jun; Xiao, Jing-Hua; Yan, Jie-Yun; Tian, Bo
2012-01-01
Periodic waves are presented in this Letter. With symbolic computation, equations for monochromatic waves are studied, and analytic periodic waves are obtained. Factors affecting properties of periodic waves are analyzed. Nonlinear metamaterials, with the continuous distribution of the dielectric permittivity obtained, are different from the ones with the discrete distribution. -- Highlights: ► Equations for the monochromatic waves in transverse magnetic polarization have been studied. ► Analytic periodic waves for the equations have been obtained. ► Periodic waves are theoretically presented and studied in the nonlinear metamaterials.
Physical Processes Involved In Yellow Sea Solitary Waves
Warn-Varnas, A.; Chin-Bing, S.; King, D.; Lamb, K.; Hawkins, J.; Teixeira, M.
The study area is located south of the Shandong peninsula. In this area, soliton gener- ation and propagation studies are per formed with the Lamb(1994) model. The model is nonhydrostatic and is formulated in 2 1/2 dimensions for terrain following c oordi- nates. In the area, 20 to 30 m topographic variations over distances of 10 to 20 km are found to occur in the digit al atlas of Choi (1999). The area is shallow with maximum depths ranging from 40 m to 70 m. Along the southern boundary of the region the semi-diurnal tidal strength magnitude varies from .6 m/sec to 1.2 m/sec, Fang(1994). We show that, for sum mer conditions, the existing physical processes associated with the semi-diurnal tidal flow over the topographic variations , in the shelfbreak region, lead to the formation of internal bores in the model simulations. Through acting phys- ical proce sses, the internal bores propagate on and off the shelf. A disintegration process of internal bores into solitary waves occ urs through frequency and ampli- tude dispersion. SAR observations of the area show images containing six events con- sisting of internal bores and solitary waves that travel in a well-defined direction for two and a half days. The origin of the trains appeared to be at a point along a steep topo graphic drop. The SAR observations are used for guiding and tuning the model simulations, by comparing spectra of observed and modeled wavelengths. The tuned model yields wavelengths that are within a factor of 2 of the SAR data. The modeled amp litudes are within a factor of 2 of amplitudes obtained with a two-layer model and the SAR data The signature on the acoustical field of ongoing physical processes through the interaction of the resultant oceanic struct ure with the acoustical field is pursued. Internal bore and solitary wave structures interact with the acoustic field. A re distribution of acoustical energy to higher acoustical modes occurs at some fre- quencies. Mode decomposition of the
Experiments and computation of onshore breaking solitary waves
DEFF Research Database (Denmark)
Jensen, A.; Mayer, Stefan; Pedersen, G.K.
2005-01-01
This is a combined experimental and computational study of solitary waves that break on-shore. Velocities and accelerations are measured by a two-camera PIV technique and compared to theoretical values from an Euler model with a VOF method for the free surface. In particular, the dynamics of a so......-called collapsing breaker is scrutinized and the closure between the breaker and the beach is found to be akin to slamming. To the knowledge of the authors, no velocity measurements for this kind of breaker have been previously reported....
Deep-water bedforms induced by refracting Internal Solitary Waves
Falcini, Federico; Droghei, Riccardo; Casalbore, Daniele; Martorelli, Eleonora; Mosetti, Renzo; Sannino, Gianmaria; Santoleri, Rosalia; Latino Chiocci, Francesco
2017-04-01
Subaqueous bedforms (or sand waves) are typically observed in those environments that are exposed to strong currents, characterized by a dominant unidirectional flow. However, sand-wave fields may be also observed in marine environments where no such current exists; the physical processes driving their formation are enigmatic or not well understood. We propose that internal solitary waves (ISWs), induced by tides, can produce an effective, unidirectional boundary flow filed that forms asymmetric sand waves. We test this idea by examining a sand-wave field off the Messina Strait, where we hypothesize that ISWs formed at the interface between intermediate and surface waters are refracted by topography. Hence, we argue that the deflected pattern (i.e., the depth-dependent orientation) of the sand-wave field is due to refraction of such ISWs. Combining field observations and numerical modelling, we show that ISWs can account for three key features: ISWs produce fluid velocities capable of mobilizing bottom sediments; the predicted refraction pattern resulting from the interaction of ISWs with bottom topography matches the observed deflection of the sand waves; and predicted migration rates of sand waves match empirical estimates. This work shows how ISWs may contribute to sculpting the structure of continental margins and it represents a promising link between the geological and oceanographic communities.
Asymptotic expansions for solitary gravity-capillary waves in two and three dimensions
International Nuclear Information System (INIS)
Ablowitz, M J; Haut, T S
2010-01-01
High-order asymptotic series are obtained for gravity-capillary solitary waves, where the first term in the series is the well-known sech 2 solution of the KdV equation. The asymptotic series is used, with nine terms included, to investigate the effects of surface tension on the height and energy of large amplitude waves, and waves close to the solitary version of Stokes' extreme wave. In particular, for surface tension below a critical value, the solitary wave with the maximum energy is obtained. For large surface tension, the series is also used to study the energy related to the solitary waves of depression. Energy considerations suggest that, for large enough surface tension, there are solitary waves that can get close to the fluid bottom. Comparisons are also made with recent experiments.
Traveling waves and conservation laws for highly nonlinear wave equations modeling Hertz chains
Przedborski, Michelle; Anco, Stephen C.
2017-09-01
A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, homogeneous, discrete chains with a general power-law contact interaction is studied. For this wave equation, all solitary wave solutions and all nonlinear periodic wave solutions, along with all conservation laws, are derived. The solutions are explicitly parameterized in terms of the asymptotic value of the wave amplitude in the case of solitary waves and the peak of the wave amplitude in the case of nonlinear periodic waves. All cases in which the solution expressions can be stated in an explicit analytic form using elementary functions are worked out. In these cases, explicit expressions for the total energy and total momentum for all solutions are obtained as well. The derivation of the solutions uses the conservation laws combined with an energy analysis argument to reduce the wave equation directly to a separable first-order differential equation that determines the wave amplitude in terms of the traveling wave variable. This method can be applied more generally to other highly nonlinear wave equations.
Energy Technology Data Exchange (ETDEWEB)
Ata-ur-Rahman,; Qamar, A. [Institute of Physics and Electronics, University of Peshawar, Peshawar 25000 (Pakistan); National Centre for Physics, QAU Campus, Shahdrah Valley Road, Islamabad 44000 (Pakistan); Masood, W. [National Centre for Physics, QAU Campus, Shahdrah Valley Road, Islamabad 44000 (Pakistan); COMSATS, Institute of Information Technology, Park Road, Chak Shahzad, Islamabad 44000 (Pakistan); Eliasson, B. [Physics Department, University of Strathclyde, Glasgow G4 0NG, Scotland (United Kingdom)
2013-09-15
In this paper, small but finite amplitude electrostatic solitary waves in a relativistic degenerate magnetoplasma, consisting of relativistically degenerate electrons and non-degenerate cold ions, are investigated. The Zakharov-Kuznetsov equation is derived employing the reductive perturbation technique and its solitary wave solution is analyzed. It is shown that only compressive electrostatic solitary structures can propagate in such a degenerate plasma system. The effects of plasma number density, ion cyclotron frequency, and direction cosines on the profiles of ion acoustic solitary waves are investigated and discussed at length. The relevance of the present investigation vis-a-vis pulsating white dwarfs is also pointed out.
International Nuclear Information System (INIS)
Heidari, E; Aslaninejad, M; Eshraghi, H
2010-01-01
Using a set of relativistic equations for plasmas with warm electrons and cold ions, we have investigated the effects of trapped electrons in the propagation of an electrosound wave and discussed the possibility of the formation of electromagnetic solitons in a plasma. The effective potential energy and deviations of the electron and ion number densities in this relativistic model have been found. We have obtained the governing equations for the amplitude of the HF field with relativistic corrections. In order to show the destructive impact of the trapped electrons on the solitary wave, a relativistic effective potential and the governing equation have been found. It is shown that for certain values of the parameters the condition of localization of the HF amplitude is violated. In addition, it is shown that as the flow velocity of the plasma changes, the shape of the solitary wave shows two opposing behaviours, depending on whether the solitary wave velocity is larger than the flow velocity or smaller. Also, the existence of stationary solitary waves which are prohibited for nonrelativistic plasma has been predicted. Finally, we have obtained the Korteweg-de Vries equation showing the relativistic, trapping and nonlinearity effects.
Solitary Alfven wave envelopes and the modulational instability
International Nuclear Information System (INIS)
Kennel, C.F.
1987-06-01
The derivative nonlinear Schroedinger equation describes the modulational instability of circularly polarized dispersive Alfven wave envelopes. It also may be used to determine the properties of finite amplitude localized stationary wave envelopes. Such envelope solitons exist only in conditions of modulational stability. This leaves open the question of whether, and if so, how, the modulational instability produces envelope solitons. 12 refs
Nonlinear waves and weak turbulence
Zakharov, V E
1997-01-01
This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincaré normal forms, and the inverse scattering method.
Collapse of nonlinear Langmuir waves
International Nuclear Information System (INIS)
Malkin, V.M.
1986-01-01
The dispersion of sufficiently intensive Langmuir waves is determined by intrinsic (electron) nonlinearity. During Langmuir collapse the wave energy density required for the appearance of electron nonlinearity is attained, generally speaking, prior to the development of dissipative processes. Up to now, the effect of electron nonlinearity on the collapse dynamics and spectrum of strong Langmuir turbulence ( which may be very appreciable ) has not been studied extensively because of the difficulty of describing nonlinear Langmuir waves. In the present paper the positive determinacy of the electron nonlinear hamiltonian is proven, the increment of modulation instability of a nonlinear Langmuir wave cluster localized in a cavity is calculated, and the universal law of their collapse is found
Modeling stretched solitary waves along magnetic field lines
Directory of Open Access Journals (Sweden)
L. Muschietti
2002-01-01
Full Text Available A model is presented for a new type of fast solitary waves which is observed in downward current regions of the auroral zone. The three-dimensional, coherent structures are electrostatic, have a positive potential, and move along the magnetic field lines with speeds on the order of the electron drift. Their parallel potential profile is flattened and cannot fit to the Gaussian shape used in previous work. We develop a detailed BGK model which includes a flattened potential and an assumed cylindrical symmetry around a centric magnetic field line. The model envisions concentric shells of trapped electrons slowly drifting azimuthally while bouncing back and forth in the parallel direction. The electron dynamics is analysed in terms of three basic motions that occur on different time scales characterized by the cyclotron frequency We , the bounce frequency wb , and the azimuthal drift frequency wg. The ordering We >> wb >> wg is required. Self-consistent distribution functions are calculated in terms of approximate constants of motion. Constraints on the parameters characterizing the amplitude and shape of the stretched solitary wave are discussed.
Nonlinear modulation of ionization waves
International Nuclear Information System (INIS)
Bekki, Naoaki
1981-01-01
In order to investigate the nonlinear characteristics of ionization waves (moving-striations) in the positive column of glow discharge, a nonlinear modulation of ionization waves in the region of the Pupp critical current is analysed by means of the reductive perturbation method. The modulation of ionization waves is described by a nonlinear Schroedinger type equation. The coefficients of the equation are evaluated using the data of the low pressure Argon-discharge, and the simple solutions (plane wave and envelope soliton type solutions) are presented. Under a certain condition an envelope soliton is propagated through the positive column. (author)
Solitary Waves of Ice Loss Detected in Greenland Crustal Motion
Adhikari, S.; Ivins, E. R.; Larour, E. Y.
2017-12-01
The annual cycle and secular trend of Greenland mass loading are well recorded in measurements of solid Earth deformation. While bedrock vertical displacements are in phase with loading as inferred from space observations, horizontal motions have received almost no attention. The horizontal bedrock displacements can potentially track the spatiotemporal detail of mass changes with great fidelity. Our analysis of Greenland crustal motion data reveals that a significant excitation of horizontal amplitudes occurs during the intense Greenland melting. A suite of space geodetic observations and climate reanalysis data cannot explain these large horizontal displacements. We discover that solitary seasonal waves of substantial mass transport traveled through Rink Glacier in 2010 and 2012. We deduce that intense summer melting enhanced either basal lubrication or shear softening, or both, causing the glacier to thin dynamically. The newly routed upstream sublglacial water was likely to be both retarded and inefficient, thus providing a causal mechanism for the prolonged ice transport to continue well into the winter months. As the climate continues to produce increasingly warmer spring and summer, amplified seasonal waves of mass transport may become ever more present in years of future observations. Increased frequency of amplified seasonal mass transport may ultimately strengthen the Greenland's dynamic ice mass loss, a component of the balance that will have important ramifications for sea level rise. This animation shows a solitary wave passing through Rink Glacier, Greenland, in 2012, recorded by the motion of a GPS station (circle with arrow). Darker blue colors within the flow indicate mass loss, red colors show mass gain. The star marks the center of the wave. Credit: NASA/JPL-Caltech
Complex dynamical behaviors of compact solitary waves in the perturbed mKdV equation
International Nuclear Information System (INIS)
Yin Jiu-Li; Xing Qian-Qian; Tian Li-Xin
2014-01-01
In this paper, we give a detailed discussion about the dynamical behaviors of compact solitary waves subjected to the periodic perturbation. By using the phase portrait theory, we find one of the nonsmooth solitary waves of the mKdV equation, namely, a compact solitary wave, to be a weak solution, which can be proved. It is shown that the compact solitary wave easily turns chaotic from the Melnikov theory. We focus on the sufficient conditions by keeping the system stable through selecting a suitable controller. Furthermore, we discuss the chaotic threshold for a perturbed system. Numerical simulations including chaotic thresholds, bifurcation diagrams, the maximum Lyapunov exponents, and phase portraits demonstrate that there exists a special frequency which has a great influence on our system; with the increase of the controller strength, chaos disappears in the perturbed system. But if the controller strength is sufficiently large, the solitary wave vibrates violently. (general)
Nonlinear localized dust acoustic waves in a charge varying dusty plasma with nonthermal ions
International Nuclear Information System (INIS)
Tribeche, Mouloud; Amour, Rabia
2007-01-01
A numerical investigation is presented to show the existence, formation, and possible realization of large-amplitude dust acoustic (DA) solitary waves in a charge varying dusty plasma with nonthermal ions. These nonlinear localized structures are self-consistent solutions of the collisionless Vlasov equation with a population of fast particles. The spatial patterns of the variable charge DA solitary wave are significantly modified by the nonthermal effects. The results complement and provide new insights into previously published results on this problem
Berloff, Natalia G.; Roberts, Paul H.
2004-01-01
The stability of the axisymmetric solitary waves of the Gross-Pitaevskii (GP) equation is investigated. The Implicitly Restarted Arnoldi Method for banded matrices with shift-invert was used to solve the linearised spectral stability problem. The rarefaction solitary waves on the upper branch of the Jones-Roberts dispersion curve are shown to be unstable to axisymmetric infinitesimal perturbations, whereas the solitary waves on the lower branch and all two-dimensional solitary waves are linea...
Nonlinear Waves in Complex Systems
DEFF Research Database (Denmark)
2007-01-01
The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations, it is the ......The study of nonlinear waves has exploded due to the combination of analysis and computations, since the discovery of the famous recurrence phenomenon on a chain of nonlinearly coupled oscillators by Fermi-Pasta-Ulam fifty years ago. More than the discovery of new integrable equations...
Abundant general solitary wave solutions to the family of KdV type equations
Directory of Open Access Journals (Sweden)
Md. Azmol Huda
2017-03-01
Full Text Available This work explores the construction of more general exact traveling wave solutions of some nonlinear evolution equations (NLEEs through the application of the (G′/G, 1/G-expansion method. This method is allied to the widely used (G′/G-method initiated by Wang et al. and can be considered as an extension of the (G′/G-expansion method. For effectiveness, the method is applied to the family of KdV type equations. Abundant general form solitary wave solutions as well as periodic solutions are successfully obtained through this method. Moreover, in the obtained wider set of solutions, if we set special values of the parameters, some previously known solutions are revived. The approach of this method is simple and elegantly standard. Having been computerized it is also powerful, reliable and effective.
The Ion Acoustic Solitary Waves and Double Layers in the Solar Wind Plasma
Directory of Open Access Journals (Sweden)
C. R. Choi
2006-09-01
Full Text Available Ion acoustic solitary wave in a plasma consisting of electrons and ions with an external magnetic field is reinvestigated using the Sagdeev's potential method. Although the Sagdeev potential has a singularity for n<1, where n is the ion number density, we obtain new solitary wave solutions by expanding the Sagdeev potential up to δ n^4 near n=1. They are compressiv (rarefactive waves and shock type solitary waves. These waves can exist all together as a superposed wave which may be used to explain what would be observed in the solar wind plasma. We compared our theoretical results with the data of the Freja satellite in the study of Wu et al.(1996. Also it is shown that these solitary waves propagate with a subsonic speed.
Wave transmission in nonlinear lattices
International Nuclear Information System (INIS)
Hennig, D.; Tsironis, G.P.
1999-01-01
The interplay of nonlinearity with lattice discreteness leads to phenomena and propagation properties quite distinct from those appearing in continuous nonlinear systems. For a large variety of condensed matter and optics applications the continuous wave approximation is not appropriate. In the present review we discuss wave transmission properties in one dimensional nonlinear lattices. Our paradigmatic equations are discrete nonlinear Schroedinger equations and their study is done through a dynamical systems approach. We focus on stationary wave properties and utilize well known results from the theory of dynamical systems to investigate various aspects of wave transmission and wave localization. We analyze in detail the more general dynamical system corresponding to the equation that interpolates between the non-integrable discrete nonlinear Schroedinger equation and the integrable Albowitz-Ladik equation. We utilize this analysis in a nonlinear Kronig-Penney model and investigate transmission and band modification properties. We discuss the modifications that are effected through an electric field and the nonlinear Wannier-Stark localization effects that are induced. Several applications are described, such as polarons in one dimensional lattices, semiconductor superlattices and one dimensional nonlinear photonic band gap systems. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
Solitary wave and periodic wave solutions for Burgers, Fisher ...
Indian Academy of Sciences (India)
It is shown that the (′/)-expansion method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear partial differential equations. ... Mehrdad Lakestani1. Department of Applied Mathematics, Faculty of Mathematics Science, University of Tabriz, Tabriz, Iran ...
Nonlinear hyperbolic waves in multidimensions
Prasad, Phoolan
2001-01-01
The propagation of curved, nonlinear wavefronts and shock fronts are very complex phenomena. Since the 1993 publication of his work Propagation of a Curved Shock and Nonlinear Ray Theory, author Phoolan Prasad and his research group have made significant advances in the underlying theory of these phenomena. This volume presents their results and provides a self-contained account and gradual development of mathematical methods for studying successive positions of these fronts.Nonlinear Hyperbolic Waves in Multidimensions includes all introductory material on nonlinear hyperbolic waves and the theory of shock waves. The author derives the ray theory for a nonlinear wavefront, discusses kink phenomena, and develops a new theory for plane and curved shock propagation. He also derives a full set of conservation laws for a front propagating in two space dimensions, and uses these laws to obtain successive positions of a front with kinks. The treatment includes examples of the theory applied to converging wavefronts...
From bell-shaped solitary wave to W/M-shaped solitary wave
Indian Academy of Sciences (India)
The bifurcation theory of dynamical systems is applied to an integrable non- linear wave equation. ... pointed out in [4], 'a lack of proper mathematical tools makes this goal at the present time .... c2 − aφ2. Setting ψ2 = c2−aφ2, we have y2 = 1 a.
On nonlinear periodic drift waves
International Nuclear Information System (INIS)
Kauschke, U.; Schlueter, H.
1990-09-01
Nonlinear periodic drift waves are investigated on the basis of a simple perturbation scheme for both the amplitude and inverse frequency. The coefficients for the generation of the forced harmonics are derived, a nonlinear dispersion relation is suggested and a criterion for the onset of the modulational instability is obtained. The results are compared with the ones obtained with the help of a standard KBM-treatment. Moreover cnoidal drift waves are suggested and compared to an experimental observation. (orig.)
Weak nonlinear matter waves in a trapped two-component Bose-Einstein condensates
International Nuclear Information System (INIS)
Yong Wenmei; Xue Jukui
2008-01-01
The dynamics of the weak nonlinear matter solitary waves in two-component Bose-Einstein condensates (BEC) with cigar-shaped external potential are investigated analytically by a perturbation method. In the small amplitude limit, the two-components can be decoupled and the dynamics of solitary waves are governed by a variable-coefficient Korteweg-de Vries (KdV) equation. The reduction to the KdV equation may be useful to understand the dynamics of nonlinear matter waves in two-component BEC. The analytical expressions for the evolution of soliton, emitted radiation profiles and soliton oscillation frequency are also obtained
A Solitary Wave-Based Sensor to Monitor the Setting of Fresh Concrete
Directory of Open Access Journals (Sweden)
Piervincenzo Rizzo
2014-07-01
Full Text Available We present a proof-of-principle study about the use of a sensor for the nondestructive monitoring of strength development in hydrating concrete. The nondestructive evaluation technique is based on the propagation of highly nonlinear solitary waves (HNSWs, which are non-dispersive mechanical waves that can form and travel in highly nonlinear systems, such as one-dimensional particle chains. A built-in transducer is adopted to excite and detect the HNSWs. The waves are partially reflected at the transducer/concrete interface and partially transmitted into the concrete. The time-of-flight and the amplitude of the waves reflected at the interface are measured and analyzed with respect to the hydration time, and correlated to the initial and final set times established by the penetration test (ASTM C 403. The results show that certain features of the HNSWs change as the concrete curing progresses indicating that it has the potential of being an efficient, cost-effective tool for monitoring strengths/stiffness development.
International Nuclear Information System (INIS)
Bandyopadhyay, Anup; Das, K.P.
2002-01-01
The evolution equations describing both kinetic Alfven wave and ion-acoustic wave in a nonthermal magnetized plasma with warm ions including weak nonlinearity and weak dispersion with the effect of Landau damping have been derived. These equations reduce to two coupled equations constituting the KdV-ZK (Korteweg-de Vries-Zakharov-Kuznetsov) equation for both kinetic Alfven wave and ion-acoustic wave, including an extra term accounting for the effect of Landau damping. When the coefficient of the nonlinear term of the evolution equation for ion-acoustic wave vanishes, the nonlinear behavior of ion-acoustic wave, including the effect of Landau damping, is described by two coupled equations constituting the modified KdV-ZK (MKdV-ZK) equation, including an extra term accounting for the effect of Landau damping. It is found that there is no effect of Landau damping on the solitary structures of the kinetic Alfven wave. Both the macroscopic evolution equations for the ion-acoustic wave admits solitary wave solutions, the former having a sech 2 profile and the latter having a sech profile. In either case, it is found that the amplitude of the ion-acoustic solitary wave decreases slowly with time
Solitary impulse wave run-up and overland flow
International Nuclear Information System (INIS)
Fuchs, H.
2013-04-01
Impulse waves are generated by landslides, rockfalls or avalanches impacting a reservoir or natural lake. These long waves generated by the impulse transferred to the water body in combination with the usually short propagation distance within a lake lead to a large damage potential due to wave run-up or dam overtopping. Damages are then caused by (1) direct wave load on structures, (2) driftwood and float impact and (3) their deposits after water retreat. Major historic events occurred at Lituya Bay, Alaska, in 1958, or at the Vaiont Reservoir, Italy, in 1963. Recent events were observed at Lake Chehalis, Canada, or Lake Lucerne, Switzerland, both in 2007, or at the Lower Grindelwald proglacial lake, Switzerland, in 2009. Whereas previous VAW research aimed at the generation phase of landslide-generated impulse waves with a special focus on the wave characteristics, the current research concentrates on the opposite wave-shore interaction. A particular focus is given to the transition point from the shore slope to the horizontal plane where the orbital wave motion is transformed into a shore-parallel flow. As most literature relates only to plain wave run-up on a linearly-inclined plane and the few studies focussing on wave-induced overland flow are case studies considering only a specific bathymetry, currently no general conclusions on wave-induced overland flow can be drawn. The present study therefore intends to fill in this gap by physical modeling. Testing involved a new test-setup including a piston-type wave maker to generate solitary waves, and a smooth impermeable PVC shore of height w = 0.25 m with a connected horizontal overland flow portion. By varying the shore slope tanβ = 1/1.5, 1/2.5 and 1/5.0, the still water depth h = 0.16 - 0.24 m, and the relative wave height H/h = 0.1 -0.7, a wide range of basic parameters was covered. Overland flow depths and front velocities were measured along the shore using Ultrasonic Distance Sensors. Further, flow
Solitary impulse wave run-up and overland flow
Energy Technology Data Exchange (ETDEWEB)
Fuchs, H.
2013-04-15
Impulse waves are generated by landslides, rockfalls or avalanches impacting a reservoir or natural lake. These long waves generated by the impulse transferred to the water body in combination with the usually short propagation distance within a lake lead to a large damage potential due to wave run-up or dam overtopping. Damages are then caused by (1) direct wave load on structures, (2) driftwood and float impact and (3) their deposits after water retreat. Major historic events occurred at Lituya Bay, Alaska, in 1958, or at the Vaiont Reservoir, Italy, in 1963. Recent events were observed at Lake Chehalis, Canada, or Lake Lucerne, Switzerland, both in 2007, or at the Lower Grindelwald proglacial lake, Switzerland, in 2009. Whereas previous VAW research aimed at the generation phase of landslide-generated impulse waves with a special focus on the wave characteristics, the current research concentrates on the opposite wave-shore interaction. A particular focus is given to the transition point from the shore slope to the horizontal plane where the orbital wave motion is transformed into a shore-parallel flow. As most literature relates only to plain wave run-up on a linearly-inclined plane and the few studies focussing on wave-induced overland flow are case studies considering only a specific bathymetry, currently no general conclusions on wave-induced overland flow can be drawn. The present study therefore intends to fill in this gap by physical modeling. Testing involved a new test-setup including a piston-type wave maker to generate solitary waves, and a smooth impermeable PVC shore of height w = 0.25 m with a connected horizontal overland flow portion. By varying the shore slope tanβ = 1/1.5, 1/2.5 and 1/5.0, the still water depth h = 0.16 - 0.24 m, and the relative wave height H/h = 0.1 -0.7, a wide range of basic parameters was covered. Overland flow depths and front velocities were measured along the shore using Ultrasonic Distance Sensors. Further, flow
Nonlinear effects in water waves
International Nuclear Information System (INIS)
Janssen, P.A.E.M.
1989-05-01
This set of lecture notes on nonlinear effects in water waves was written on the occasion of the first ICTP course on Ocean Waves and Tides held from 26 September until 28 October 1988 in Trieste, Italy. It presents a summary and unification of my knowledge on nonlinear effects of gravity waves on an incompressible fluid without vorticity. The starting point of the theory is the Hamiltonian for water waves. The evolution equations of both weakly nonlinear, shallow water and deep water gravity waves are derived by suitable approximation of the energy of the waves, resulting in the Korteweg-de Vries equation and the Zakharov equation, respectively. Next, interesting properties of the KdV equation (solitons) and the Zakharov equation (instability of a finite amplitude wave train) are discussed in some detail. Finally, the evolution of a homogeneous, random wave field due to resonant four wave processes is considered and the importance of this process for ocean wave prediction is pointed out. 38 refs, 21 figs
Batool, Fiza; Akram, Ghazala
2018-05-01
An improved (G'/G)-expansion method is proposed for extracting more general solitary wave solutions of the nonlinear fractional Cahn-Allen equation. The temporal fractional derivative is taken in the sense of Jumarie's fractional derivative. The results of this article are generalized and extended version of previously reported solutions.
Bridges, Thomas J.; Donaldson, Neil M.
2007-07-01
A geometric view of criticality for two-layer flows is presented. Uniform flows are classified by diagrams in the momentum-massflux space for fixed Bernoulli energy, and cuspoidal curves on these diagrams correspond to critical uniform flows. Restriction of these surfaces to critical flow leads to new subsurfaces in energy-massflux space. While the connection between criticality and the generation of solitary waves is well known, we find that the nonlinear properties of these bifurcating solitary waves are also determined by the properties of the criticality surfaces. To be specific, the case of two layers with a rigid lid is considered, and application of the theory to other multilayer flows is sketched.
Existence domain of electrostatic solitary waves in the lunar wake
Rubia, R.; Singh, S. V.; Lakhina, G. S.
2018-03-01
Electrostatic solitary waves (ESWs) and double layers are explored in a four-component plasma consisting of hot protons, hot heavier ions (He++), electron beam, and suprathermal electrons having κ-distribution using the Sagdeev pseudopotential method. Three modes exist: slow and fast ion-acoustic modes and electron-acoustic mode. The occurrence of ESWs and their existence domain as a function of various plasma parameters, such as the number densities of ions and electron beam, the spectral index, κ, the electron beam velocity, the temperatures of ions, and electron beam, are analyzed. It is observed that both the slow and fast ion-acoustic modes support both positive and negative potential solitons as well as their coexistence. Further, they support a "forbidden gap," the region in which the soliton ceases to propagate. In addition, slow ion-acoustic solitons support the existence of both positive and negative potential double layers. The electron-acoustic mode is only found to support negative potential solitons for parameters relevant to the lunar wake plasma. Fast Fourier transform of a soliton electric field produces a broadband frequency spectrum. It is suggested that all three soliton types taken together can provide a good explanation for the observed electrostatic waves in the lunar wake.
2015-05-07
associated with the lattice background; the nonlinearity is derived from the inclusion of cubic nonlinearity. Often the background potential is periodic...dispersion branch we can find discrete evolution equations for the envelope associated with the lattice NLS equation (1) by looking for solutions of...spatial operator in the above NLS equation can be elliptic, hyperbolic or parabolic . We remark that further reduction is possible by going into a moving
Ion acoustic waves in pair-ion plasma: Linear and nonlinear analyses
International Nuclear Information System (INIS)
Saeed, R.; Mushtaq, A.
2009-01-01
Linear and nonlinear properties of low frequency ion acoustic wave (IAW) in pair-ion plasma in the presence of electrons are investigated. The dispersion relation and Kadomtsev-Petviashvili equation for linear/nonlinear IAW are derived from sets of hydrodynamic equations where the ion pairs are inertial while electrons are Boltzmannian. The dispersion curves for various concentrations of electrons are discussed and compared with experimental results. The predicted linear IAW propagates at the same frequencies as those of the experimentally observed IAW if n e0 ∼10 4 cm -3 . It is found that nonlinear profile of the ion acoustic solitary waves is significantly affected by the percentage ratio of electron number density and temperature. It is also determined that rarefactive solitary waves can propagate in this system. It is hoped that the results presented in this study would be helpful in understanding the salient features of the finite amplitude localized ion acoustic solitary pulses in a laboratory fullerene plasma.
Seadawy, Aly R.
2017-12-01
In this study, we presented the problem formulations of models for internal solitary waves in a stratified shear flow with a free surface. The nonlinear higher order of extended KdV equations for the free surface displacement is generated. We derived the coefficients of the nonlinear higher-order extended KdV equation in terms of integrals of the modal function for the linear long-wave theory. The wave amplitude potential and the fluid pressure of the extended KdV equation in the form of solitary-wave solutions are deduced. We discussed and analyzed the stability of the obtained solutions and the movement role of the waves by making graphs of the exact solutions.
Jia, T.; Liang, J. J.; Li, X.-M.; Sha, J.
2018-01-01
The refraction and reconnection of internal solitary waves (ISWs) around the Dongsha Atoll (DSA) in the northern South China Sea (SCS) are investigated based on spaceborne synthetic aperture radar (SAR) observations and numerical simulations. In general, a long ISW front propagating from the deep basin of the northern SCS splits into northern and southern branches when it passes the DSA. In this study, the statistics of Envisat Advanced SAR (ASAR) images show that the northern and southern wave branches can reconnect behind the DSA, but the reconnection location varies. A previously developed nonlinear refraction model is set up to simulate the refraction and reconnection of the ISWs behind the DSA, and the model is used to evaluate the effects of ocean stratification, background currents, and incoming ISW characteristics at the DSA on the variation in reconnection locations. The results of the first realistic simulation agree with consecutive TerraSAR-X (TSX) images captured within 12 h of each other. Further sensitivity simulations show that ocean stratification, background currents, and initial wave amplitudes all affect the phase speeds of wave branches and therefore shift their reconnection locations while shapes and locations of incoming wave branches upstream of the DSA profoundly influence the subsequent propagation paths. This study clarifies the variation in reconnection locations of ISWs downstream of the DSA and reveals the important mechanisms governing the reconnection process, which can improve our understanding of the propagation of ISWs near the DSA.
Solitary Waves in Space Dusty Plasma with Dust of Opposite Polarity
International Nuclear Information System (INIS)
Elwakil, S.A.; Zahran, M.A.; El-Shewy, E.K.; Abdelwahed, H.G.
2009-01-01
The nonlinear propagation of small but finite amplitude dust-acoustic solitary waves (DAWs) in an unmagnetized, collisionless dusty plasma has been investigated. The fluid model is a generalize to the model of Mamun and Shukla to a more realistic space dusty plasma in different regions of space viz.., cometary tails, mesosphere, Jupiter s magnetosphere, etc., by considering a four component dusty plasma consists of charged dusty plasma of opposite polarity, isothermal electrons and vortex like ion distributions in the ambient plasma. A reductive perturbation method were employed to obtain a modified Korteweg-de Vries (mKdV) equation for the first-order potential and a stationary solution is obtained. The effect of the presence of positively charged dust fluid, the specific charge ratioμ, temperature of the positively charged dust fluid, the ratio of constant temperature of free hot ions and the constant temperature of trapped ions and ion temperature are also discussed.
Energy Technology Data Exchange (ETDEWEB)
El-Shamy, E.F., E-mail: emadel_shamy@hotmail.co [Theoretical Physics Group, Physics Department, Faculty of Science, Mansoura University, Damietta-Branch, New Damietta 34517, Damietta (Egypt); Moslem, W.M., E-mail: wmmosle@hotmail.co [Department of Physics, Faculty of Science-Port Said, Suez Canal University (Egypt); Shukla, P.K., E-mail: ps@tp4.rub.d [Institut fuer Theoretische Physik IV, Fakultaet fuer Physik und Astronomie, Ruhr-Universitaet Bochum, D-44780 Bochum (Germany)
2009-12-28
Head-on collision between two ion acoustic solitary waves in a Thomas-Fermi plasma containing degenerate electrons and positrons is investigated using the extended Poincare-Lighthill-Kuo (PLK) method. The results show that the phase shifts due to the collision are strongly dependent on the positron-to-electron number density ratio, the electron-to-positron Fermi temperature ratio and the ion-to-electron Fermi temperature ratio. The present study might be helpful to understand the excitation of nonlinear ion-acoustic solitary waves in a degenerate plasma such as in superdense white dwarfs.
International Nuclear Information System (INIS)
Sabry, R.
2009-01-01
A finite amplitude theory for ion-acoustic solitary waves and double layers in multicomponent plasma consisting of hot positrons, cold ions, and electrons with two-electron temperature distributions is presented. Conditions are obtained under which large amplitude stationary ion-acoustic solitary waves and double layers can exist. For the physical parameters of interest, the ion-acoustic solitary wave (double layers) profiles and the relationship between the maximum soliton (double layers) amplitude and the Mach number are found. Also, we have presented the region of existence of the large amplitude ion-acoustic waves by analyzing the structure of the pseudopotential. For the selected range of parameters, it is found that only positive solitary waves and double layers can exist. An analysis for the small amplitude limit through the Sagdeev pseudopotential analysis and the reductive perturbation theory shows the existence of positive and negative ion-acoustic solitary waves and double layers. The effects of positron concentration and temperature ratio on the characteristics of the solitary ion-acoustic waves and double layers (namely, the amplitude and width) are discussed in detail. The relevance of this investigation to space and laboratory plasmas is pointed out.
Gaussian solitary waves for the logarithmic-KdV and the logarithmic-KP equations
International Nuclear Information System (INIS)
Wazwaz, Abdul-Majid
2014-01-01
We investigate the logarithmic-KdV equation for more Gaussian solitary waves. We extend this work to derive the logarithmic-KP (Kadomtsev–Petviashvili) equation. We show that both logarithmic models are characterized by their Gaussian solitons. (paper)
Oscillating nonlinear acoustic shock waves
DEFF Research Database (Denmark)
Gaididei, Yuri; Rasmussen, Anders Rønne; Christiansen, Peter Leth
2016-01-01
We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show that at resona......We investigate oscillating shock waves in a tube using a higher order weakly nonlinear acoustic model. The model includes thermoviscous effects and is non isentropic. The oscillating shock waves are generated at one end of the tube by a sinusoidal driver. Numerical simulations show...... polynomial in the space and time variables, we find analytical approximations to the observed single shock waves in an infinitely long tube. Using perturbation theory for the driven acoustic system approximative analytical solutions for the off resonant case are determined....
Crossing of identical solitary waves in a chain of elastic beads
International Nuclear Information System (INIS)
Manciu, Marian; Sen, Surajit; Hurd, Alan J.
2001-01-01
We consider a chain of elastic beads subjected to vanishingly weak loading conditions, i.e., the beads are barely in contact. The grains repel upon contact via the Hertz-type potential, V∝δ n , n>2, where delta≥0, delta being the grain--grain overlap. Our dynamical simulations build on several earlier studies by Nesterenko, Coste, and Sen and co-workers that have shown that an impulse propagates as a solitary wave of fixed spatial extent (dependent only upon n) through a chain of Hertzian beads and demonstrate, to our knowledge for the first time, that colliding solitary waves in the chain spawn a well-defined hierarchy of multiple secondary solitary waves, which is ∼ 0.5% of the energy of the original solitary waves. Our findings have interesting parallels with earlier observations by Rosenau and colleagues [P. Rosenau and J. M. Hyman, Phys. Rev. Lett. 70, 564 (1993); P. Rosenau, ibid. 73, 1737 (1994); Phys. Lett. A 211, 265 (1996)] regarding colliding compactons. To the best of our knowledge, there is no formal theory that describes the dynamics associated with the formation of secondary solitary waves. Calculations suggest that the formation of secondary solitary waves may be a fundamental property of certain discrete systems
Effect of Dust Grains on Solitary Kinetic Alfven Wave
International Nuclear Information System (INIS)
Li Yangfang; Wu, D. J.; Morfill, G. E.
2008-01-01
Solitary kinetic Alfven wave has been studied in dusty plasmas. The effect of the dust charge-to-mass ratio is considered. We derive the Sagdeev potential for the soliton solutions based on the hydrodynamic equations. A singularity in the Sagdeev potential is found and this singularity results in a bell-shaped soliton. The soliton solutions comprise two branches. One branch is sub-Alfvenic and the soliton velocities are much smaller than the Alfven speed. The other branch is super-Alfvenic and the soliton velocities are very close to or greater than the Alfven speed. Both compressive and rarefactive solitons can exist in each branch. For the sub-Alfvenic branch, the rarefactive soliton is a bell shape curve which is much narrower than the compressive one. In the super-Alfvenic branch, however, the compressive soliton is bell-shaped and the rarefactive one is broadened. We also found that the super-Alfvenic solitons can develop to other structures. When the charge-to-mass ratio of the dust grains is sufficiently high, the width of the rarefactive soliton will increase extremely and an electron density depletion will be observed. When the velocity is much higher than the Alfven speed, the bell-shaped soliton will transit to a cusped structure.
Solitary waves observed in the auroral zone: the Cluster multi-spacecraft perspective
Directory of Open Access Journals (Sweden)
J. S. Pickett
2004-01-01
Full Text Available We report on recent measurements of solitary waves made by the Wideband Plasma Wave Receiver located on each of the four Cluster spacecraft at 4.5-6.5RE (well above the auroral acceleration region as they cross field lines that map to the auroral zones. These solitary waves are observed in the Wideband data as isolated bipolar and tripolar waveforms. Examples of the two types of pulses are provided. The time durations of the majority of both types of solitary waves observed in this region range from about 0.3 up to 5ms. Their peak-to-peak amplitudes range from about 0.05 up to 20mV/m, with a few reaching up to almost 70mV/m. There is essentially no potential change across the bipolar pulses. There appears to be a small, measurable potential change, up to 0.5V, across the tripolar pulses, which is consistent with weak or hybrid double layers. A limited cross-spacecraft correlation study was carried out in order to identify the same solitary wave on more than one spacecraft. We found no convincing correlations of the bipolar solitary waves. In the two cases of possible correlation of the tripolar pulses, we found that the solitary waves are propagating at several hundred to a few thousand km/s and that they are possibly evolving (growing, decaying as they propagate from one spacecraft to the next. Further, they have a perpendicular (to the magnetic field width of 50km or greater and a parallel width of about 2-5km. We conclude, in general, however, that the Cluster spacecraft at separations along and perpendicular to the local magnetic field direction of tens of km and greater are too large to obtain positive correlations in this region. Looking at the macroscale of the auroral zone at 4.5-6.5RE, we find that the onsets of the broadband electrostatic noise associated with the solitary waves observed in the spectrograms of the WBD data are generally consistent with propagation of the solitary waves up the field lines (away from Earth, or with
New approaches to nonlinear waves
2016-01-01
The book details a few of the novel methods developed in the last few years for studying various aspects of nonlinear wave systems. The introductory chapter provides a general overview, thematically linking the objects described in the book. Two chapters are devoted to wave systems possessing resonances with linear frequencies (Chapter 2) and with nonlinear frequencies (Chapter 3). In the next two chapters modulation instability in the KdV-type of equations is studied using rigorous mathematical methods (Chapter 4) and its possible connection to freak waves is investigated (Chapter 5). The book goes on to demonstrate how the choice of the Hamiltonian (Chapter 6) or the Lagrangian (Chapter 7) framework allows us to gain a deeper insight into the properties of a specific wave system. The final chapter discusses problems encountered when attempting to verify the theoretical predictions using numerical or laboratory experiments. All the chapters are illustrated by ample constructive examples demonstrating the app...
Viscous damping of solitary waves in the mud banks of Kerala, West coast of India
Digital Repository Service at National Institute of Oceanography (India)
Shenoi, S.S.C.; Murty, C.S.
Analysis of wave damping in mud bank region following the process of transfer of wave energy to the interior of fluid column through the boundary layer and the energy loss computations owing to viscous shear beneath the solitary wave over a smooth...
Directory of Open Access Journals (Sweden)
Weiguo Rui
2014-01-01
Full Text Available By using the integral bifurcation method together with factoring technique, we study a water wave model, a high-order nonlinear wave equation of KdV type under some newly solvable conditions. Based on our previous research works, some exact traveling wave solutions such as broken-soliton solutions, periodic wave solutions of blow-up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. In particular, a series of smooth solitary wave solutions and nonsmooth peakon solutions are obtained. In order to show the properties of these exact solutions visually, we plot the graphs of some representative traveling wave solutions.
Directory of Open Access Journals (Sweden)
H. Kojima
1999-01-01
Full Text Available We present the characteristics of the Electrostatic Solitary Waves (ESW observed by the Geotail spacecraft in the plasma sheet boundary layer based on the statistical analyses. We also discuss the results referring to a model of ESW generation due to electron beams, which is proposed by computer simulations. In this generation model, the nonlinear evolution of Langmuir waves excited by electron bump-on-tail instabilities leads to formation of isolated electrostatic potential structures corresponding to "electron hole" in the phase space. The statistical analyses of the Geotail data, which we conducted under the assumption that polarity of ESW potentials is positive, show that most of ESW propagate in the same direction of electron beams, which are observed by the plasma instrument, simultaneously. Further, we also find that the ESW potential energy is much smaller than the background electron thermal energy and that the ESW potential widths are typically shorter than 60 times of local electron Debye length when we assume that the ESW potentials travel in the same velocity of electron beams. These results are very consistent with the ESW generation model that the nonlinear evolution of electron bump-on-tail instability leads to the formation of electron holes in the phase space.
Bacterial population solitary waves can defeat rings of funnels
International Nuclear Information System (INIS)
Morris, Ryan J; Phan, Trung V; Austin, Robert H; Black, Matthew; Bos, Julia A; Lin, Ke-Chih; Kevrekidis, Ioannis G
2017-01-01
We have constructed a microfabricated circular corral for bacteria made of rings of concentric funnels which channel motile bacteria outwards via non-hydrodynamic interactions with the funnel walls. Initially bacteria do move rapidly outwards to the periphery of the corral. At the edge, nano-slits allow for the transport of nutrients into the device while keeping the bacteria from escaping. After a period of time in which the bacteria increase their cell density in this perimeter region, they are then able to defeat the physical constrains of the funnels by launching back-propagating collective waves. We present the basic data and some nonlinear modeling which can explain how bacterial population waves propagate through a physical funnel, and discuss possible biological implications. (paper)
Weakly nonlinear electromagnetic waves in an electron-ion positron plasma
International Nuclear Information System (INIS)
Rizzato, F.B.; Schneider, R.S.; Dillenburg, D.
1987-01-01
The modulation of a high-frequency electromagnetic wave which is circulary polarized and propagates in a plasma made up of electrons, ions and positrons is investigated. The coefficient of the cubic nonlinear term in the Schroedinger equation may change sign as the relative particle concentrations vary, and consequently a marginal state of modulation instability may exist. To described the system in the neighbourhood of this state an appropriate equation is derived. Particular stationary solutions of this equation are envelope solitary waves, envelope Kinks and envelope hole solitary waves. The dependence of the amplitude of the solutions on the propagation velocity and the particle concentrations is discussed. (author) [pt
On the generation of solitary waves observed by Cluster in the near-Earth magnetosheath
Directory of Open Access Journals (Sweden)
J. S. Pickett
2005-01-01
Full Text Available Through case studies involving Cluster waveform observations, solitary waves in the form of bipolar and tripolar pulses have recently been found to be quite abundant in the near-Earth dayside magnetosheath. We expand on the results of those previous studies by examining the distribution of solitary waves from the bow shock to the magnetopause using Cluster waveform data. Cluster's orbit allows for the measurement of solitary waves in the magnetosheath from about 10 RE to 19.5 RE. Our results clearly show that within the magnetosheath, solitary waves are likely to be observed at any distance from the bow shock and that this distance has no dependence on the time durations and amplitudes of the solitary waves. In addition we have found that these same two quantities show no dependence on either the ion velocity or the angle between the ion velocity and the local magnetic field direction. These results point to the conclusion that the solitary waves are probably created locally in the magnetosheath at multiple locations, and that the generation mechanism is most likely not solely related to ion dynamics, if at all. To gain insight into a possible local generation mechanism, we have examined the electron differential energy flux characteristics parallel and perpendicular to the magnetic field, as well as the local electron plasma and cyclotron frequencies and the type of bow shock that Cluster is behind, for several time intervals where solitary waves were observed in the magnetosheath. We have found that solitary waves are most likely to be observed when there are counterstreaming (~parallel and anti-parallel to the magnetic field electrons at or below about 100eV. However, there are times when these counterstreaming electrons are present when solitary waves are not. During these times the background magnetic field strength is usually very low (<10nT, implying that the amplitudes of the solitary waves, if present, would be near or below those of
Solitary Wave Solutions to a Class of Modified Green-Naghdi Systems
Duchêne, Vincent; Nilsson, Dag; Wahlén, Erik
2017-12-01
We provide the existence and asymptotic description of solitary wave solutions to a class of modified Green-Naghdi systems, modeling the propagation of long surface or internal waves. This class was recently proposed by Duchêne et al. (Stud Appl Math 137:356-415, 2016) in order to improve the frequency dispersion of the original Green-Naghdi system while maintaining the same precision. The solitary waves are constructed from the solutions of a constrained minimization problem. The main difficulties stem from the fact that the functional at stake involves low order non-local operators, intertwining multiplications and convolutions through Fourier multipliers.
Travelling Solitary Wave Solutions for Generalized Time-delayed Burgers-Fisher Equation
International Nuclear Information System (INIS)
Deng Xijun; Han Libo; Li Xi
2009-01-01
In this paper, travelling wave solutions for the generalized time-delayed Burgers-Fisher equation are studied. By using the first-integral method, which is based on the ring theory of commutative algebra, we obtain a class of travelling solitary wave solutions for the generalized time-delayed Burgers-Fisher equation. A minor error in the previous article is clarified. (general)
On the generation and evolution of internal solitary waves in the southern Red Sea
Guo, Daquan; Akylas, T. R.; Zhan, Peng; Kartadikaria, Aditya R.; Hoteit, Ibrahim
2016-01-01
Satellite observations recently revealed trains of internal solitary waves (ISWs) in the off-shelf region between 16.0 degrees N and 16.5 degrees N in the southern Red Sea. The generation mechanism of these waves is not entirely clear, though
Nonlinear waves and pattern dynamics
Pelinovsky, Efim; Mutabazi, Innocent
2018-01-01
This book addresses the fascinating phenomena associated with nonlinear waves and spatio-temporal patterns. These appear almost everywhere in nature from sand bed forms to brain patterns, and yet their understanding still presents fundamental scientific challenges. The reader will learn here, in particular, about the current state-of-the art and new results in: Nonlinear water waves: resonance, solitons, focusing, Bose-Einstein condensation, as well as and their relevance for the sea environment (sea-wind interaction, sand bed forms, fiber clustering) Pattern formation in non-equilibrium media: soap films, chimera patterns in oscillating media, viscoelastic Couette-Taylor flow, flow in the wake behind a heated cylinder, other pattern formation. The editors and authors dedicate this book to the memory of Alexander Ezersky, Professor of Fluid Mechanics at the University of Caen Normandie (France) from September 2007 to July 2016. Before 2007, he had served as a Senior Scientist at the Institute of Applied Physi...
HIMAWARI-8 Geostationary Satellite Observation of the Internal Solitary Waves in the South China Sea
Gao, Q.; Dong, D.; Yang, X.; Husi, L.; Shang, H.
2018-04-01
The new generation geostationary meteorological satellite, Himawari-8 (H-8), was launched in 2015. Its main payload, the Advanced Himawari Imager (AHI), can observe the earth with 10-minute interval and as high as 500-m spatial resolution. This makes the H-8 satellite an ideal data source for marine and atmospheric phenomena monitoring. In this study, the propagation of internal solitary waves (ISWs) in the South China Sea is investigated using AHI imagery time series for the first time. Three ISWs cases were studied at 3:30-8:00 UTC on 30 May, 2016. In all, 28 ISWs were detected and tracked between the time series image pairs. The propagation direction and phase speeds of these ISWs are calculated and analyzed. The observation results show that the properties of ISW propagation not stable and maintains nonlinear during its lifetime. The resultant ISW speeds agree well with the theoretical values estimated from the Taylor-Goldstein equation using Argo dataset. This study has demonstrated that the new generation geostationary satellite can be a useful tool to monitor and investigate the oceanic internal waves.
Simulation of nonlinear wave run-up with a high-order Boussinesq model
DEFF Research Database (Denmark)
Fuhrman, David R.; Madsen, Per A.
2008-01-01
This paper considers the numerical simulation of nonlinear wave run-up within a highly accurate Boussinesq-type model. Moving wet–dry boundary algorithms based on so-called extrapolating boundary techniques are utilized, and a new variant of this approach is proposed in two horizontal dimensions....... As validation, computed results involving the nonlinear run-up of periodic as well as transient waves on a sloping beach are considered in a single horizontal dimension, demonstrating excellent agreement with analytical solutions for both the free surface and horizontal velocity. In two horizontal dimensions...... cases involving long wave resonance in a parabolic basin, solitary wave evolution in a triangular channel, and solitary wave run-up on a circular conical island are considered. In each case the computed results compare well against available analytical solutions or experimental measurements. The ability...
Directory of Open Access Journals (Sweden)
O. D. Shishkina
2013-10-01
Full Text Available An interaction of internal solitary waves with the shelf edge in the time periods related to the presence of a pronounced seasonal pycnocline in the Red Sea and in the Alboran Sea is analysed via satellite photos and SAR images. Laboratory data on transformation of a solitary wave of depression while passing along the transverse bottom step were obtained in a tank with a two-layer stratified fluid. The certain difference between two characteristic types of hydrophysical phenomena was revealed both in the field observations and in experiments. The hydrological conditions for these two processes were named the "deep" and the "shallow" shelf respectively. The first one provides the generation of the secondary periodic short internal waves – "runaway" edge waves – due to change in the polarity of a part of a soliton approaching the shelf normally. Another one causes a periodic shear flow in the upper quasi-homogeneous water layer with the period of incident solitary wave. The strength of the revealed mechanisms depends on the thickness of the water layer between the pycnocline and the shelf bottom as well as on the amplitude of the incident solitary wave.
International Nuclear Information System (INIS)
Zheng Chunlong; Qiang Jiye; Wang Shaohua
2010-01-01
In the paper, the variable separation approach, homoclinic test technique and bilinear method are successfully extended to a (1 + 1)-dimensional Caudry-Dodd-Gibbon-Sawada-Kortera (CDGSK) system, respectively. Based on the derived exact solutions, some significant types of localized excitations such as standing waves, periodic waves, solitary waves are simultaneously derived from the (1 + 1)-dimensional Caudry-Dodd-Gibbon-Sawada-Kortera system by entrancing appropriate parameters. (general)
Nonlinear Waves in a Cigar-Shaped Bose-Einstein Condensate with Dissipation
International Nuclear Information System (INIS)
Yang Xiaoxian; Shi Yuren; Duan Wenshan
2008-01-01
We discuss the possible nonlinear waves of atomic matter waves in a cigar-shaped Bose-Einstein condensate with dissipation. The waves can be described by a KdV-type equation. The KdV-type equation has a solitary wave solution. The amplitude, speed, and width of the wave vary exponentially with time t. The dissipative term of γ plays an important role for the wave amplitude, speed, and width. Comparisons have been given between the analytical solutions and the numerical results. It is shown that both are in good agreement.
Roshid, Harun-Or; Kabir, Md Rashed; Bhowmik, Rajandra Chadra; Datta, Bimal Kumar
2014-01-01
In this paper, we have described two dreadfully important methods to solve nonlinear partial differential equations which are known as exp-function and the exp(-ϕ(ξ)) -expansion method. Recently, there are several methods to use for finding analytical solutions of the nonlinear partial differential equations. The methods are diverse and useful for solving the nonlinear evolution equations. With the help of these methods, we are investigated the exact travelling wave solutions of the Vakhnenko- Parkes equation. The obtaining soliton solutions of this equation are described many physical phenomena for weakly nonlinear surface and internal waves in a rotating ocean. Further, three-dimensional plots of the solutions such as solitons, singular solitons, bell type solitary wave i.e. non-topological solitons solutions and periodic solutions are also given to visualize the dynamics of the equation.
Acoustic solitary waves in dusty and/or multi-ion plasmas with cold, adiabatic, and hot constituents
International Nuclear Information System (INIS)
Verheest, Frank; Hellberg, Manfred A.; Kourakis, Ioannis
2008-01-01
Large nonlinear acoustic waves are discussed in a four-component plasma, made up of two superhot isothermal species, and two species with lower thermal velocities, being, respectively, adiabatic and cold. First a model is considered in which the isothermal species are electrons and ions, while the cooler species are positive and/or negative dust. Using a Sagdeev pseudopotential formalism, large dust-acoustic structures have been studied in a systematic way, to delimit the compositional parameter space in which they can be found, without restrictions on the charges and masses of the dust species and their charge signs. Solitary waves can only occur for nonlinear structure velocities smaller than the adiabatic dust thermal velocity, leading to a novel dust-acoustic-like mode based on the interplay between the two dust species. If the cold and adiabatic dust are oppositely charged, only solitary waves exist, having the polarity of the cold dust, their parameter range being limited by infinite compression of the cold dust. However, when the charges of the cold and adiabatic species have the same sign, solitary structures are limited for increasing Mach numbers successively by infinite cold dust compression, by encountering the adiabatic dust sonic point, and by the occurrence of double layers. The latter have, for smaller Mach numbers, the same polarity as the charged dust, but switch at the high Mach number end to the opposite polarity. Typical Sagdeev pseudopotentials and solitary wave profiles have been presented. Finally, the analysis has nowhere used the assumption that the dust would be much more massive than the ions and hence, one or both dust species can easily be replaced by positive and/or negative ions and the conclusions will apply to that plasma model equally well. This would cover a number of different scenarios, such as, for example, very hot electrons and ions, together with a mix of adiabatic ions and dust (of either polarity) or a very hot electron
Wave modulation in a nonlinear dispersive medium
International Nuclear Information System (INIS)
Kim, Y.C.; Khadra, L.; Powers, E.J.
1980-01-01
A model describing the simultaneous amplitude and phase modulation of a carrier wave propagating in a nonlinear dispersive medium is developed in terms of nonlinear wave-wave interactions between the sidebands and a low frequency wave. It is also shown that the asymmetric distribution of sidebands is determined by the wavenumber dependence of the coupling coefficient. Digital complex demodulation techniques are used to study modulated waves in a weakly ionized plasma and the experimental results support the analytical model
Nonlinear electromagnetic waves in a degenerate electron-positron plasma
Energy Technology Data Exchange (ETDEWEB)
El-Labany, S.K., E-mail: skellabany@hotmail.com [Department of Physics, Faculty of Science, Damietta University, New Damietta (Egypt); El-Taibany, W.F., E-mail: eltaibany@hotmail.com [Department of Physics, College of Science for Girls in Abha, King Khalid University, Abha (Saudi Arabia); El-Samahy, A.E.; Hafez, A.M.; Atteya, A., E-mail: ahmedsamahy@yahoo.com, E-mail: am.hafez@sci.alex.edu.eg, E-mail: ahmed_ateya2002@yahoo.com [Department of Physics, Faculty of Science, Alexandria University, Alexandria (Egypt)
2015-08-15
Using the reductive perturbation technique (RPT), the nonlinear propagation of magnetosonic solitary waves in an ultracold, degenerate (extremely dense) electron-positron (EP) plasma (containing ultracold, degenerate electron, and positron fluids) is investigated. The set of basic equations is reduced to a Korteweg-de Vries (KdV) equation for the lowest-order perturbed magnetic field and to a KdV type equation for the higher-order perturbed magnetic field. The solutions of these evolution equations are obtained. For better accuracy and searching on new features, the new solutions are analyzed numerically based on compact objects (white dwarf) parameters. It is found that including the higher-order corrections results as a reduction (increment) of the fast (slow) electromagnetic wave amplitude but the wave width is increased in both cases. The ranges where the RPT can describe adequately the total magnetic field including different conditions are discussed. (author)
Advection of pollutants by internal solitary waves in oceanic and atmospheric stable stratifications
Directory of Open Access Journals (Sweden)
G. W. Haarlemmer
1998-01-01
Full Text Available When a pollutant is released into the ocean or atmosphere under turbulent conditions, even a steady release is captured by large eddies resulting in localized patches of high concentration of the pollutant. If such a cloud of pollutant subsequently enters a stable stratification-either a pycnocline or thermocline-then internal waves are excited. Since large solitary internal waves have a recirculating core, pollutants may be trapped in the sclitary wave, and advected large distances through the waveguide provided by the stratification. This paper addresses the mechanisms, through computer and physical simulation, by which a localized release of a dense pollutant results in solitary waves that trap the pollutant or disperse the pollutant faster than in the absence of the waves.
Structural changes of small amplitude kinetic Alfvén solitary waves due to second-order corrections
International Nuclear Information System (INIS)
Choi, Cheong R.
2015-01-01
The structural changes of kinetic Alfvén solitary waves (KASWs) due to higher-order terms are investigated. While the first-order differential equation for KASWs provides the dispersion relation for kinetic Alfvén waves, the second-order differential equation describes the structural changes of the solitary waves due to higher-order nonlinearity. The reductive perturbation method is used to obtain the second-order and third-order partial differential equations; then, Kodama and Taniuti's technique [J. Phys. Soc. Jpn. 45, 298 (1978)] is applied in order to remove the secularities in the third-order differential equations and derive a linear second-order inhomogeneous differential equation. The solution to this new second-order equation indicates that, as the amplitude increases, the hump-type Korteweg-de Vries solution is concentrated more around the center position of the soliton and that dip-type structures form near the two edges of the soliton. This result has a close relationship with the interpretation of the complex KASW structures observed in space with satellites
Nonlinear lattice waves in heterogeneous media
International Nuclear Information System (INIS)
Laptyeva, T V; Ivanchenko, M V; Flach, S
2014-01-01
We discuss recent advances in the understanding of the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry–André localization for quasiperiodic potentials. Additional nonlinear terms in the wave equations can either preserve the phase-coherent localization of waves, or destroy it through nonintegrability and deterministic chaos. Spreading wave packets are observed to show universal features in their dynamics which are related to properties of nonlinear diffusion equations. (topical review)
Interactions of solitary waves and compression/expansion waves in core-annular flows
Maiden, Michelle; Anderson, Dalton; El, Gennady; Franco, Nevil; Hoefer, Mark
2017-11-01
The nonlinear hydrodynamics of an initial step leads to the formation of rarefaction waves and dispersive shock waves in dispersive media. Another hallmark of these media is the soliton, a localized traveling wave whose speed is amplitude dependent. Although compression/expansion waves and solitons have been well-studied individually, there has been no mathematical description of their interaction. In this talk, the interaction of solitons and shock/rarefaction waves for interfacial waves in viscous, miscible core-annular flows are modeled mathematically and explored experimentally. If the interior fluid is continuously injected, a deformable conduit forms whose interfacial dynamics are well-described by a scalar, dispersive nonlinear partial differential equation. The main focus is on interactions of solitons with dispersive shock waves and rarefaction waves. Theory predicts that a soliton can either be transmitted through or trapped by the extended hydrodynamic state. The notion of reciprocity is introduced whereby a soliton interacts with a shock wave in a reciprocal or dual fashion as with the rarefaction. Soliton reciprocity, trapping, and transmission are observed experimentally and are found to agree with the modulation theory and numerical simulations. This work was partially supported by NSF CAREER DMS-1255422 (M.A.H.) and NSF GRFP (M.D.M.).
Directory of Open Access Journals (Sweden)
Mostafa M.A. Khater
Full Text Available In this article and for the first time, we introduce and describe Khater method which is a new technique for solving nonlinear partial differential equations (PDEs.. We apply this method for each of the following models Bogoyavlenskii equation, couple Boiti-Leon-Pempinelli system and Time-fractional Cahn-Allen equation. Khater method is very powerful, Effective, felicitous and fabulous method to get exact and solitary wave solution of (PDEs.. Not only just like that but it considers too one of the general methods for solving that kind of equations since it involves some methods as we will see in our discuss of the results. We make a comparison between the results of this new method and another method. Keywords: Bogoyavlenskii equations system, Couple Boiti-Leon-Pempinelli equations system, Time-fractional Cahn-Allen equation, Khater method, Traveling wave solutions, Solitary wave solutions
Solitary waves in dusty plasmas with weak relativistic effects in electrons and ions
Energy Technology Data Exchange (ETDEWEB)
Kalita, B. C., E-mail: bckalita123@gmail.com [Gauhati University, Department of Mathematics (India); Choudhury, M., E-mail: choudhurymamani@gmail.com [Handique Girls’ College, Department of Mathematics (India)
2016-10-15
Two distinct classes of dust ion acoustic (DIA) solitary waves based on relativistic ions and electrons, dust charge Z{sub d} and ion-to-dust mass ratio Q’ = m{sub i}/m{sub d} are established in this model of multicomponent plasmas. At the increase of mass ratio Q’ due to increase of relativistic ion mass and accumulation of more negative dust charges into the plasma causing decrease of dust mass, relativistic DIA solitons of negative potentials are abundantly observed. Of course, relativistic compressive DIA solitons are also found to exist simultaneously. Further, the decrease of temperature inherent in the speed of light c causes the nonlinear term to be more active that increases the amplitude of the rarefactive solitons and dampens the growth of compressive solitons for relatively low and high mass ratio Q’, respectively. The impact of higher initial streaming of the massive ions is observed to identify the point of maximum dust density N{sub d} to yield rarefactive relativistic solitons of maximum amplitude.
Yan, Zhen-Ya; Xie, Fu-Ding; Zhang, Hong-Qing
2001-07-01
Both the direct method due to Clarkson and Kruskal and the improved direct method due to Lou are extended to reduce the high-order modified Boussinesq equation with the damping term (HMBEDT) arising in the general Fermi-Pasta-Ulam model. As a result, several types of similarity reductions are obtained. It is easy to show that the nonlinear wave equation is not integrable under the sense of Ablowitz's conjecture from the reduction results obtained. In addition, kink-shaped solitary wave solutions, which are of important physical significance, are found for HMBEDT based on the obtained reduction equation. The project supported by National Natural Science Foundation of China under Grant No. 19572022, the National Key Basic Research Development Project Program of China under Grant No. G1998030600 and Doctoral Foundation of China under Grant No. 98014119
Nonlinear Electron Waves in Strongly Magnetized Plasmas
DEFF Research Database (Denmark)
Pécseli, Hans; Juul Rasmussen, Jens
1980-01-01
Weakly nonlinear dispersive electron waves in strongly magnetized plasma are considered. A modified nonlinear Schrodinger equation is derived taking into account the effect of particles resonating with the group velocity of the waves (nonlinear Landau damping). The possibility of including the ion...... dynamics in the analysis is also demonstrated. As a particular case the authors investigate nonlinear waves in a strongly magnetized plasma filled wave-guide, where the effects of finite geometry are important. The relevance of this problem to laboratory experiments is discussed....
Periodic and solitary-wave solutions of the Degasperis-Procesi equation
International Nuclear Information System (INIS)
Vakhnenko, V.O.; Parkes, E.J.
2004-01-01
Travelling-wave solutions of the Degasperis-Procesi equation are investigated. The solutions are characterized by two parameters. For propagation in the positive x-direction, hump-like, inverted loop-like and coshoidal periodic-wave solutions are found; hump-like, inverted loop-like and peakon solitary-wave solutions are obtained as well. For propagation in the negative x-direction, there are solutions which are just the mirror image in the x-axis of the aforementioned solutions. A transformed version of the Degasperis-Procesi equation, which is a generalization of the Vakhnenko equation, is also considered. For propagation in the positive x-direction, hump-like, loop-like, inverted loop-like, bell-like and coshoidal periodic-wave solutions are found; loop-like, inverted loop-like and kink-like solitary-wave solutions are obtained as well. For propagation in the negative x-direction, well-like and inverted coshoidal periodic-wave solutions are found; well-like and inverted peakon solitary-wave solutions are obtained as well. In an appropriate limit, the previously known solutions of the Vakhnenko equation are recovered
Controlling wave propagation through nonlinear engineered granular systems
Leonard, Andrea
We study the fundamental dynamic behavior of a special class of ordered granular systems in order to design new, structured materials with unique physical properties. The dynamic properties of granular systems are dictated by the nonlinear, Hertzian, potential in compression and zero tensile strength resulting from the discrete material structure. Engineering the underlying particle arrangement of granular systems allows for unique dynamic properties, not observed in natural, disordered granular media. While extensive studies on 1D granular crystals have suggested their usefulness for a variety of engineering applications, considerably less attention has been given to higher-dimensional systems. The extension of these studies in higher dimensions could enable the discovery of richer physical phenomena not possible in 1D, such as spatial redirection and anisotropic energy trapping. We present experiments, numerical simulation (based on a discrete particle model), and in some cases theoretical predictions for several engineered granular systems, studying the effects of particle arrangement on the highly nonlinear transient wave propagation to develop means for controlling the wave propagation pathways. The first component of this thesis studies the stress wave propagation resulting from a localized impulsive loading for three different 2D particle lattice structures: square, centered square, and hexagonal granular crystals. By varying the lattice structure, we observe a wide range of properties for the propagating stress waves: quasi-1D solitary wave propagation, fully 2D wave propagation with tunable wave front shapes, and 2D pulsed wave propagation. Additionally the effects of weak disorder, inevitably present in real granular systems, are investigated. The second half of this thesis studies the solitary wave propagation through 2D and 3D ordered networks of granular chains, reducing the effective density compared to granular crystals by selectively placing wave
International Nuclear Information System (INIS)
Salahuddin, M.
1990-01-01
Using the reductive perturbation technique the Korteweg-de Vries (KdV) equation is derived for ion acoustic waves, in the presence of weak relativistic effects and warm ions, in a magnetized plasma. The influence of non ideal effects on the amplitude and width of the ion acoustic solitary waves is also discussed. The results are depicted in the figures. It is shown that the simultaneous presence of ion streaming and magnetic field stops the tendency of soliton breaking. (author)
Stable solitary waves in super dense plasmas at external magnetic fields
Ghaani, Azam; Javidan, Kurosh; Sarbishaei, Mohsen
2015-07-01
Propagation of localized waves in a Fermi-Dirac distributed super dense matter at the presence of strong external magnetic fields is studied using the reductive perturbation method. We have shown that stable solitons can be created in such non-relativistic fluids in the presence of an external magnetic field. Such solitary waves are governed by the Zakharov-Kuznetsov (ZK) equation. Properties of solitonic solutions are studied in media with different values of background mass density and strength of magnetic field.
Directory of Open Access Journals (Sweden)
Sophie S. Shamailov, Joachim Brand
2018-03-01
Full Text Available Superconducting Josephson vortices have direct analogues in ultracold-atom physics as solitary-wave excitations of two-component superfluid Bose gases with linear coupling. Here we numerically extend the zero-velocity Josephson vortex solutions of the coupled Gross-Pitaevskii equations to non-zero velocities, thus obtaining the full dispersion relation. The inertial mass of the Josephson vortex obtained from the dispersion relation depends on the strength of linear coupling and has a simple pole divergence at a critical value where it changes sign while assuming large absolute values. Additional low-velocity quasiparticles with negative inertial mass emerge at finite momentum that are reminiscent of a dark soliton in one component with counter-flow in the other. In the limit of small linear coupling we compare the Josephson vortex solutions to sine-Gordon solitons and show that the correspondence between them is asymptotic, but significant differences appear at finite values of the coupling constant. Finally, for unequal and non-zero self- and cross-component nonlinearities, we find a new solitary-wave excitation branch. In its presence, both dark solitons and Josephson vortices are dynamically stable while the new excitations are unstable.
On the Dynamics of Two-Dimensional Capillary-Gravity Solitary Waves with a Linear Shear Current
Directory of Open Access Journals (Sweden)
Dali Guo
2014-01-01
Full Text Available The numerical study of the dynamics of two-dimensional capillary-gravity solitary waves on a linear shear current is presented in this paper. The numerical method is based on the time-dependent conformal mapping. The stability of different kinds of solitary waves is considered. Both depression wave and large amplitude elevation wave are found to be stable, while small amplitude elevation wave is unstable to the small perturbation, and it finally evolves to be a depression wave with tails, which is similar to the irrotational capillary-gravity waves.
Solitary waves, steepening and initial collapse in the Maxwell-Lorentz system
DEFF Research Database (Denmark)
Sørensen, Mads Peter; Brio, Moysey; Webb, Garry
2002-01-01
We present a numerical study of Maxwell's equations in nonlinear dispersive optical media describing propagation of pulses in one Cartesian space dimension. Dispersion and nonlinearity are accounted for by a linear Lorentz model and an instantaneous Kerr nonlinearity, respectively. The dispersion......–Rosales weakly dispersive system. The weak dispersion in general cannot prevent the wave breaking with instantaneous or delayed nonlinearities....
Nonlinear wave propagation in discrete and continuous systems
Rothos, V. M.
2016-09-01
In this review we try to capture some of the recent excitement induced by a large volume of theoretical and computational studies addressing nonlinear Schrödinger models (discrete and continuous) and the localized structures that they support. We focus on some prototypical structures, namely the breather solutions and solitary waves. In particular, we investigate the bifurcation of travelling wave solution in Discrete NLS system applying dynamical systems methods. Next, we examine the combined effects of cubic and quintic terms of the long range type in the dynamics of a double well potential. The relevant bifurcations, the stability of the branches and their dynamical implications are examined both in the reduced (ODE) and in the full (PDE) setting. We also offer an outlook on interesting possibilities for future work on this theme.
Nonlinear evolution of astrophysical Alfven waves
Spangler, S. R.
1984-01-01
Nonlinear Alfven waves were studied using the derivative nonlinear Schrodinger equation as a model. The evolution of initial conditions, such as envelope solitons, amplitude-modulated waves, and band-limited noise was investigated. The last two furnish models for naturally occurring Alfven waves in an astrophysical plasma. A collapse instability in which a wave packet becomes more intense and of smaller spatial extent was analyzed. It is argued that this instability leads to enhanced plasma heating. In studies in which the waves are amplified by an electron beam, the instability tends to modestly inhibit wave growth.
Nonlinear waves in plasma with negative ion
International Nuclear Information System (INIS)
Saito, Maki; Watanabe, Shinsuke; Tanaca, Hiroshi.
1984-01-01
The propagation of nonlinear ion wave is investigated theoretically in a plasma with electron, positive ion and negative ion. The ion wave of long wavelength is described by a modified K-dV equation instead of a K-dV equation when the nonlinear coefficient of the K-dV equation vanishes at the critical density of negative ion. In the vicinity of the critical density, the ion wave is described by a coupled K-dV and modified K-dV equation. The transition from a compressional soliton to a rarefactive soliton and vice versa are examined by the coupled equation as a function of the negative ion density. The ion wave of short wavelength is described by a nonlinear Schroedinger equation. In the plasma with a negative ion, the nonlinear coefficient of the nonlinear Schroedinger equation changes the sign and the ion wave becomes modulationally unstable. (author)
An efficient algorithm for computation of solitary wave solutions to ...
Indian Academy of Sciences (India)
KAMRAN AYUB
2017-09-08
Sep 8, 2017 ... solutions has attracted lots of attention by scientists in the field of nonlinear science ... The procedure of this technique is quite simple, explicit, and can easily be extended ... divided into different sections. In the next section, we.
Nonlinear coupled Alfven and gravitational waves
International Nuclear Information System (INIS)
Kaellberg, Andreas; Brodin, Gert; Bradley, Michael
2004-01-01
In this paper we consider nonlinear interaction between gravitational and electromagnetic waves in a strongly magnetized plasma. More specifically, we investigate the propagation of gravitational waves with the direction of propagation perpendicular to a background magnetic field and the coupling to compressional Alfven waves. The gravitational waves are considered in the high-frequency limit and the plasma is modeled by a multifluid description. We make a self-consistent, weakly nonlinear analysis of the Einstein-Maxwell system and derive a wave equation for the coupled gravitational and electromagnetic wave modes. A WKB-approximation is then applied and as a result we obtain the nonlinear Schroedinger equation for the slowly varying wave amplitudes. The analysis is extended to 3D wave pulses, and we discuss the applications to radiation generated from pulsar binary mergers. It turns out that the electromagnetic radiation from a binary merger should experience a focusing effect, that in principle could be detected
Quantum corrections to nonlinear ion acoustic wave with Landau damping
Energy Technology Data Exchange (ETDEWEB)
Mukherjee, Abhik; Janaki, M. S. [Saha Institute of Nuclear Physics, Calcutta (India); Bose, Anirban [Serampore College, West Bengal (India)
2014-07-15
Quantum corrections to nonlinear ion acoustic wave with Landau damping have been computed using Wigner equation approach. The dynamical equation governing the time development of nonlinear ion acoustic wave with semiclassical quantum corrections is shown to have the form of higher KdV equation which has higher order nonlinear terms coming from quantum corrections, with the usual classical and quantum corrected Landau damping integral terms. The conservation of total number of ions is shown from the evolution equation. The decay rate of KdV solitary wave amplitude due to the presence of Landau damping terms has been calculated assuming the Landau damping parameter α{sub 1}=√(m{sub e}/m{sub i}) to be of the same order of the quantum parameter Q=ℏ{sup 2}/(24m{sup 2}c{sub s}{sup 2}L{sup 2}). The amplitude is shown to decay very slowly with time as determined by the quantum factor Q.
Zou, Li; Tian, Shou-Fu; Feng, Lian-Li
2017-12-01
In this paper, we consider the (2+1)-dimensional breaking soliton equation, which describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis. By virtue of the truncated Painlevé expansion method, we obtain the nonlocal symmetry, Bäcklund transformation and Schwarzian form of the equation. Furthermore, by using the consistent Riccati expansion (CRE), we prove that the breaking soliton equation is solvable. Based on the consistent tan-function expansion, we explicitly derive the interaction solutions between solitary waves and cnoidal periodic waves.
Directory of Open Access Journals (Sweden)
C. Cattell
2003-01-01
Full Text Available Solitary waves with large electric fields (up to 100's of mV/m have been observed throughout the magnetosphere and in the bow shock. We discuss observations by Polar at high altitudes ( ~ 4-8 RE , during crossings of the plasma sheet boundary and cusp, and new measurements by Polar at the equatorial magnetopause and by Cluster near the bow shock, in the cusp and at the plasma sheet boundary. We describe the results of a statistical study of electron solitary waves observed by Polar at high altitudes. The mean solitary wave duration was ~ 2 ms. The waves have velocities from ~ 1000 km/s to > 2500 km/s. Observed scale sizes (parallel to the magnetic field are on the order of 1-10lD, with eF/kTe from ~ 0.01 to O(1. The average speed of solitary waves at the plasma sheet boundary is faster than the average speed observed in the cusp and at cusp injections. The amplitude increases with both velocity and scale size. These observations are all consistent with the identification of the solitary waves as electron hole modes. We also report the discovery of solitary waves at the magnetopause, observed in Polar data obtained at the subsolar equatorial magnetopause. Both positive and negative potential structures have been observed with amplitudes up to ~ 25 mV/m. The velocities range from 150 km/s to >2500 km/s, with scale sizes the order of a kilometer (comparable to the Debye length. Initial observations of solitary waves by the four Cluster satellites are utilized to discuss the scale sizes and time variability of the regions where the solitary waves occur. Preliminary results from the four Cluster satellites have given a glimpse of the spatial and temporal variability of the occurrence of solitary waves and their association with other wave modes. In all the events studied, significant differences were observed in the waveforms observed simultaneously at the four locations separated by ~ 1000 km. When solitary waves were seen at one satellite, they
Nonlinear wave collapse and strong turbulence
International Nuclear Information System (INIS)
Robinson, P.A.
1997-01-01
The theory and applications of wave self-focusing, collapse, and strongly nonlinear wave turbulence are reviewed. In the last decade, the theory of these phenomena and experimental realizations have progressed rapidly. Various nonlinear wave systems are discussed, but the simplest case of collapse and strong turbulence of Langmuir waves in an unmagnetized plasma is primarily used in explaining the theory and illustrating the main ideas. First, an overview of the basic physics of linear waves and nonlinear wave-wave interactions is given from an introductory perspective. Wave-wave processes are then considered in more detail. Next, an introductory overview of the physics of wave collapse and strong turbulence is provided, followed by a more detailed theoretical treatment. Later sections cover numerical simulations of Langmuir collapse and strong turbulence and experimental applications to space, ionospheric, and laboratory plasmas, including laser-plasma and beam-plasma interactions. Generalizations to self-focusing, collapse, and strong turbulence of waves in other systems are also discussed, including nonlinear optics, solid-state systems, magnetized auroral and astrophysical plasmas, and deep-water waves. The review ends with a summary of the main ideas of wave collapse and strong-turbulence theory, a collection of open questions in the field, and a brief discussion of possible future research directions. copyright 1997 The American Physical Society
Xu, Jiexin; Chen, Zhiwu; Xie, Jieshuo; Cai, Shuqun
2016-03-01
In this paper, the generation and evolution of seaward propagating internal solitary waves (ISWs) detected by satellite image in the northwestern South China Sea (SCS) are investigated by a fully nonlinear, non-hydrostatic, three-dimensional Massachusetts Institute of Technology general circulation model (MITgcm). The three-dimensional (3D) modeled ISWs agree favorably with those by satellite image, indicating that the observed seaward propagating ISWs may be generated by the interaction of barotropic tidal flow with the arc-like continental slope south of Hainan Island. Though the tidal current is basically in east-west direction, different types of internal waves are generated by tidal currents flowing over the slopes with different shaped shorelines. Over the slope where the shoreline is straight, only weak internal tides are generated; over the slope where the shoreline is seaward concave, large-amplitude internal bores are generated, and since the concave isobaths of the arc-like continental slope tend to focus the baroclinic tidal energy which is conveyed to the internal bores, the internal bores can efficiently disintegrate into a train of rank-ordered ISWs during their propagation away from the slope; while over the slope where the shoreline is seaward convex, no distinct internal tides are generated. It is also implied that the internal waves over the slope are generated due to mixed lee wave mechanism. Furthermore, the effects of 3D model, continental slope curvature, stratification, rotation and tidal forcing on the generation of ISWs are discussed, respectively. It is shown that, the amplitude and phase speed of ISWs derived from a two-dimensional (2D) model are smaller than those from the 3D one, and the 3D model has an advantage over 2D one in simulating the ISWs generated by the interaction between tidal currents and 3D curved continental slope; the reduced continental slope curvature hinders the extension of ISW crestline; both weaker stratification
On the stability of solitary waves for classical scalar fields
International Nuclear Information System (INIS)
Blanchard, P.; Stubbe, J.; Vazquez, L.
1986-01-01
We study the stability for the bound states of lowest action of certain nonlinear Klein-Gordon and Schroedinger equations by applying the Shatah-Strauss formalism. We extend the range of application of this formalism by using a recent existence theorem for minimum action solutions to a large class of equations including logarithmic Klein-Gordon equation and logarithmic Schroedinger equation and scalar fields with fractional non-linearities. Furthermore we discuss the relation between different stability criteria considered in the literature. (orig.)
Self-focusing of nonlinear waves in a relativistic plasma with positive and negative ions
International Nuclear Information System (INIS)
Mukherjee, Joydeep; Chowdhury, A.R.
1994-01-01
The phenomenon of self-focusing of nonlinear waves was analysed in a relativistic plasma consisting of both positive and negative ions, which are assumed to be hot. The effect of the inertia of the relativistic electron is also considered by treating it dynamically. A modified form of reductive perturbation is used to deduce a nonlinear Schroedinger equation describing the purely spatial variation of the nonlinear wave. Self-focusing of the wave can be ascertained by analysing the transversal stability of the solitary wave. It is shown that the zones of stability of the wave may become wider due to the mutual influence of various factors present in the plasma, thus favouring the process of self-focusing. 10 refs., 2 figs
Linear superposition solutions to nonlinear wave equations
International Nuclear Information System (INIS)
Liu Yu
2012-01-01
The solutions to a linear wave equation can satisfy the principle of superposition, i.e., the linear superposition of two or more known solutions is still a solution of the linear wave equation. We show in this article that many nonlinear wave equations possess exact traveling wave solutions involving hyperbolic, triangle, and exponential functions, and the suitable linear combinations of these known solutions can also constitute linear superposition solutions to some nonlinear wave equations with special structural characteristics. The linear superposition solutions to the generalized KdV equation K(2,2,1), the Oliver water wave equation, and the k(n, n) equation are given. The structure characteristic of the nonlinear wave equations having linear superposition solutions is analyzed, and the reason why the solutions with the forms of hyperbolic, triangle, and exponential functions can form the linear superposition solutions is also discussed
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Uday Narayan, E-mail: unghosh1@rediffmail.com; Chatterjee, Prasanta; Roychoudhury, Rajkumar [Department of Mathematics, Siksha Bhavana, Visva Bharati, Santiniketan 731235 (India)
2015-07-15
Recently Gun Li et al. discussed “Effects of damping solitary wave in a viscosity bounded plasma” [Phys. Plasmas 21, 022118 (2014)]. The paper contains some serious errors which have been pointed out in this Comment.
International Nuclear Information System (INIS)
Berloff, Natalia G.
2005-01-01
Axisymmetric disturbances that preserve their form as they move along the vortex lines in uniform Bose-Einstein condensates are obtained numerically by the solution of the Gross-Pitaevskii equation. A continuous family of such solitary waves is shown in the momentum (p)-substitution energy (E-circumflex) plane with p→0.09ρκ 3 /c 2 , E-circumflex→0.091ρκ 3 /c as U→c, where ρ is the density, c is the speed of sound, κ is the quantum of circulation, and U is the solitary wave velocity. It is shown that collapse of a bubble captured by a vortex line leads to the generation of such solitary waves in condensates. The various stages of collapse are elucidated. In particular, it is shown that during collapse the vortex core becomes significantly compressed, and after collapse two solitary wave trains moving in opposite directions are formed on the vortex line
Solitary Rossby waves in the lower tropical troposphere | Lenouo ...
African Journals Online (AJOL)
Weakly nonlinear approximation is used to study the theoretical comportment of large-scale disturbances around the inter-tropical mid-tropospheric jet. We show here that the Korteweg de Vries (KdV) theory is appropriated to describe the structure of the streamlines around the African easterly jet (AEJ) region.
Nonlinear theory of ion-acoustic waves in an ideal plasma with degenerate electrons
International Nuclear Information System (INIS)
Dubinov, A. E.; Dubinova, A. A.
2007-01-01
A nonlinear theory is constructed that describes steady-state ion-acoustic waves in an ideal plasma in which the electron component is a degenerate Fermi gas and the ion component is a classical gas. The parameter ranges in which such a plasma can exist are determined, and dispersion relations for ion-acoustic waves are obtained that make it possible to find the linear ion-acoustic velocity. Analytic gas-dynamic models of ion sound are developed for a plasma with the ion component as a cold, an isothermal, or an adiabatic gas, and moreover, the solutions to the equations of all the models are brought to a quadrature form. Profiles of a subsonic periodic and a supersonic solitary wave are calculated, and the upper critical Mach numbers of a solitary wave are determined. For a plasma with cold ions, the critical Mach number is expressed by an explicit exact formula
Interaction of two solitary waves in quantum electron-positron-ion plasma
International Nuclear Information System (INIS)
Xu Yanxia; Lin Maimai; Shi Yuren; Duan Wenshan; Liu Zongming; Chen Jianmin
2011-01-01
The collision between two ion-acoustic solitary waves with arbitrary colliding angle θ in an unmagnetized, ultracold quantum three-component e-p-i plasma has been investigated. By using the extended Poincare-Lighthill-Kuo (PLK) perturbation method, we obtain the KdV equations and the analytical phase shifts after the collision of two solitary waves in this three-component plasma. The effects of the quantum parameter H, the ratio of Fermi positron temperature to Fermi electron temperature σ, the ratio of Fermi positron number density to Fermi electron number density μ, and the ratio of Fermi ion temperature to Fermi electron temperature ρ on the phase shifts are studied. It is found that these parameters can significantly influence the phase shifts of the solitons.
Nonlinear dynamics of resistive electrostatic drift waves
DEFF Research Database (Denmark)
Korsholm, Søren Bang; Michelsen, Poul; Pécseli, H.L.
1999-01-01
The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which is pertur......The evolution of weakly nonlinear electrostatic drift waves in an externally imposed strong homogeneous magnetic field is investigated numerically in three spatial dimensions. The analysis is based on a set of coupled, nonlinear equations, which are solved for an initial condition which...... polarity, i.e. a pair of electrostatic convective cells....
The propagation of nonlinear rayleigh waves in layered elastic half-space
International Nuclear Information System (INIS)
Ahmetolan, S.
2004-01-01
In this work, the propagation of small but finite amplitude generalized Rayleigh waves in an elastic half-space covered by a different elastic layer of uniform and finite thickness is considered. The constituent materials are assumed to be homogeneous, isotropic, compressible hyperelastic. Excluding the harmonic resonance phenomena, it is shown that the nonlinear self modulation of generalized Rayleigh waves is governed asymptotically by a nonlinear Schrodinger (NLS) equation. The stability of the solutions and the existence of solitary wave-type solutions a NLS are strongly depend on the sign of the product of the coefficients of the nonlinear and dipersion terms of the equation.Therefore the analysis continues with the examination of dependence of these coefficients on the nonlinear material parameters. Three different models have been considered which are nonlinear layer-nonlinear half space, linear layer-nonlinear half space and nonlinear layer-linear half space. The behavior of the coefficients of the NLS equation was also analyzed the limit as h(thickness of the layer) goes to zero and k(the wave number) is constant. Then conclusions are drawn about the effect of nonlinear material parameters on the wave modulation. In the numerical investigations both hypothetical and real material models are used
Nonlinear ion-acoustic cnoidal waves in a dense relativistic degenerate magnetoplasma.
El-Shamy, E F
2015-03-01
The complex pattern and propagation characteristics of nonlinear periodic ion-acoustic waves, namely, ion-acoustic cnoidal waves, in a dense relativistic degenerate magnetoplasma consisting of relativistic degenerate electrons and nondegenerate cold ions are investigated. By means of the reductive perturbation method and appropriate boundary conditions for nonlinear periodic waves, a nonlinear modified Korteweg-de Vries (KdV) equation is derived and its cnoidal wave is analyzed. The various solutions of nonlinear ion-acoustic cnoidal and solitary waves are presented numerically with the Sagdeev potential approach. The analytical solution and numerical simulation of nonlinear ion-acoustic cnoidal waves of the nonlinear modified KdV equation are studied. Clearly, it is found that the features (amplitude and width) of nonlinear ion-acoustic cnoidal waves are proportional to plasma number density, ion cyclotron frequency, and direction cosines. The numerical results are applied to high density astrophysical situations, such as in superdense white dwarfs. This research will be helpful in understanding the properties of compact astrophysical objects containing cold ions with relativistic degenerate electrons.
Nonlinear plasma waves excited near resonance
International Nuclear Information System (INIS)
Cohen, B.I.; Kaufman, A.N.
1977-01-01
The nonlinear resonant response of a uniform plasma to an external plane-wave field is formulated in terms of the mismatch Δ/sub n l/ between the driving frequency and the time-dependent, complex, nonlinear normal mode frequency at the driving wavenumber. This formalism is applied to computer simulations of this process, yielding a deduced nonlinear frequency shift. The time dependence of the nonlinear phenomena, at frequency Δ/sub n l/ and at the bounce frequency of the resonant particles, is analyzed. The interdependence of the nonlinear features is described by means of energy and momentum relations
Nonlinear interactions of counter-travelling waves
International Nuclear Information System (INIS)
Matsuuchi, Kazuo
1980-01-01
Nonlinear interactions between two waves travelling in opposite directions are investigated. When a nonlinear Klein-Gordon equation is adopted as a model equation, it is shown that such a wave system is governed by a simple set of equations for their complex amplitudes. Steady progressive waves governed by this set are investigated for various cases classified according to the signs of the coefficients. It is then found that one wave travelling in one direction appears from a certain point and the other travelling in the opposite direction has a constant amplitude from that point. This phenomenon may be regarded as a sort of reflection in spite of no rigid boundary. (author)
Nonlinear Electron Acoustic Waves in Dissipative Plasma with Superthermal Electrons
El-Hanbaly, A. M.; El-Shewy, E. K.; Kassem, A. I.; Darweesh, H. F.
2016-01-01
The nonlinear properties of small amplitude electron-acoustic ( EA) solitary and shock waves in a homogeneous system of unmagnetized collisionless plasma consisted of a cold electron fluid and superthermal hot electrons obeying superthermal distribution, and stationary ions have been investigated. A reductive perturbation method was employed to obtain the Kadomstev-Petviashvili-Burgers (KP-Brugers) equation. Some solutions of physical interest are obtained. These solutions are related to soliton, monotonic and oscillatory shock waves and their behaviour are shown graphically. The formation of these solutions depends crucially on the value of the Burgers term and the plasma parameters as well. By using the tangent hyperbolic (tanh) method, another interesting type of solution which is a combination between shock and soliton waves is obtained. The topology of phase portrait and potential diagram of the KP-Brugers equation is investigated.The advantage of using this method is that one can predict different classes of the travelling wave solutions according to different phase orbits. The obtained results may be helpful in better understanding of waves propagation in various space plasma environments as well as in inertial confinement fusion laboratory plasmas.
Energy Technology Data Exchange (ETDEWEB)
Mitsotakis, Dimitrios, E-mail: dmitsot@gmail.com [Victoria University of Wellington, School of Mathematics, Statistics and Operations Research, PO Box 600, Wellington 6140 (New Zealand); Dutykh, Denys, E-mail: Denys.Dutykh@univ-savoie.fr [LAMA, UMR 5127 CNRS, Université Savoie Mont Blanc, Campus Scientifique, F-73376 Le Bourget-du-Lac Cedex (France); Assylbekuly, Aydar, E-mail: asylbekuly@mail.ru [Khoja Akhmet Yassawi International Kazakh–Turkish University, Faculty of Natural Science, Department of Mathematics, 161200 Turkestan (Kazakhstan); Zhakebayev, Dauren, E-mail: daurjaz@mail.ru [Al-Farabi Kazakh National University, Faculty of Mechanics and Mathematics, Department of Mathematical and Computer Modelling, 050000 Almaty (Kazakhstan)
2017-05-25
In this Letter we consider long capillary–gravity waves described by a fully nonlinear weakly dispersive model. First, using the phase space analysis methods we describe all possible types of localized travelling waves. Then, we especially focus on the critical regime, where the surface tension is exactly balanced by the gravity force. We show that our long wave model with a critical Bond number admits stable travelling wave solutions with a singular crest. These solutions are usually referred to in the literature as peakons or peaked solitary waves. They satisfy the usual speed-amplitude relation, which coincides with Scott–Russel's empirical formula for solitary waves, while their decay rate is the same regardless their amplitude. Moreover, they can be of depression or elevation type independent of their speed. The dynamics of these solutions are studied as well. - Highlights: • A model for long capillary–gravity weakly dispersive and fully nonlinear water waves is derived. • Shallow capillary–gravity waves are classified using phase plane analysis. • Peaked travelling waves are found in the critical regime. • The dynamics of peakons in Serre–Green–Naghdi equations is studied numerically.
Solitary wave solutions of selective nonlinear diffusion-reaction ...
Indian Academy of Sciences (India)
An auto-Bäcklund transformation derived in the homogeneous balance method is employed to obtain several new exact solutions of certain kinds of nonlin- ear diffusion-reaction (D-R) equations. These equations arise in a variety of problems in physical, chemical, biological, social and ecological sciences. Keywords.
Nonlinear Electrostatic Wave Equations for Magnetized Plasmas
DEFF Research Database (Denmark)
Dysthe, K.B.; Mjølhus, E.; Pécseli, Hans
1984-01-01
The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed.......The lowest order kinetic effects are included in the equations for nonlinear electrostatic electron waves in a magnetized plasma. The modifications of the authors' previous analysis based on a fluid model are discussed....
Solitons and Weakly Nonlinear Waves in Plasmas
DEFF Research Database (Denmark)
Pécseli, Hans
1985-01-01
Theoretical descriptions of solitons and weakly nonlinear waves propagating in plasma media are reviewed, with particular attention to the Korteweg-de Vries (KDV) equation and the Nonlinear Schrödinger equation (NLS). The modifications of these basic equations due to the effects of resonant...
Parshenkova, I G; Dutov, V V; Rumjancev, A A; Mamedov, E A
2015-01-01
The article presents results of extracorporeal shock wave lithotripsy (ESWL) in 62 patients with urolithiasis of a solitary kidney. In 50 (80.6%) patients calculi were located in the kidney and in 12 (19.4%) patients in the ureter. Effectiveness of ESWL at 3 month follow-up was 85.5%, which is somewhat lower than in patients with two healthy kidneys due to the choice of sparing low-energy modes of lithotripsy. The effectiveness of ESWL depended on the size of the original calculi (ppre-drainage of the kidney before a session of ESWL in patients with large and multiple calculi. There was no correlation between the occurrence of complications during treatment and the clinical form of a solitary kidney (p>0.05). In patients with stones larger than 1 cm and a moderate baseline abnormalities of the upper urinary tract urodynamics ESWL was less effective (pcalculus (p=0.504). Extracorporeal shock wave lithotripsy is a highly effective and safe treatment of stones of a solitary kidney. Rational choice of indications and contraindications for the use of ESWL in a specific clinical situation is of great importance.
Measurement and modelling of bed shear induced by solitary waves
Digital Repository Service at National Institute of Oceanography (India)
JayaKumar, S.
kleiner reibung. Z. Math. Phys., 56: 1- 37. Burbidge, D. and Cummins, P., 2007. Assessing the threat to western australia from tsunami generated by earthquakes along the sunda arc. Natural Hazards, 43(3): 319-331. Christian, J.T., Taylor, P.K., Yen, J....E. and Bernard, E.N., 2006. Tsunami science before and beyond boxing day 2004. Philosophical Transactions - A Math Physics Engineering Science, 364(1845): 2231-2265. Tadepalli, S. and Synolakis, C.E., 1994. The run-up of n-waves on sloping beaches...
Elliptical optical solitary waves in a finite nematic liquid crystal cell
Minzoni, Antonmaria A.; Sciberras, Luke W.; Smyth, Noel F.; Worthy, Annette L.
2015-05-01
The addition of orbital angular momentum has been previously shown to stabilise beams of elliptic cross-section. In this article the evolution of such elliptical beams is explored through the use of an approximate methodology based on modulation theory. An approximate method is used as the equations that govern the optical system have no known exact solitary wave solution. This study brings to light two distinct phases in the evolution of a beam carrying orbital angular momentum. The two phases are determined by the shedding of radiation in the form of mass loss and angular momentum loss. The first phase is dominated by the shedding of angular momentum loss through spiral waves. The second phase is dominated by diffractive radiation loss which drives the elliptical solitary wave to a steady state. In addition to modulation theory, the "chirp" variational method is also used to study this evolution. Due to the significant role radiation loss plays in the evolution of an elliptical solitary wave, an attempt is made to couple radiation loss to the chirp variational method. This attempt furthers understanding as to why radiation loss cannot be coupled to the chirp method. The basic reason for this is that there is no consistent manner to match the chirp trial function to the generated radiating waves which is uniformly valid in time. Finally, full numerical solutions of the governing equations are compared with solutions obtained using the various variational approximations, with the best agreement achieved with modulation theory due to its ability to include both mass and angular momentum losses to shed diffractive radiation.
Radiation from nonlinear coupling of plasma waves
International Nuclear Information System (INIS)
Fung, S.F.
1986-01-01
The author examines the generation of electromagnetic radiation by nonlinear resonant interactions of plasma waves in a cold, uniformly magnetized plasma. In particular, he considers the up-conversion of two electrostatic wave packets colliding to produce high frequency electromagnetic radiation. Efficient conversion of electrostatic to electromagnetic wave energy occurs when the pump amplitudes approach and exceed the pump depletion threshold. Results from the inverse scattering transform analysis of the three-wave interaction equations are applied. When the wave packets are initially separated, the fully nonlinear set of coupling equations, which describe the evolution of the wave packets, can be reduced to three separate eigenvalue problems; each can be considered as a scattering problem, analogous to eh Schroedinger equation. In the scattering space, the wave packet profiles act as the scattering potentials. When the wavepacket areas approach (or exceed) π/2, the wave functions are localized (bound states) and the scattering potentials are said to contain solitons. Exchange of solitons occurs during the interaction. The transfer of solitons from the pump waves to the electromagnetic wave leads to pump depletion and the production of strong radiation. The emission of radio waves is considered by the coupling of two upper-hybrid branch wave packets, and an upper-hybrid and a lower hybrid branch wave packet
Laser-based linear and nonlinear guided elastic waves at surfaces (2D) and wedges (1D).
Hess, Peter; Lomonosov, Alexey M; Mayer, Andreas P
2014-01-01
The characteristic features and applications of linear and nonlinear guided elastic waves propagating along surfaces (2D) and wedges (1D) are discussed. Laser-based excitation, detection, or contact-free analysis of these guided waves with pump-probe methods are reviewed. Determination of material parameters by broadband surface acoustic waves (SAWs) and other applications in nondestructive evaluation (NDE) are considered. The realization of nonlinear SAWs in the form of solitary waves and as shock waves, used for the determination of the fracture strength, is described. The unique properties of dispersion-free wedge waves (WWs) propagating along homogeneous wedges and of dispersive wedge waves observed in the presence of wedge modifications such as tip truncation or coatings are outlined. Theoretical and experimental results on nonlinear wedge waves in isotropic and anisotropic solids are presented. Copyright © 2013 Elsevier B.V. All rights reserved.
Variation principle for nonlinear wave propagation
International Nuclear Information System (INIS)
Watanabe, T.; Lee, Y.C.; Nishikawa, Kyoji; Hojo, H.; Yoshida, Y.
1976-01-01
Variation principle is derived which determines stationary nonlinear propagation of electrostatic waves in the self-consistent density profile. Example is given for lower-hybrid waves and the relation to the variation principle for the Lagrangian density of electromagnetic fluids is discussed
Nonlinear Evolution of Alfvenic Wave Packets
Buti, B.; Jayanti, V.; Vinas, A. F.; Ghosh, S.; Goldstein, M. L.; Roberts, D. A.; Lakhina, G. S.; Tsurutani, B. T.
1998-01-01
Alfven waves are a ubiquitous feature of the solar wind. One approach to studying the evolution of such waves has been to study exact solutions to approximate evolution equations. Here we compare soliton solutions of the Derivative Nonlinear Schrodinger evolution equation (DNLS) to solutions of the compressible MHD equations.
Interpretation of nonlinearity in wind generated ocean surface waves
Digital Repository Service at National Institute of Oceanography (India)
Varkey, M.J.
of sinusoidal component waves; a consequent idea arising out of Fourier analysis. It is hypothesised that a sea state which is always nonlinear to various degrees is a result of interaction, both linear and nonlinear, between nonlinear component waves...
Nonlinear Waves in the Terrestrial Quasiparallel Foreshock.
Hnat, B; Kolotkov, D Y; O'Connell, D; Nakariakov, V M; Rowlands, G
2016-12-02
We provide strongly conclusive evidence that the cubic nonlinearity plays an important part in the evolution of the large amplitude magnetic structures in the terrestrial foreshock. Large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency are identified after nonharmonic slow variations are filtered out by applying the empirical mode decomposition. Numerical solutions of the derivative nonlinear Schrödinger equation, predicted analytically by the use of a pseudopotential approach, are found to be consistent with the observed wave forms. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfvén speed. We suggest that the feedback of the large amplitude fluctuations on background plasma is reflected in the evolution of the pseudopotential.
Cuevas-Maraver, Jesús; Kevrekidis, Panayotis G.; Vainchtein, Anna; Xu, Haitao
2017-09-01
In this work, we provide two complementary perspectives for the (spectral) stability of solitary traveling waves in Hamiltonian nonlinear dynamical lattices, of which the Fermi-Pasta-Ulam and the Toda lattice are prototypical examples. One is as an eigenvalue problem for a stationary solution in a cotraveling frame, while the other is as a periodic orbit modulo shifts. We connect the eigenvalues of the former with the Floquet multipliers of the latter and using this formulation derive an energy-based spectral stability criterion. It states that a sufficient (but not necessary) condition for a change in the wave stability occurs when the functional dependence of the energy (Hamiltonian) H of the model on the wave velocity c changes its monotonicity. Moreover, near the critical velocity where the change of stability occurs, we provide an explicit leading-order computation of the unstable eigenvalues, based on the second derivative of the Hamiltonian H''(c0) evaluated at the critical velocity c0. We corroborate this conclusion with a series of analytically and numerically tractable examples and discuss its parallels with a recent energy-based criterion for the stability of discrete breathers.
Analysis of the geometric parameters of a solitary waves-based harvester to enhance its power output
Rizzo, Piervincenzo; Li, Kaiyuan
2017-07-01
We present a harvester formed by a metamaterial, an isotropic medium bonded to the metamaterial, and a wafer-type transducer glued to the medium. The harvester conveys the distributed energy of a mechanical oscillator into a focal point where this energy is converted into electricity. The metamaterial is made with an array of granular chains that host the propagation of highly nonlinear solitary waves triggered by the impact of the oscillator. At the interface between the chains and the isotropic solid, part of the acoustic energy refracts into the solid where it triggers the vibration of the solid and coalesces at a point. Here, the transducer converts the focalized stress wave and the waves generated by the reverberation with the edges into electric potential. The effects of the harvester’s geometric parameters on the amount of electrical power that can be harvested are quantified numerically. The results demonstrate that the power output of the harvester increases a few orders of magnitude when the appropriate geometric parameters are selected.
Nonlinear theory of localized standing waves
Denardo, Bruce; Larraza, Andrés; Putterman, Seth; Roberts, Paul
1992-01-01
An investigation of the nonlinear dispersive equations of continuum mechanics reveals localized standing-wave solutions that are domain walls between regions of different wave number. These states can appear even when the dispersion law is a single-valued function of the wave number. In addition, we calculate solutions for kinks in cutoff and noncutoff modes, as well as cutoff breather solitons. Division of Engineering and Geophysics of the Office of Basic Energy Science of U.S. DOE for su...
Nonlinear extraordinary wave in dense plasma
Energy Technology Data Exchange (ETDEWEB)
Krasovitskiy, V. B., E-mail: krasovit@mail.ru [Russian Academy of Sciences, Keldysh Institute of Applied Mathematics (Russian Federation); Turikov, V. A. [Russian University of Peoples’ Friendship (Russian Federation)
2013-10-15
Conditions for the propagation of a slow extraordinary wave in dense magnetized plasma are found. A solution to the set of relativistic hydrodynamic equations and Maxwell’s equations under the plasma resonance conditions, when the phase velocity of the nonlinear wave is equal to the speed of light, is obtained. The deviation of the wave frequency from the resonance frequency is accompanied by nonlinear longitudinal-transverse oscillations. It is shown that, in this case, the solution to the set of self-consistent equations obtained by averaging the initial equations over the period of high-frequency oscillations has the form of an envelope soliton. The possibility of excitation of a nonlinear wave in plasma by an external electromagnetic pulse is confirmed by numerical simulations.
International Nuclear Information System (INIS)
Zhang Weiguo; Dong Chunyan; Fan Engui
2006-01-01
In this paper, we discuss conditional stability of solitary-wave solutions in the sense of Liapunov for the generalized compound KdV equation and the generalized compound KdV-Burgers equations. Linear stability of the exact solitary-wave solutions is proved for the above two types of equations when the small disturbance of travelling wave form satisfies some special conditions.
Wave propagation in a strongly nonlinear locally resonant granular crystal
Vorotnikov, K.; Starosvetsky, Y.; Theocharis, G.; Kevrekidis, P. G.
2018-02-01
In this work, we study the wave propagation in a recently proposed acoustic structure, the locally resonant granular crystal. This structure is composed of a one-dimensional granular crystal of hollow spherical particles in contact, containing linear resonators. The relevant model is presented and examined through a combination of analytical approximations (based on ODE and nonlinear map analysis) and of numerical results. The generic dynamics of the system involves a degradation of the well-known traveling pulse of the standard Hertzian chain of elastic beads. Nevertheless, the present system is richer, in that as the primary pulse decays, secondary ones emerge and eventually interfere with it creating modulated wavetrains. Remarkably, upon suitable choices of parameters, this interference "distills" a weakly nonlocal solitary wave (a "nanopteron"). This motivates the consideration of such nonlinear structures through a separate Fourier space technique, whose results suggest the existence of such entities not only with a single-side tail, but also with periodic tails on both ends. These tails are found to oscillate with the intrinsic oscillation frequency of the out-of-phase motion between the outer hollow bead and its internal linear attachment.
Nonlinear ultrasonic imaging with X wave
Du, Hongwei; Lu, Wei; Feng, Huanqing
2009-10-01
X wave has a large depth of field and may have important application in ultrasonic imaging to provide high frame rate (HFR). However, the HFR system suffers from lower spatial resolution. In this paper, a study of nonlinear imaging with X wave is presented to improve the resolution. A theoretical description of realizable nonlinear X wave is reported. The nonlinear field is simulated by solving the KZK nonlinear wave equation with a time-domain difference method. The results show that the second harmonic field of X wave has narrower mainlobe and lower sidelobes than the fundamental field. In order to evaluate the imaging effect with X wave, an imaging model involving numerical calculation of the KZK equation, Rayleigh-Sommerfeld integral, band-pass filtering and envelope detection is constructed to obtain 2D fundamental and second harmonic images of scatters in tissue-like medium. The results indicate that if X wave is used, the harmonic image has higher spatial resolution throughout the entire imaging region than the fundamental image, but higher sidelobes occur as compared to conventional focus imaging. A HFR imaging method with higher spatial resolution is thus feasible provided an apodization method is used to suppress sidelobes.
Smooth and non-smooth travelling waves in a nonlinearly dispersive Boussinesq equation
International Nuclear Information System (INIS)
Shen Jianwei; Xu Wei; Lei Youming
2005-01-01
The dynamical behavior and special exact solutions of nonlinear dispersive Boussinesq equation (B(m,n) equation), u tt -u xx -a(u n ) xx +b(u m ) xxxx =0, is studied by using bifurcation theory of dynamical system. As a result, all possible phase portraits in the parametric space for the travelling wave system, solitary wave, kink and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions are obtained. It can be shown that the existence of singular straight line in the travelling wave system is the reason why smooth waves converge to cusp waves, finally. When parameter are varied, under different parametric conditions, various sufficient conditions guarantee the existence of the above solutions are given
Topological horseshoes in travelling waves of discretized nonlinear wave equations
International Nuclear Information System (INIS)
Chen, Yi-Chiuan; Chen, Shyan-Shiou; Yuan, Juan-Ming
2014-01-01
Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes
Topological horseshoes in travelling waves of discretized nonlinear wave equations
Energy Technology Data Exchange (ETDEWEB)
Chen, Yi-Chiuan, E-mail: YCChen@math.sinica.edu.tw [Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan (China); Chen, Shyan-Shiou, E-mail: sschen@ntnu.edu.tw [Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan (China); Yuan, Juan-Ming, E-mail: jmyuan@pu.edu.tw [Department of Financial and Computational Mathematics, Providence University, Shalu, Taichung 43301, Taiwan (China)
2014-04-15
Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes.
Directory of Open Access Journals (Sweden)
Hsi-Lin Hsiao
2008-10-01
Full Text Available The purpose of this study was to investigate the impact of hydronephrosis on the treatment outcome of patients with a solitary proximal ureteral stone after extracorporeal shock wave lithotripsy (ESWL. A total of 182 consecutive patients who underwent ESWL for a solitary proximal ureteral stone of between 5 and 20 mm in size in our institution were included in this study. The degree of hydronephrosis was defined by renal ultrasonography. Patient data, stone size, shock wave numbers and shock wave energy were also recorded. Treatment outcome was evaluated 3 months after the first session of ESWL. In multivariate analysis, only the maximal stone length (odds ratio [OR], 0.15; 95% confidence interval [CI], 0.03–0.91; p = 0.04 and the degree of hydronephrosis (OR, 0.40; 95% CI, 0.16–0.98; p = 0.045 were significant predicting factors for stone-free status 3 months after ESWL. For stones ≤ 10 mm, the stone-free rate decreased from 80% in patients with mild hydronephrosis to 56.4% in those with moderate to severe hydro-nephrosis. For stones > 10 mm, the stone-free rate decreased further, from 65.2% in patients with mild hydronephrosis to 33.3% in those with moderate to severe hydronephrosis. In summary, patients with a solitary proximal ureteral stone and a stone > 10 mm, the treatment outcome after ESWL was not good if moderate to severe hydronephrosis was noted on ultrasonography. Alternative treatments, such as ureteroscopic lithotripsy, may be appropriate as initial treatment or after failure of one session of ESWL.
International Nuclear Information System (INIS)
Shang Yadong
2005-01-01
In this paper, the evolution equations with strong nonlinear term describing the resonance interaction between the long wave and the short wave are studied. Firstly, based on the qualitative theory and bifurcation theory of planar dynamical systems, all of the explicit and exact solutions of solitary waves are obtained by qualitative seeking the homoclinic and heteroclinic orbits for a class of Lienard equations. Then the singular travelling wave solutions, periodic travelling wave solutions of triangle functions type are also obtained on the basis of the relationships between the hyperbolic functions and that between the hyperbolic functions with the triangle functions. The varieties of structure of exact solutions of the generalized long-short wave equation with strong nonlinear term are illustrated. The methods presented here also suitable for obtaining exact solutions of nonlinear wave equations in multidimensions
International Nuclear Information System (INIS)
Abbasbandy, S.
2009-01-01
Solitary wave solutions to the modified form of Camassa-Holm (CH) equation are sought. In this work, the homotopy analysis method (HAM), one of the most effective method, is applied to obtain the soliton wave solutions with and without continuity of first derivatives at crest
Numerical assessment of factors affecting nonlinear internal waves in the South China Sea
Li, Qiang
2014-02-01
Nonlinear internal waves in the South China Sea exhibit diverse characteristics, which are associated with the complex conditions in Luzon Strait, such as the double ridge topography, the Earth’s rotation, variations in stratification and the background current induced by the Kuroshio. These effects are individually assessed using the MITgcm. The performance of the model is first validated through comparison with field observations. Because of in-phased ray interaction, the western ridge in Luzon Strait intensifies the semidiurnal internal tides generated from the eastern ridge, thus reinforcing the formation of nonlinear internal waves. However, the ray interaction for K1 forcing becomes anti-phased so that the K1 internal tide generation is reduced by the western ridge. Not only does the rotational dispersion suppress internal tide generation, it also inhibits nonlinear steepening and consequent internal solitary wave formation. As a joint effect, the double ridges and the rotational dispersion result in a paradoxical phenomenon: diurnal barotropic tidal forcing is dominant in Luzon Strait, but semidiurnal internal tides prevail in the deep basin of the South China Sea. The seasonal variation of the Kuroshio is consistent with the seasonal appearance of nonlinear internal waves in the South China Sea. The model results show that the westward inflow due to the Kuroshio intrusion reduces the amplitude of internal tides in the South China Sea, causing the weakening or absence of internal solitary waves. Winter stratification cannot account for the significant reduction of nonlinear internal waves, because the amplitude growth of internal tides due to increased thermocline tilting counteracts the reduced nonlinearity caused by thermocline deepening.
Malaspina, David M.; Newman, David L.; Wilson, Lynn Bruce; Goetz, Keith; Kellogg, Paul J.; Kerstin, Kris
2013-01-01
A strong spatial association between bipolar electrostatic solitary waves (ESWs) and magnetic current sheets (CSs) in the solar wind is reported here for the first time. This association requires that the plasma instabilities (e.g., Buneman, electron two stream) which generate ESWs are preferentially localized to solar wind CSs. Distributions of CS properties (including shear angle, thickness, solar wind speed, and vector magnetic field change) are examined for differences between CSs associated with ESWs and randomly chosen CSs. Possible mechanisms for producing ESW-generating instabilities at solar wind CSs are considered, including magnetic reconnection.
On the generation of solitary waves observed by Cluster in the near-Earth magnetosheath
Czech Academy of Sciences Publication Activity Database
Pickett, J. S.; Chen, L. J.; Kahler, S. W.; Santolík, Ondřej; Goldstein, M. L.; Lavraud, B.; Décréau, P. M. E.; Kessel, R.; Lucek, E.; Lakhina, G. S.; Tsurutani, B. T.; Gurnett, D. A.; Cornilleau-Wehrlin, N.; Fazakerley, A.; Rème, H.; Balogh, A.
2005-01-01
Roč. 12, - (2005), s. 181-193 ISSN 1023-5809 R&D Projects: GA MŠk(CZ) ME 650; GA ČR(CZ) GA202/03/0832; GA MŠk(CZ) 1P05ME811 Grant - others: NASA GSFC(US) NAG5-9974; NASA GSFC(US) NNG04GB98G; NSF(US) ATM 03-27450; NSF(US) 0307319; ESA PECS(XE) 98025 Institutional research plan: CEZ:AV0Z30420517 Keywords : solitary waves * Cluster * near-Earth magnetosheath Subject RIV: BL - Plasma and Gas Discharge Physics Impact factor: 1.464, year: 2005
Effect of non-Maxwellian particle trapping and dust grain charging on dust acoustic solitary waves
International Nuclear Information System (INIS)
Rubab, N.; Murtaza, G.; Mushtaq, A.
2006-01-01
The role of adiabatic trapped ions on a small but finite amplitude dust acoustic wave, including the effect of adiabatic dust charge variation, is investigated in an unmagnetized three-component dusty plasma consisting of electrons, ions and massive micron sized negatively charged dust particulates. We have assumed that electrons and ions obey (r,q) velocity distribution while the dust species is treated fluid dynamically. It is found that the dynamics of dust acoustic waves is governed by a modified r dependent Korteweg-de Vries equation. Further, the spectral indices (r,q) affect the charge fluctuation as well as the trapping of electrons and ions and consequently modify the dust acoustic solitary wave
Dust ion-acoustic solitary waves in a dusty plasma with nonextensive electrons
Bacha, Mustapha; Tribeche, Mouloud; Shukla, Padma Kant
2012-05-01
The dust-modified ion-acoustic waves of Shukla and Silin are revisited within the theoretical framework of the Tsallis statistical mechanics. Nonextensivity may originate from correlation or long-range plasma interactions. Interestingly, we find that owing to electron nonextensivity, dust ion-acoustic (DIA) solitary waves may exhibit either compression or rarefaction. Our analysis is then extended to include self-consistent dust charge fluctuation. In this connection, the correct nonextensive electron charging current is rederived. The Korteweg-de Vries equation, as well as the Korteweg-de Vries-Burgers equation, is obtained, making use of the reductive perturbation method. The DIA waves are then analyzed for parameters corresponding to space dusty plasma situations.
Nonlocal nonlinear coupling of kinetic sound waves
Directory of Open Access Journals (Sweden)
O. Lyubchyk
2014-11-01
Full Text Available We study three-wave resonant interactions among kinetic-scale oblique sound waves in the low-frequency range below the ion cyclotron frequency. The nonlinear eigenmode equation is derived in the framework of a two-fluid plasma model. Because of dispersive modifications at small wavelengths perpendicular to the background magnetic field, these waves become a decay-type mode. We found two decay channels, one into co-propagating product waves (forward decay, and another into counter-propagating product waves (reverse decay. All wavenumbers in the forward decay are similar and hence this decay is local in wavenumber space. On the contrary, the reverse decay generates waves with wavenumbers that are much larger than in the original pump waves and is therefore intrinsically nonlocal. In general, the reverse decay is significantly faster than the forward one, suggesting a nonlocal spectral transport induced by oblique sound waves. Even with low-amplitude sound waves the nonlinear interaction rate is larger than the collisionless dissipation rate. Possible applications regarding acoustic waves observed in the solar corona, solar wind, and topside ionosphere are briefly discussed.
Cnoidal waves as solutions of the nonlinear liquid drop model
International Nuclear Information System (INIS)
Ludu, Andrei; Sandulescu, Aureliu; Greiner Walter
1997-01-01
By introducing in the hydrodynamic model, i.e. in the hydrodynamic equation and the corresponding boundary conditions, the higher order terms in the deviation of the shape, we obtain in the second order the Korteweg de Vries equations (KdV). The same equation is obtained by introducing in the liquid drop model (LDM), i.e. in the kinetic, surface and Coulomb terms, the higher terms in the second order. The KdV equation has the cnoidal waves as steady-state solutions. These waves could describe the small anharmonic vibrations of spherical nuclei up to the solitary waves. The solitons could describe the preformation of clusters on the nuclear surface. We apply this nonlinear liquid drop model to the alpha formation in heavy nuclei. We find an additional minimum in the total energy of such systems, corresponding to the solitons as clusters on the nuclear surface. By introducing the shell effects we choose this minimum to be degenerated with the ground state. The spectroscopic factor is given by ratio of the square amplitudes in the two minima. (authors)
International Nuclear Information System (INIS)
Zhang, W. L.; Qiao, B.; Huang, T. W.; Shen, X. F.; You, W. Y.; Yan, X. Q.; Wu, S. Z.; Zhou, C. T.; He, X. T.
2016-01-01
Ion acceleration in near-critical plasmas driven by intense laser pulses is investigated theoretically and numerically. A theoretical model has been given for clarification of the ion acceleration dynamics in relation to different laser and target parameters. Two distinct regimes have been identified, where ions are accelerated by, respectively, the laser-induced shock wave in the weakly driven regime (comparatively low laser intensity) and the nonlinear solitary wave in the strongly driven regime (comparatively high laser intensity). Two-dimensional particle-in-cell simulations show that quasi-monoenergetic proton beams with a peak energy of 94.6 MeV and an energy spread 15.8% are obtained by intense laser pulses at intensity I_0 = 3 × 10"2"0" W/cm"2 and pulse duration τ = 0.5 ps in the strongly driven regime, which is more advantageous than that got in the weakly driven regime. In addition, 233 MeV proton beams with narrow spread can be produced by extending τ to 1.0 ps in the strongly driven regime.
Energy Technology Data Exchange (ETDEWEB)
Zhang, W. L.; Qiao, B., E-mail: bqiao@pku.edu.cn; Huang, T. W.; Shen, X. F.; You, W. Y. [Center for Applied Physics and Technology, HEDPS, and State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871 (China); Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, Shanxi 030006 (China); Yan, X. Q. [Center for Applied Physics and Technology, HEDPS, and State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871 (China); Wu, S. Z. [Institute of Applied Physics and Computational Mathematics, Beijing 100094 (China); Zhou, C. T.; He, X. T. [Center for Applied Physics and Technology, HEDPS, and State Key Laboratory of Nuclear Physics and Technology, School of Physics, Peking University, Beijing 100871 (China); Institute of Applied Physics and Computational Mathematics, Beijing 100094 (China)
2016-07-15
Ion acceleration in near-critical plasmas driven by intense laser pulses is investigated theoretically and numerically. A theoretical model has been given for clarification of the ion acceleration dynamics in relation to different laser and target parameters. Two distinct regimes have been identified, where ions are accelerated by, respectively, the laser-induced shock wave in the weakly driven regime (comparatively low laser intensity) and the nonlinear solitary wave in the strongly driven regime (comparatively high laser intensity). Two-dimensional particle-in-cell simulations show that quasi-monoenergetic proton beams with a peak energy of 94.6 MeV and an energy spread 15.8% are obtained by intense laser pulses at intensity I{sub 0} = 3 × 10{sup 20 }W/cm{sup 2} and pulse duration τ = 0.5 ps in the strongly driven regime, which is more advantageous than that got in the weakly driven regime. In addition, 233 MeV proton beams with narrow spread can be produced by extending τ to 1.0 ps in the strongly driven regime.
Pickett, J. S.; Chen, L.-J.; Santolík, O.; Grimald, S.; Lavraud, B.; Verkhoglyadova, O. P.; Tsurutani, B. T.; Lefebvre, B.; Fazakerley, A.; Lakhina, G. S.; Ghosh, S. S.; Grison, B.; Décréau, P. M. E.; Gurnett, D. A.; Torbert, R.; Cornilleau-Wehrlin, N.; Dandouras, I.; Lucek, E.
2009-06-01
Electrostatic Solitary Waves (ESWs) have been observed by several spacecraft in the current layers of Earth's magnetosphere since 1982. ESWs are manifested as isolated pulses (one wave period) in the high time resolution waveform data obtained on these spacecraft. They are thus nonlinear structures generated out of nonlinear instabilities and processes. We report the first observations of ESWs associated with the onset of a super-substorm that occurred on 24 August 2005 while the Cluster spacecraft were located in the magnetotail at around 18-19 RE and moving northward from the plasma sheet to the lobes. These ESWs were detected in the waveform data of the WBD plasma wave receiver on three of the Cluster spacecraft. The majority of the ESWs were detected about 5 min after the super-substorm onset during which time 1) the PEACE electron instrument detected significant field-aligned electron fluxes from a few 100 eV to 3.5 keV, 2) the EDI instrument detected bursts of field-aligned electron currents, 3) the FGM instrument detected substantial magnetic fluctuations and the presence of Alfvén waves, 4) the STAFF experiment detected broadband electric and magnetic waves, ion cyclotron waves and whistler mode waves, and 5) CIS detected nearly comparable densities of H+ and O+ ions and a large tailward H+ velocity. We compare the characteristics of the ESWs observed during this event to those created in the laboratory at the University of California-Los Angeles Plasma Device (LAPD) with an electron beam. We find that the time durations of both space and LAPD ESWs are only slightly larger than the respective local electron plasma periods, indicating that electron, and not ion, dynamics are responsible for generation of the ESWs. We have discussed possible mechanisms for generating the ESWs in space, including the beam and kinetic Buneman type instabilities and the acoustic instabilities. Future studies will examine these mechanisms in more detail using the space
Directory of Open Access Journals (Sweden)
J. S. Pickett
2009-06-01
Full Text Available Electrostatic Solitary Waves (ESWs have been observed by several spacecraft in the current layers of Earth's magnetosphere since 1982. ESWs are manifested as isolated pulses (one wave period in the high time resolution waveform data obtained on these spacecraft. They are thus nonlinear structures generated out of nonlinear instabilities and processes. We report the first observations of ESWs associated with the onset of a super-substorm that occurred on 24 August 2005 while the Cluster spacecraft were located in the magnetotail at around 18–19 R_{E} and moving northward from the plasma sheet to the lobes. These ESWs were detected in the waveform data of the WBD plasma wave receiver on three of the Cluster spacecraft. The majority of the ESWs were detected about 5 min after the super-substorm onset during which time 1 the PEACE electron instrument detected significant field-aligned electron fluxes from a few 100 eV to 3.5 keV, 2 the EDI instrument detected bursts of field-aligned electron currents, 3 the FGM instrument detected substantial magnetic fluctuations and the presence of Alfvén waves, 4 the STAFF experiment detected broadband electric and magnetic waves, ion cyclotron waves and whistler mode waves, and 5 CIS detected nearly comparable densities of H+ and O+ ions and a large tailward H+ velocity. We compare the characteristics of the ESWs observed during this event to those created in the laboratory at the University of California-Los Angeles Plasma Device (LAPD with an electron beam. We find that the time durations of both space and LAPD ESWs are only slightly larger than the respective local electron plasma periods, indicating that electron, and not ion, dynamics are responsible for generation of the ESWs. We have discussed possible mechanisms for generating the ESWs in space, including the beam and kinetic Buneman type instabilities and the acoustic instabilities. Future studies will examine these mechanisms in
Solitons and nonlinear waves in space plasmas
International Nuclear Information System (INIS)
Stasiewicz, K.
2005-01-01
Recent measurements made on the ESA/NASA Cluster mission to the Earth's magnetosphere have provided first detailed measurements of magnetosonic solitons in space. The solitons represent localized enhancements of the magnetic field by a factor of 2-10, or depressions down to 10% of the ambient field. The magnetic field signatures are associated with density depressions/enhancements A two-fluid model of nonlinear electron and ion inertial waves in anisotropic plasmas explains the main properties of these structures. It is shown that warm plasmas support four types of nonlinear waves, which correspond to four linear modes: Alfvenic, magnetosonic, sound, and electron inertial waves. Each of these nonlinear modes has slow and fast versions. It is shown by direct integration that the exponential growth rate of nonlinear modes is balanced by the ion and electron dispersion leading to solutions in the form of trains of solitons or cnoidal waves. By using a novel technique of phase portraits it is shown how the dispersive properties of electron and ion inertial waves change at the transition between warm and hot plasmas, and how trains of solitons ('' mirror modes '') are produced in a hot, anisotropic plasma. The applicability of the model is illustrated with data from Cluster spacecraft. (author)
New exact travelling wave solutions of nonlinear physical models
International Nuclear Information System (INIS)
Bekir, Ahmet; Cevikel, Adem C.
2009-01-01
In this work, we established abundant travelling wave solutions for some nonlinear evolution equations. This method was used to construct travelling wave solutions of nonlinear evolution equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. The ((G ' )/G )-expansion method presents a wider applicability for handling nonlinear wave equations.
Vortex shedding induced by a solitary wave propagating over a submerged vertical plate
International Nuclear Information System (INIS)
Lin Chang; Ho, T.-C.; Chang, S.-C.; Hsieh, S.-C.; Chang, K.-A.
2005-01-01
Experimental study was conducted on the vortex shedding process induced by the interaction between a solitary wave and a submerged vertical plate. Particle image velocimetry (PIV) was used for quantitative velocity measurement while a particle tracing technique was used for qualitative flow visualization. Vortices are generated at the tip of each side of the plate. The largest vortices at each side of the plate eventually grow to the size of the water depth. Although the fluid motion under the solitary wave is only translatory, vortices are shed in both the upstream and downstream directions due to the interaction of the generated vortices as well as the vortices with the plate and the bottom. The process can be divided into four phases: the formation of a separated shear layer, the generation and shedding of vortices, the formation of a vertical jet, and the impingement of the jet onto the free surface. Similarity velocity profiles were found both in the separated shear layer and in the vertical jet
Nonlinear wave equation with intrinsic wave particle dualism
International Nuclear Information System (INIS)
Klein, J.J.
1976-01-01
A nonlinear wave equation derived from the sine-Gordon equation is shown to possess a variety of solutions, the most interesting of which is a solution that describes a wave packet travelling with velocity usub(e) modulating a carrier wave travelling with velocity usub(c). The envelop and carrier wave speeds agree precisely with the group and phase velocities found by de Broglie for matter waves. No spreading is exhibited by the soliton, so that it behaves exactly like a particle in classical mechanics. Moreover, the classically computed energy E of the disturbance turns out to be exactly equal to the frequency ω of the carrier wave, so that the Planck relation is automatically satisfied without postulating a particle-wave dualism. (author)
Seismic, satellite, and site observations of internal solitary waves in the NE South China Sea
Tang, Qunshu; Wang, Caixia; Wang, Dongxiao; Pawlowicz, Rich
2014-01-01
Internal solitary waves (ISWs) in the NE South China Sea (SCS) are tidally generated at the Luzon Strait. Their propagation, evolution, and dissipation processes involve numerous issues still poorly understood. Here, a novel method of seismic oceanography capable of capturing oceanic finescale structures is used to study ISWs in the slope region of the NE SCS. Near-simultaneous observations of two ISWs were acquired using seismic and satellite imaging, and water column measurements. The vertical and horizontal length scales of the seismic observed ISWs are around 50 m and 1–2 km, respectively. Wave phase speeds calculated from seismic observations, satellite images, and water column data are consistent with each other. Observed waveforms and vertical velocities also correspond well with those estimated using KdV theory. These results suggest that the seismic method, a new option to oceanographers, can be further applied to resolve other important issues related to ISWs. PMID:24948180
Solitary Wave Solutions of the Boussinesq Equation and Its Improved Form
Directory of Open Access Journals (Sweden)
Reza Abazari
2013-01-01
Full Text Available This paper presents the general case study of previous works on generalized Boussinesq equations, (Abazari, 2011 and (Kılıcman and Abazari, 2012, that focuses on the application of G′/G-expansion method with the aid of Maple to construct more general exact solutions for the coupled Boussinesq equations. In this work, the mentioned method is applied to construct more general exact solutions of Boussinesq equation and improved Boussinesq equation, which the French scientist Joseph Valentin Boussinesq (1842–1929 described in the 1870s model equations for the propagation of long waves on the surface of water with small amplitude. Our work is motivated by the fact that the G′/G-expansion method provides not only more general forms of solutions but also periodic, solitary waves and rational solutions. The method appears to be easier and faster by means of a symbolic computation.
Seismic, satellite, and site observations of internal solitary waves in the NE South China Sea.
Tang, Qunshu; Wang, Caixia; Wang, Dongxiao; Pawlowicz, Rich
2014-06-20
Internal solitary waves (ISWs) in the NE South China Sea (SCS) are tidally generated at the Luzon Strait. Their propagation, evolution, and dissipation processes involve numerous issues still poorly understood. Here, a novel method of seismic oceanography capable of capturing oceanic finescale structures is used to study ISWs in the slope region of the NE SCS. Near-simultaneous observations of two ISWs were acquired using seismic and satellite imaging, and water column measurements. The vertical and horizontal length scales of the seismic observed ISWs are around 50 m and 1-2 km, respectively. Wave phase speeds calculated from seismic observations, satellite images, and water column data are consistent with each other. Observed waveforms and vertical velocities also correspond well with those estimated using KdV theory. These results suggest that the seismic method, a new option to oceanographers, can be further applied to resolve other important issues related to ISWs.
Jefrey, A
1964-01-01
In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation;methods for low-rank mat
Nonlinear waves: some biomedical applications
International Nuclear Information System (INIS)
Rudenko, Oleg V
2007-01-01
The field of nonlinear physics, item No. 11 on Ginzburg's list of 'the most important and interesting problems', is reviewed. An example at the intersection of applied physics, medicine, and instrument engineering is discussed to illustrate the range and scope of the field and how deep the ideas and approaches it involves are incorporated in modern natural science and engineering. Results of relevant research and development, which has attracted much recent interest and financial support, are briefly examined. (oral issue of the journal 'uspekhi fizicheskikh nauk')
Topics in nonlinear wave theory with applications
International Nuclear Information System (INIS)
Tracy, E.R.
1984-01-01
Selected topics in nonlinear wave theory are discussed, and applications to the study of modulational instabilities are presented. A historical survey is given of topics relating to solitons and modulational problems. A method is then presented for generating exact periodic and quasi-periodic solutions to several nonlinear wave equations, which have important physical applications. The method is then specialized for the purposes of studying the modulational instability of a plane wave solution of the nonlinear Schroedinger equation, an equation with general applicability in one-dimensional modulational problems. Some numerical results obtained in conjunction with the analytic study are presented. The analytic approach explains the recurrence phenomena seen in the numerical studies, and the numerical work of other authors. The method of solution (related to the inverse scattering method) is then analyzed within the context of Hamiltonian dynamics where it is shown that the method can be viewed as simply a pair of canonical transformations. The Abel Transformation, which appears here and in the work of other authors, is shown to be a special form of Liouville's transformation to action-angle variables. The construction of closed form solutions of these nonlinear wave equations, via the solution of Jacobi's inversion problem, is surveyed briefly
Four Wave Mixing using Intermodal Nonlinearities
DEFF Research Database (Denmark)
Rishøj, Lars Søgaard
The nonlinear process of four-wave mixing (FWM) enables coupling of energy between wavelengths. This is useful for both optical amplification and wavelength conversion. A crucial prerequisite for the process is phase matching. This PhD project investigates how higher order modes (HOMs) in fibers...
Spectro-spatial analysis of wave packet propagation in nonlinear acoustic metamaterials
Zhou, W. J.; Li, X. P.; Wang, Y. S.; Chen, W. Q.; Huang, G. L.
2018-01-01
The objective of this work is to analyze wave packet propagation in weakly nonlinear acoustic metamaterials and reveal the interior nonlinear wave mechanism through spectro-spatial analysis. The spectro-spatial analysis is based on full-scale transient analysis of the finite system, by which dispersion curves are generated from the transmitted waves and also verified by the perturbation method (the L-P method). We found that the spectro-spatial analysis can provide detailed information about the solitary wave in short-wavelength region which cannot be captured by the L-P method. It is also found that the optical wave modes in the nonlinear metamaterial are sensitive to the parameters of the nonlinear constitutive relation. Specifically, a significant frequency shift phenomenon is found in the middle-wavelength region of the optical wave branch, which makes this frequency region behave like a band gap for transient waves. This special frequency shift is then used to design a direction-biased waveguide device, and its efficiency is shown by numerical simulations.
Nonlinear wavenumber of an electron plasma wave
International Nuclear Information System (INIS)
Vidmar, P.J.; Malmberg, J.H.; Starke, T.P.
1976-01-01
The wavenumber of a large-amplitude electron plasma wave propagating on a collisionless plasma column is measured. The wavenumber is shifted from that of a small-amplitude wave of the same frequency. This nonlinear wavenumber shift, deltak/subr/, depends on position, frequency, and initial wave amplitude, Phi. The observed spatial oscillations of deltak/subr/ agree qualitatively with recent theories. Experimentally deltak/subr/proportionalk/subi/S (Phi) rootPhi where k/subi/ is the linear Landau damping coefficient, S (Phi) equivalentk/subi/(Phi)/k/subi/, and k/subi/(Phi) is the initial damping coefficient which depends on Phi
Li, Nianqiang; Susanto, H; Cemlyn, B R; Henning, I D; Adams, M J
2018-02-19
We study the nonlinear dynamics of solitary and optically injected two-element laser arrays with a range of waveguide structures. The analysis is performed with a detailed direct numerical simulation, where high-resolution dynamic maps are generated to identify regions of dynamic instability in the parameter space of interest. Our combined one- and two-parameter bifurcation analysis uncovers globally diverse dynamical regimes (steady-state, oscillation, and chaos) in the solitary laser arrays, which are greatly influenced by static design waveguiding structures, the amplitude-phase coupling factor of the electric field, i.e. the linewidth-enhancement factor, as well as the control parameter, e.g. the pump rate. When external optical injection is introduced to one element of the arrays, we show that the whole system can be either injection-locked simultaneously or display rich, different dynamics outside the locking region. The effect of optical injection is to significantly modify the nature and the regions of nonlinear dynamics from those found in the solitary case. We also show similarities and differences (asymmetry) between the oscillation amplitude of the two elements of the array in specific well-defined regions, which hold for all the waveguiding structures considered. Our findings pave the way to a better understanding of dynamic instability in large arrays of lasers.
Bansal, Sona; Aggarwal, Munish; Gill, Tarsem Singh
2018-04-01
Effects of electron temperature on the propagation of electron acoustic solitary waves in plasma with stationary ions, cold and superthermal hot electrons is investigated in non-planar geometry employing reductive perturbation method. Modified Korteweg-de Vries equation is derived in the small amplitude approximation limit. The analytical and numerical calculations of the KdV equation reveal that the phase velocity of the electron acoustic waves increases as one goes from planar to non planar geometry. It is shown that the electron temperature ratio changes the width and amplitude of the solitary waves and when electron temperature is not taken into account,our results completely agree with the results of Javidan & Pakzad (2012). It is found that at small values of τ , solitary wave structures behave differently in cylindrical ( {m} = 1), spherical ( {m} = 2) and planar geometry ( {m} = 0) but looks similar at large values of τ . These results may be useful to understand the solitary wave characteristics in laboratory and space environments where the plasma have multiple temperature electrons.
Nonlinear MHD Waves in a Prominence Foot
Ofman, L.; Knizhnik, K.; Kucera, T.; Schmieder, B.
2015-11-01
We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ˜ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5-11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5-14 G. For the typical prominence density the corresponding fast magnetosonic speed is ˜20 km s-1, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.
NONLINEAR MHD WAVES IN A PROMINENCE FOOT
Energy Technology Data Exchange (ETDEWEB)
Ofman, L. [Catholic University of America, Washington, DC 20064 (United States); Knizhnik, K.; Kucera, T. [NASA Goddard Space Flight Center, Code 671, Greenbelt, MD 20771 (United States); Schmieder, B. [LESIA, Observatoire de Paris, PSL Research University, CNRS, Sorbonne Universités, UPMC Univ. Paris 06, Univ. Paris-Diderot, Sorbonne Paris Cit, 5 place Jules Janssen, F-92195 Meudon (France)
2015-11-10
We study nonlinear waves in a prominence foot using a 2.5D MHD model motivated by recent high-resolution observations with Hinode/Solar Optical Telescope in Ca ii emission of a prominence on 2012 October 10 showing highly dynamic small-scale motions in the prominence material. Observations of Hα intensities and of Doppler shifts show similar propagating fluctuations. However, the optically thick nature of the emission lines inhibits a unique quantitative interpretation in terms of density. Nevertheless, we find evidence of nonlinear wave activity in the prominence foot by examining the relative magnitude of the fluctuation intensity (δI/I ∼ δn/n). The waves are evident as significant density fluctuations that vary with height and apparently travel upward from the chromosphere into the prominence material with quasi-periodic fluctuations with a typical period in the range of 5–11 minutes and wavelengths <2000 km. Recent Doppler shift observations show the transverse displacement of the propagating waves. The magnetic field was measured with the THEMIS instrument and was found to be 5–14 G. For the typical prominence density the corresponding fast magnetosonic speed is ∼20 km s{sup −1}, in qualitative agreement with the propagation speed of the detected waves. The 2.5D MHD numerical model is constrained with the typical parameters of the prominence waves seen in observations. Our numerical results reproduce the nonlinear fast magnetosonic waves and provide strong support for the presence of these waves in the prominence foot. We also explore gravitational MHD oscillations of the heavy prominence foot material supported by dipped magnetic field structure.
Symmetries of the triple degenerate DNLS equations for weakly nonlinear dispersive MHD waves
International Nuclear Information System (INIS)
Webb, G. M.; Brio, M.; Zank, G. P.
1996-01-01
A formulation of Hamiltonian and Lagrangian variational principles, Lie point symmetries and conservation laws for the triple degenerate DNLS equations describing the propagation of weakly nonlinear dispersive MHD waves along the ambient magnetic field, in β∼1 plasmas is given. The equations describe the interaction of the Alfven and magnetoacoustic modes near the triple umbilic point, where the fast magnetosonic, slow magnetosonic and Alfven speeds coincide and a g 2 =V A 2 where a g is the gas sound speed and V A is the Alfven speed. A discussion is given of the travelling wave similarity solutions of the equations, which include solitary wave and periodic traveling waves. Strongly compressible solutions indicate the necessity for the insertion of shocks in the flow, whereas weakly compressible, near Alfvenic solutions resemble similar, shock free travelling wave solutions of the DNLS equation
Nonlinear wave breaking in self-gravitating viscoelastic quantum fluid
Energy Technology Data Exchange (ETDEWEB)
Mitra, Aniruddha, E-mail: anibabun@gmail.com [Center for Plasma Studies, Department of Instrumentation Science, Jadavpur University, Kolkata, 700 032 (India); Roychoudhury, Rajkumar, E-mail: rajdaju@rediffmail.com [Advanced Centre for Nonlinear and Complex Phenomena, 1175 Survey Park, Kolkata 700075 (India); Department of Mathematics, Bethune College, Kolkata 700006 (India); Bhar, Radhaballav [Center for Plasma Studies, Department of Instrumentation Science, Jadavpur University, Kolkata, 700 032 (India); Khan, Manoranjan, E-mail: mkhan.ju@gmail.com [Center for Plasma Studies, Department of Instrumentation Science, Jadavpur University, Kolkata, 700 032 (India)
2017-02-12
The stability of a viscoelastic self-gravitating quantum fluid has been studied. Symmetry breaking instability of solitary wave has been observed through ‘viscosity modified Ostrovsky equation’ in weak gravity limit. In presence of strong gravitational field, the solitary wave breaks into shock waves. Response to a Gaussian perturbation, the system produces quasi-periodic short waves, which in terns predicts the existence of gravito-acoustic quasi-periodic short waves in lower solar corona region. Stability analysis of this dynamical system predicts gravity has the most prominent effect on the phase portraits, therefore, on the stability of the system. The non-existence of chaotic solution has also been observed at long wavelength perturbation through index value theorem. - Highlights: • In weak gravitational field, viscoelastic quantum fluid exhibits symmetry breaking instability. • Gaussian perturbation produces quasi-periodic gravito-acoustic waves into the system. • There exists no chaotic state of the system against long wavelength perturbations.
Topological soliton solutions for some nonlinear evolution equations
Directory of Open Access Journals (Sweden)
Ahmet Bekir
2014-03-01
Full Text Available In this paper, the topological soliton solutions of nonlinear evolution equations are obtained by the solitary wave ansatz method. Under some parameter conditions, exact solitary wave solutions are obtained. Note that it is always useful and desirable to construct exact solutions especially soliton-type (dark, bright, kink, anti-kink, etc. envelope for the understanding of most nonlinear physical phenomena.
Nonlinear water waves: introduction and overview
Constantin, A.
2017-12-01
For more than two centuries progress in the study of water waves proved to be interdependent with innovative and deep developments in theoretical and experimental directions of investigation. In recent years, considerable progress has been achieved towards the understanding of waves of large amplitude. Within this setting one cannot rely on linear theory as nonlinearity becomes an essential feature. Various analytic methods have been developed and adapted to come to terms with the challenges encountered in settings where approximations (such as those provided by linear or weakly nonlinear theory) are ineffective. Without relying on simpler models, progress becomes contingent upon the discovery of structural properties, the exploitation of which requires a combination of creative ideas and state-of-the-art technical tools. The successful quest for structure often reveals unexpected patterns and confers aesthetic value on some of these studies. The topics covered in this issue are both multi-disciplinary and interdisciplinary: there is a strong interplay between mathematical analysis, numerical computation and experimental/field data, interacting with each other via mutual stimulation and feedback. This theme issue reflects some of the new important developments that were discussed during the programme `Nonlinear water waves' that took place at the Isaac Newton Institute for Mathematical Sciences (Cambridge, UK) from 31st July to 25th August 2017. A cross-section of the experts in the study of water waves who participated in the programme authored the collected papers. These papers illustrate the diversity, intensity and interconnectivity of the current research activity in this area. They offer new insight, present emerging theoretical methodologies and computational approaches, and describe sophisticated experimental results. This article is part of the theme issue 'Nonlinear water waves'.
Response of internal solitary waves to tropical storm Washi in the northwestern South China Sea
Directory of Open Access Journals (Sweden)
Z. H. Xu
2011-11-01
Full Text Available Based on in-situ time series data from an array of temperature sensors and an acoustic Doppler current profiler on the continental shelf of the northwestern South China Sea, a sequence of internal solitary waves (ISWs were observed during the passage of tropical storm Washi in the summer of 2005, which provided a unique opportunity to investigate the ISW response to the tropical cyclone. The passing tropical storm is found to play an important role in affecting the stratification structure of the water column, and consequently leading to significant variability in the propagating features of the ISWs, such as the polarity reversal and amplitude variations of the waves. The response of the ISWs to Washi can be divided into two stages, direct forcing by the strong wind (during the arrival of Washi and remote forcing via the near-inertial internal waves induced by the tropical storm (after the passage of Washi. The field observations as well as a theoretical analysis suggest that the variations of the ISWs closely coincide with the changing stratification structure and shear currents in accompanied by the typhoon wind and near-inertial waves. This study presents the first observations and analysis of the ISW response to the tropical cyclone in the South China Sea.
Dust ion acoustic solitary waves in a magnetized dusty plasma with anisotropic ion pressure
International Nuclear Information System (INIS)
Choi, Cheong Rim; Ryu, Chang-Mo; Lee, D.-Y.; Lee, Nam C.; Kim, Y.-H.
2007-01-01
The influence of anisotropic ion pressure on the dust ion acoustic solitary wave (DIASW) and the double layer (DL) obliquely propagating to a magnetic field are investigated by using the Sagdeev potential. The anisotropic ion pressure is defined by applying the Chew-Goldberger-Low (CGL) theory, p-perpendicular=p-perpendicular 0 n and p-parallel=p-parallel 0 n 3 , where n is the normalized ion density. The solutions of DIASWs and DLs obliquely propagating to an external magnetic field are obtained in the small amplitude limit. It is found that the perpendicular component of anisotropic ion pressure works differently from that of the parallel component on the DIASWs in a magnetized dusty plasma, deviating from a straight extension of the isotropic pressure effect
Vladimirov, Vsevolod A.; Maçzka, Czesław; Sergyeyev, Artur; Skurativskyi, Sergiy
2014-06-01
We consider a hydrodynamic-type system of balance equations for mass and momentum closed by the dynamical equation of state taking into account the effects of spatial nonlocality. We study higher symmetry admitted by this system and establish its non-integrability for the generic values of parameters. A system of ODEs obtained from the system under study through the group theory reduction is investigated. The reduced system is shown to possess a family of the homoclinic solutions describing solitary waves of compression and rarefaction. The waves of compression are shown to be unstable. On the contrary, the waves of rarefaction are likely to be stable. Numerical simulations reveal some peculiarities of solitary waves of rarefaction, and, in particular, the recovery of their shape after the collisions.
Nonlinear wave forces on large ocean structures
Huang, Erick T.
1993-04-01
This study explores the significance of second-order wave excitations on a large pontoon and tests the feasibility of reducing a nonlinear free surface problem by perturbation expansions. A simulation model has been developed based on the perturbation expansion technique to estimate the wave forces. The model uses a versatile finite element procedure for the solution of the reduced linear boundary value problems. This procedure achieves a fair compromise between computation costs and physical details by using a combination of 2D and 3D elements. A simple hydraulic model test was conducted to observe the wave forces imposed on a rectangle box by Cnoidal waves in shallow water. The test measurements are consistent with the numerical predictions by the simulation model. This result shows favorable support to the perturbation approach for estimating the nonlinear wave forces on shallow draft vessels. However, more sophisticated model tests are required for a full justification. Both theoretical and experimental results show profound second-order forces that could substantially impact the design of ocean facilities.
Symmetry, phase modulation and nonlinear waves
Bridges, Thomas J
2017-01-01
Nonlinear waves are pervasive in nature, but are often elusive when they are modelled and analysed. This book develops a natural approach to the problem based on phase modulation. It is both an elaboration of the use of phase modulation for the study of nonlinear waves and a compendium of background results in mathematics, such as Hamiltonian systems, symplectic geometry, conservation laws, Noether theory, Lagrangian field theory and analysis, all of which combine to generate the new theory of phase modulation. While the build-up of theory can be intensive, the resulting emergent partial differential equations are relatively simple. A key outcome of the theory is that the coefficients in the emergent modulation equations are universal and easy to calculate. This book gives several examples of the implications in the theory of fluid mechanics and points to a wide range of new applications.
Nonlinear waves in waveguides with stratification
Leble, Sergei B
1991-01-01
S.B. Leble's book deals with nonlinear waves and their propagation in metallic and dielectric waveguides and media with stratification. The underlying nonlinear evolution equations (NEEs) are derived giving also their solutions for specific situations. The reader will find new elements to the traditional approach. Various dispersion and relaxation laws for different guides are considered as well as the explicit form of projection operators, NEEs, quasi-solitons and of Darboux transforms. Special points relate to: 1. the development of a universal asymptotic method of deriving NEEs for guide propagation; 2. applications to the cases of stratified liquids, gases, solids and plasmas with various nonlinearities and dispersion laws; 3. connections between the basic problem and soliton- like solutions of the corresponding NEEs; 4. discussion of details of simple solutions in higher- order nonsingular perturbation theory.
International Nuclear Information System (INIS)
Zhu Yonggui; Lu Chao
2007-01-01
In this paper, the Boussinesq-like equations with fully nonlinear dispersion, B(2n, 2n) equations: u tt + (u 2n ) xx + (u 2n ) xxxx 0 which exhibit compactons: solitons with compact support, are studied. New exact solitary solutions with compact support are found. The special case B(2, 2) is chosen to illustrate the concrete scheme of the decomposition method in B(2n, 2n) equations. General formulas for the solutions of B(2n, 2n) equations are established
Alfven wave. [Book on linear and nonlinear properties for fusion applications
Energy Technology Data Exchange (ETDEWEB)
Hasegawa, A.; Uberoi, C.
1978-11-01
Seven chapters are included. Chapters 1 and 2 introduce the Alfven wave and describe its linear properties in a homogeneous medium. Chapters 3 and 4 cover the effects of inhomogeneities on these linear properties. Particular emphasis is placed on the appearance of a continuum spectrum and the associated absorption of the Alfven wave which arise due to the inhomogeneity. The explanation of the physical origin of absorption is given using kinetic theory. Chapter 5 is devoted to the associated plasma instabilities. Nonlinear effects discussed in Chapter 6 include quasilinear diffusion, decay, a solitary wave, and a modulational instability. The principles of Alfven wave heating, a design example and present-day experimental results are described in Chapter 7.
International Nuclear Information System (INIS)
Pickett, J. S.; Christopher, I. W.; Gurnett, D. A.; Grison, B.; Grimald, S.; Santolik, O.; Decreau, P. M. E.; Lefebvre, B.; Kistler, L. M.; Chen, L.-J.; Engebretson, M. J.; Constantinescu, D.; Omura, Y.; Lakhina, G. S.; Cornilleau-Wehrlin, N.; Fazakerley, A. N.; Dandouras, I.; Lucek, E.
2011-01-01
We present the results of a study of Electrostatic Solitary Waves (ESWs) in which propagation of a series of noncyclical ESWs is observed from one Cluster spacecraft to another over distances as great as tens of km and time lags as great as a few tens of ms. This propagation study was conducted for locations near the magnetopause on the magnetosheath side. Propagation was found primarily toward the earth with speeds on the order of 1500 to 2400 km/s. The sizes of the ESWs obtained from these velocities were on the order of 1 km along the magnetic field direction and several tens of km perpendicular. These results are consistent with measurements on single spacecraft in which the ESW propagation is observed with time lags of only ∼0.1 ms. Our results thus show the stability of ESWs over time periods much greater than their own characteristic pulse durations of a few 100s of microseconds. We present also the results of a study of ESW modulation at the magnetopause on the earthward side. We found that ESWs were modulated at ∼1.3 Hz, consistent with a Pc1 wave which was observed concurrently. During this time, tens of eV electron beams are present. We propose a Buneman type instability in which the E '''' component of the Pc1 waves provides a mechanism for accelerating electrons, resulting in the generation of the ESWs modulated at the Pc1 frequency.
Pickett, J. S.; Christopher, I. W.; Grison, B.; Grimald, S.; Santolík, O.; Décréau, P. M. E.; Lefebvre, B.; Engebretson, M. J.; Kistler, L. M.; Constantinescu, D.; Chen, L.-J.; Omura, Y.; Lakhina, G. S.; Gurnett, D. A.; Cornilleau-Wehrlin, N.; Fazakerley, A. N.; Dandouras, I.; Lucek, E.
2011-01-01
We present the results of a study of Electrostatic Solitary Waves (ESWs) in which propagation of a series of noncyclical ESWs is observed from one Cluster spacecraft to another over distances as great as tens of km and time lags as great as a few tens of ms. This propagation study was conducted for locations near the magnetopause on the magnetosheath side. Propagation was found primarily toward the earth with speeds on the order of 1500 to 2400 km/s. The sizes of the ESWs obtained from these velocities were on the order of 1 km along the magnetic field direction and several tens of km perpendicular. These results are consistent with measurements on single spacecraft in which the ESW propagation is observed with time lags of only ˜0.1 ms. Our results thus show the stability of ESWs over time periods much greater than their own characteristic pulse durations of a few 100s of microseconds. We present also the results of a study of ESW modulation at the magnetopause on the earthward side. We found that ESWs were modulated at ˜1.3 Hz, consistent with a Pc1 wave which was observed concurrently. During this time, tens of eV electron beams are present. We propose a Buneman type instability in which the E″″ component of the Pc1 waves provides a mechanism for accelerating electrons, resulting in the generation of the ESWs modulated at the Pc1 frequency.
Cox, Brian N.; Landis, Chad M.
2018-02-01
We present a simple theory of a strain pulse propagating as a solitary wave through a continuous two-dimensional population of cells. A critical strain is assumed to trigger a strain transformation, while, simultaneously, cells move as automata to tend to restore a preferred cell density. We consider systems in which the strain transformation is a shape change, a burst of proliferation, or the commencement of growth (which changes the shape of the population sheet), and demonstrate isomorphism among these cases. Numerical and analytical solutions describe a strain pulse whose height does not depend on how the strain disturbance was first launched, or the rate at which the strain transformation is achieved, or the rate constant in the rule for the restorative cell motion. The strain pulse is therefore very stable, surviving the imposition of strong perturbations: it would serve well as a timing signal in development. The automatous wave formulation is simple, with few model parameters. A strong case exists for the presence of a strain pulse during amelogenesis. Quantitative analysis reveals a simple relationship between the velocity of the leading edge of the pulse in amelogenesis and the known speed of migration of ameloblast cells. This result and energy arguments support the depiction of wave motion as an automatous cell response to strain, rather than as a response to an elastic energy gradient. The theory may also contribute to understanding the determination front in somitogenesis, moving fronts of convergent-extension transformation, and mitotic wavefronts in the syncytial drosophila embryo.
International Nuclear Information System (INIS)
Ghosh, S. S.; Sekar Iyengar, A. N.
2014-01-01
It is observed that the presence of a minority component of cooler electrons in a three component plasma plays a deterministic role in the evolution of solitary waves, double layers, or the newly discovered structures called supersolitons. The inclusion of the cooler component of electrons in a single electron plasma produces sharp increase in nonlinearity in spite of a decrease in the overall energy of the system. The effect maximizes at certain critical value of the number density of the cooler component (typically 15%–20%) giving rise to a hump in the amplitude variation profile. For larger amplitudes, the hump leads to a forbidden region in the ambient cooler electron concentration which dissociates the overall existence domain of solitary wave solutions in two distinct parameter regime. It is observed that an inclusion of the cooler component of electrons as low as < 1% affects the plasma system significantly resulting in compressive double layers. The solution is further affected by the cold to hot electron temperature ratio. In an adequately hotter bulk plasma (i.e., moderately low cold to hot electron temperature ratio), the parameter domain of compressive double layers is bounded by a sharp discontinuity in the corresponding amplitude variation profile which may lead to supersolitons
Energy Technology Data Exchange (ETDEWEB)
Ghosh, S. S., E-mail: sukti@iigs.iigm.res.in [Indian Institute of Geomagnetism, New Panvel, Navi Mumbai 410218 (India); Sekar Iyengar, A. N. [Plasma Physics Division, Saha Institute of Nuclear Physics, Kolkata 700064 (India)
2014-08-15
It is observed that the presence of a minority component of cooler electrons in a three component plasma plays a deterministic role in the evolution of solitary waves, double layers, or the newly discovered structures called supersolitons. The inclusion of the cooler component of electrons in a single electron plasma produces sharp increase in nonlinearity in spite of a decrease in the overall energy of the system. The effect maximizes at certain critical value of the number density of the cooler component (typically 15%–20%) giving rise to a hump in the amplitude variation profile. For larger amplitudes, the hump leads to a forbidden region in the ambient cooler electron concentration which dissociates the overall existence domain of solitary wave solutions in two distinct parameter regime. It is observed that an inclusion of the cooler component of electrons as low as < 1% affects the plasma system significantly resulting in compressive double layers. The solution is further affected by the cold to hot electron temperature ratio. In an adequately hotter bulk plasma (i.e., moderately low cold to hot electron temperature ratio), the parameter domain of compressive double layers is bounded by a sharp discontinuity in the corresponding amplitude variation profile which may lead to supersolitons.
Non-Linear Excitation of Ion Acoustic Waves
DEFF Research Database (Denmark)
Michelsen, Poul; Hirsfield, J. L.
1974-01-01
The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation.......The excitation of ion acoustic waves by nonlinear coupling of two transverse magnetic waves generated in a microwave cavity was investigated. Measurements of the wave amplitude showed good agreement with calculations based on the Vlasov equation....
Highly Nonlinear Wave Propagation in Elastic Woodpile Periodic Structures
2016-08-03
called a nanopteron, is not only motivated theoretically and numerically, but are also visualized experimentally by means of a laser Doppler vibrometer...velocity, which clearly follow the prin- cipal solitary wave (highlighted in red color ). It should be noted that the velocities involved in the
International Nuclear Information System (INIS)
Dossmann, Yvan; Paci, Alexandre; Auclair, Francis; Lepilliez, Mathieu; Cid, Emmanuel
2014-01-01
Internal solitary waves (ISWs) are large amplitude stable waves propagating in regions of high density gradients such as the ocean pycnocline. Their dynamics has often been investigated in two-dimensional approaches, however, their three-dimensional evolution is still poorly known. Experiments have been conducted in the large stratified water tank of CNRM-GAME to study the generation of ISWs in two academic configurations inspired by oceanic regimes. First, ultrasonic probes are used to measure the interfacial displacement in the two configurations. In the primary generation case for which the two layers are of constant density, the generation of ISWs is investigated in two series of experiments with varying amplitude and forcing frequency. In the secondary generation case for which the lower layer is stratified, the generation of ISWs from the impact of an internal wave beam on the pycnocline and their subsequent dynamics is studied. The dynamics of ISWs in these two regimes accords well with analytical approaches and numerical simulations performed in analogous configurations. Then, recent developments of a stereo correlation technique are used to describe the three-dimensional structure of propagating ISWs. In the primary generation configuration, small transverse effects are observed in the course of the ISW propagation. In the secondary generation configuration, larger transverse structures are observed in the interfacial waves dynamics. The interaction between interfacial troughs and internal waves propagating in the lower stratified layer are a possible cause for the generation of these structures. The magnitude of these transverse structures is quantified with a nondimensional parameter in the two configurations. They are twice as large in the secondary generation case as in the primary generation case
Rao, Chengping; Zhang, Youlin; Wan, Decheng
2017-12-01
Fluid-Structure Interaction (FSI) caused by fluid impacting onto a flexible structure commonly occurs in naval architecture and ocean engineering. Research on the problem of wave-structure interaction is important to ensure the safety of offshore structures. This paper presents the Moving Particle Semi-implicit and Finite Element Coupled Method (MPS-FEM) to simulate FSI problems. The Moving Particle Semi-implicit (MPS) method is used to calculate the fluid domain, while the Finite Element Method (FEM) is used to address the structure domain. The scheme for the coupling of MPS and FEM is introduced first. Then, numerical validation and convergent study are performed to verify the accuracy of the solver for solitary wave generation and FSI problems. The interaction between the solitary wave and an elastic structure is investigated by using the MPS-FEM coupled method.
Initial-value problem for the Gardner equation applied to nonlinear internal waves
Rouvinskaya, Ekaterina; Kurkina, Oxana; Kurkin, Andrey; Talipova, Tatiana; Pelinovsky, Efim
2017-04-01
The Gardner equation is a fundamental mathematical model for the description of weakly nonlinear weakly dispersive internal waves, when cubic nonlinearity cannot be neglected. Within this model coefficients of quadratic and cubic nonlinearity can both be positive as well as negative, depending on background conditions of the medium, where waves propagate (sea water density stratification, shear flow profile) [Rouvinskaya et al., 2014, Kurkina et al., 2011, 2015]. For the investigation of weakly dispersive behavior in the framework of nondimensional Gardner equation with fixed (positive) sign of quadratic nonlinearity and positive or negative cubic nonlinearity {eq1} partial η/partial t+6η( {1± η} )partial η/partial x+partial ^3η/partial x^3=0, } the series of numerical experiments of initial-value problem was carried out for evolution of a bell-shaped impulse of negative polarity (opposite to the sign of quadratic nonlinear coefficient): {eq2} η(x,t=0)=-asech2 ( {x/x0 } ), for which amplitude a and width x0 was varied. Similar initial-value problem was considered in the paper [Trillo et al., 2016] for the Korteweg - de Vries equation. For the Gardner equation with different signs of cubic nonlinearity the initial-value problem for piece-wise constant initial condition was considered in detail in [Grimshaw et al., 2002, 2010]. It is widely known, for example, [Pelinovsky et al., 2007], that the Gardner equation (1) with negative cubic nonlinearity has a family of classic solitary wave solutions with only positive polarity,and with limiting amplitude equal to 1. Therefore evolution of impulses (2) of negative polarity (whose amplitudes a were varied from 0.1 to 3, and widths at the level of a/2 were equal to triple width of solitons with the same amplitude for a 1) was going on a universal scenario with the generation of nonlinear Airy wave. For the Gardner equation (1) with the positive cubic nonlinearity coefficient there exist two one-parametric families of
Parametric study of nonlinear electrostatic waves in two-dimensional quantum dusty plasmas
International Nuclear Information System (INIS)
Ali, S; Moslem, W M; Kourakis, I; Shukla, P K
2008-01-01
The nonlinear properties of two-dimensional cylindrical quantum dust-ion-acoustic (QDIA) and quantum dust-acoustic (QDA) waves are studied in a collisionless, unmagnetized and dense (quantum) dusty plasma. For this purpose, the reductive perturbation technique is employed to the quantum hydrodynamical equations and the Poisson equation, obtaining the cylindrical Kadomtsev-Petviashvili (CKP) equations. The effects of quantum diffraction, as well as quantum statistical and geometric effects on the profiles of QDIA and QDA solitary waves are examined. It is found that the amplitudes and widths of the nonplanar QDIA and QDA waves are significantly affected by the quantum electron tunneling effect. The addition of a dust component to a quantum plasma is seen to affect the propagation characteristics of localized QDIA excitations. In the case of low-frequency QDA waves, this effect is even stronger, since the actual form of the potential solitary waves, in fact, depends on the dust charge polarity (positive/negative) itself (allowing for positive/negative potential forms, respectively). The relevance of the present investigation to metallic nanostructures is highlighted
Linear and Nonlinear Electrostatic Waves in Unmagnetized Dusty Plasmas
International Nuclear Information System (INIS)
Mamun, A. A.; Shukla, P. K.
2010-01-01
A rigorous and systematic theoretical study has been made of linear and nonlinear electrostatic waves propagating in unmagnetized dusty plasmas. The basic features of linear and nonlinear electrostatic waves (particularly, dust-ion-acoustic and dust-acoustic waves) for different space and laboratory dusty plasma conditions are described. The experimental observations of such linear and nonlinear features of dust-ion-acoustic and dust-acoustic waves are briefly discussed.
Nonlinear instability and chaos in plasma wave-wave interactions
International Nuclear Information System (INIS)
Kueny, C.S.
1993-01-01
Conventional linear stability analysis may fail for fluid systems with an indefinite free energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes. Instability may then occur either via dissipation of the negative energy modes. Instability may then occur either via dissipitation of the negative energy modes, or nonlinearly via resonant wave-wave coupling, which leads to explosive growth. In the dissipationaless case, it is conjectured that intrinsic chaotic behavior may allow initially non-resonant systems to reach resonance by diffusion in phase space. This is illustrated for a simple equilibrium involving cold counter-streaming ions. The system is described in the fluid approximation by a Hamilitonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamilitonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, which occur generically for long enough wavelengths. Three-wave interactions which occur in isolated, but numerous, regions of parameter space can drive either decay instability or explosive instability. When the resonance for explosive growth is detuned, a stable region exists around the equilibrium point in phase space, while explosive growth occurs outside of a separatrix. These interactions may be described exactly if only one resonance is considered, while multiple nonlinear terms make the Hamiltonian nonintegradable. Simple Hamiltonians of two and three degrees of freedom are studied numerically using symplectic integration algorithms, including an explicit algorithm derived using Lie algebraic methods
Nonlinear magnetoacoustic wave propagation with chemical reactions
Margulies, Timothy Scott
2002-11-01
The magnetoacoustic problem with an application to sound wave propagation through electrically conducting fluids such as the ocean in the Earth's magnetic field, liquid metals, or plasmas has been addressed taking into account several simultaneous chemical reactions. Using continuum balance equations for the total mass, linear momentum, energy; as well as Maxwell's electrodynamic equations, a nonlinear beam equation has been developed to generalize the Khokhlov-Zabolotskaya-Kuznetsov (KZK) equation for a fluid with linear viscosity but nonlinear and diffraction effects. Thermodynamic parameters are used and not tailored to only an adiabatic fluid case. The chemical kinetic equations build on a relaxing media approach presented, for example, by K. Naugolnukh and L. Ostrovsky [Nonlinear Wave Processes in Acoustics (Cambridge Univ. Press, Cambridge, 1998)] for a linearized single reaction and thermodynamic pressure equation of state. Approximations for large and small relaxation times and for magnetohydrodynamic parameters [Korsunskii, Sov. Phys. Acoust. 36 (1990)] are examined. Additionally, Cattaneo's equation for heat conduction and its generalization for a memory process rather than a Fourier's law are taken into account. It was introduced for the heat flux depends on the temperature gradient at an earlier time to generate heat pulses of finite speed.
Collaborative research: Dynamics of electrostatic solitary waves and their effects on current layers
Energy Technology Data Exchange (ETDEWEB)
Chen, Li-Jen
2014-04-18
The project has accomplished the following achievements including the goals outlined in the original proposal. Generation and measurements of Debye-scale electron holes in laboratory: We have generated by beam injections electron solitary waves in the LAPD experiments. The measurements were made possible by the fabrication of the state-of-the-art microprobes at UCLA to measure Debye-scale electric fields [Chiang et al., 2011]. We obtained a result that challenged the state of knowledge about electron hole generation. We found that the electron holes were not due to two-stream instability, but generated by a current-driven instability that also generated whistler-mode waves [Lefebvre et al., 2011, 2010b]. Most of the grant supported a young research scientist Bertrand Lefebvre who led the dissemination of the laboratory experimental results. In addition to two publications, our work relevant to the laboratory experiments on electron holes has resulted in 7 invited talks [Chen, 2007, 2009; Pickett et al., 2009a; Lefebvre et al., 2010a; Pickett et al., 2010; Chen et al., 2011c, b] (including those given by the co-I Jolene Pickett) and 2 contributed talks [Lefebvre et al., 2009b, a]. Discovery of elecctron phase-space-hole structure in the reconnection electron layer: Our theoretical analyses and simulations under this project led to the discovery of an inversion electric field layer whose phase-space signature is an electron hole within the electron diffusion layer in 2D anti-parallel reconnection [Chen et al., 2011a]. We carried out particle tracing studies to understand the electron orbits that result in the phase-space hole structure. Most importantly, we showed that the current density in the electron layer is limited in collisionless reconnection with negligible guide field by the cyclotron turning of meandering electrons. Comparison of electrostatic solitary waves in current layers observed by Cluster and in LAPD: We compared the ESWs observed in a supersubstorm
Nonlinear diffuse scattering of the random-phased wave
International Nuclear Information System (INIS)
Kato, Yoshiaki; Arinaga, Shinji; Mima, Kunioki.
1983-01-01
First experimental observation of the nonlinear diffuse scattering is reported. This new effect was observed in the propagation of the random-phased wave through a nonlinear dielectric medium. This effect is ascribed to the diffusion of the wavevector of the electro-magnetic wave to the lateral direction due to the randomly distributed nonlinear increase in the refractive index. (author)
Nonlinear effects on mode-converted lower-hybrid waves
International Nuclear Information System (INIS)
Kuehl, H.H.
1976-01-01
Nonlinear ponderomotive force effects on mode-converted lower-hybrid waves are considered. The nonlinear distortion of these waves is shown to be governed by the cubic nonlinear Schroedinger equation. The threshold condition for self-focusing and filamentation is derived
Large-amplitude internal tides, solitary waves, and turbulence in the central Bay of Biscay
Xie, X. H.; Cuypers, Y.; Bouruet-Aubertot, P.; Ferron, B.; Pichon, A.; LourençO, A.; Cortes, N.
2013-06-01
and fine-scale measurements collected in the central Bay of Biscay during the MOUTON experiment are analyzed to investigate the dynamics of internal waves and associated mixing. Large-amplitude internal tides (ITs) that excite internal solitary waves (ISWs) in the thermocline are observed. ITs are dominated by modes 3 and 4, while ISWs projected on mode 1 that is trapped in the thermocline. Therein, ITs generate a persistent narrow shear band, which is strongly correlated with the enhanced dissipation rate in the thermocline. This strong dissipation rate is further reinforced in the presence of ISWs. Dissipation rates during the period without ISWs largely agree with the MacKinnon-Gregg scaling proposed for internal wavefields dominated by a low-frequency mode, while they show poor agreement with the Gregg-Henyey parameterization valid for internal wavefields close to the Garrett-Munk model. The agreement with the MacKinnon-Gregg scaling is consistent with the fact that turbulent mixing here is driven by the low-frequency internal tidal shear.
Optimization of nonlinear wave function parameters
International Nuclear Information System (INIS)
Shepard, R.; Minkoff, M.; Chemistry
2006-01-01
An energy-based optimization method is presented for our recently developed nonlinear wave function expansion form for electronic wave functions. This expansion form is based on spin eigenfunctions, using the graphical unitary group approach (GUGA). The wave function is expanded in a basis of product functions, allowing application to closed-shell and open-shell systems and to ground and excited electronic states. Each product basis function is itself a multiconfigurational function that depends on a relatively small number of nonlinear parameters called arc factors. The energy-based optimization is formulated in terms of analytic arc factor gradients and orbital-level Hamiltonian matrices that correspond to a specific kind of uncontraction of each of the product basis functions. These orbital-level Hamiltonian matrices give an intuitive representation of the energy in terms of disjoint subsets of the arc factors, they provide for an efficient computation of gradients of the energy with respect to the arc factors, and they allow optimal arc factors to be determined in closed form for subspaces of the full variation problem. Timings for energy and arc factor gradient computations involving expansion spaces of > 10 24 configuration state functions are reported. Preliminary convergence studies and molecular dissociation curves are presented for some small molecules
Nonlinear radial propagation of drift wave turbulence
International Nuclear Information System (INIS)
Prakash, M.
1985-01-01
We study the linear and the nonlinear radial propagation of drift wave energy in an inhomogeneous plasma. The drift mode excited in such a plasma is dispersive in nature. The drift wave energy spreads out symmetrically along the direction of inhomogeneity with a finite group velocity. To study the effect of the nonlinear coupling on the propagation of energy in a collision free plasma, we solve the Hasegawa-Mima equation as a mixed initial boundary-value problem. The solutions of the linearized equation are used to check the reliability of our numerical calculations. Additional checks are also performed on the invariants of the system. Our results reveal that a pulse gets distorted as it propagates through the medium. The peak of the pulse propagates with a finite velocity that depends on the amplitude of the initial pulse. The polarity of propagation depends on the initial parameters of the pulse. We have also studied drift wave propagation in a resistive plasma. The Hasegawa-Wakatani equations are used to investigate this problem
Integrability and Linear Stability of Nonlinear Waves
Degasperis, Antonio; Lombardo, Sara; Sommacal, Matteo
2018-03-01
It is well known that the linear stability of solutions of 1+1 partial differential equations which are integrable can be very efficiently investigated by means of spectral methods. We present here a direct construction of the eigenmodes of the linearized equation which makes use only of the associated Lax pair with no reference to spectral data and boundary conditions. This local construction is given in the general N× N matrix scheme so as to be applicable to a large class of integrable equations, including the multicomponent nonlinear Schrödinger system and the multiwave resonant interaction system. The analytical and numerical computations involved in this general approach are detailed as an example for N=3 for the particular system of two coupled nonlinear Schrödinger equations in the defocusing, focusing and mixed regimes. The instabilities of the continuous wave solutions are fully discussed in the entire parameter space of their amplitudes and wave numbers. By defining and computing the spectrum in the complex plane of the spectral variable, the eigenfrequencies are explicitly expressed. According to their topological properties, the complete classification of these spectra in the parameter space is presented and graphically displayed. The continuous wave solutions are linearly unstable for a generic choice of the coupling constants.
Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium
Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying
2015-01-01
A simple but highly efficient approach for dealing with the problem of cylindrical electromagnetic waves propagation in a nonlinear medium is proposed based on an exact solution proposed recently. We derive an analytical explicit formula, which exhibiting rich interesting nonlinear effects, to describe the propagation of any amount of cylindrical electromagnetic waves in a nonlinear medium. The results obtained by using the present method are accurately concordant with the results of using traditional coupled-wave equations. As an example of application, we discuss how a third wave affects the sum- and difference-frequency generation of two waves propagation in the nonlinear medium. PMID:26073066
Nonlocal description of X waves in quadratic nonlinear materials
DEFF Research Database (Denmark)
Larsen, Peter Ulrik Vingaard; Sørensen, Mads Peter; Bang, Ole
2006-01-01
We study localized light bullets and X-waves in quadratic media and show how the notion of nonlocality can provide an alternative simple physical picture of both types of multi-dimensional nonlinear waves. For X-waves we show that a local cascading limit in terms of a nonlinear Schrodinger equation...
Weakly nonlinear electron plasma waves in collisional plasmas
DEFF Research Database (Denmark)
Pecseli, H. L.; Rasmussen, J. Juul; Tagare, S. G.
1986-01-01
The nonlinear evolution of a high frequency plasma wave in a weakly magnetized, collisional plasma is considered. In addition to the ponderomotive-force-nonlinearity the nonlinearity due to the heating of the electrons is taken into account. A set of nonlinear equations including the effect...
Demiray, Hilmi; El-Zahar, Essam R.
2018-04-01
We consider the nonlinear propagation of electron-acoustic waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions. The basic nonlinear equations of the above described plasma are re-examined in the cylindrical (spherical) coordinates by employing the reductive perturbation technique. The modified cylindrical (spherical) KdV equation with fractional power nonlinearity is obtained as the evolution equation. Due to the nature of nonlinearity, this evolution equation cannot be reduced to the conventional KdV equation. A new family of closed form analytical approximate solution to the evolution equation and a comparison with numerical solution are presented and the results are depicted in some 2D and 3D figures. The results reveal that both solutions are in good agreement and the method can be used to obtain a new progressive wave solution for such evolution equations. Moreover, the resulting closed form analytical solution allows us to carry out a parametric study to investigate the effect of the physical parameters on the solution behavior of the modified cylindrical (spherical) KdV equation.
On the generation and evolution of internal solitary waves in the southern Red Sea
Guo, Daquan
2016-11-28
Satellite observations recently revealed trains of internal solitary waves (ISWs) in the off-shelf region between 16.0 degrees N and 16.5 degrees N in the southern Red Sea. The generation mechanism of these waves is not entirely clear, though, as the observed generation sites are far away (50 km) from the shelf break and tidal currents are considered relatively weak in the Red Sea. Upon closer examination of the tide properties in the Red Sea and the unique geometry of the basin, it is argued that the steep bathymetry and a relatively strong tidal current in the southern Red Sea provide favorable conditions for the generation of ISWs. To test this hypothesis and further explore the evolution of ISWs in the basin, 2-D numerical simulations with the nonhydrostatic MIT general circulation model (MITgcm) were conducted. The results are consistent with the satellite observations in regard to the generation sites, peak amplitudes and the speeds of first-mode ISWs. Moreover, our simulations suggest that the generation process of ISWs in the southern Red Sea is similar to the tide-topography interaction mechanism seen in the South China Sea. Specifically, instead of ISWs arising in the immediate vicinity of the shelf break via a hydraulic lee wave mechanism, a broad, energetic internal tide is first generated, which subsequently travels away from the shelf break and eventually breaks down into ISWs. Sensitivity runs suggest that ISW generation may also be possible under summer stratification conditions, characterized by an intermediate water intrusion from the strait of Bab el Mandeb.
Arqub, Omar Abu; El-Ajou, Ahmad; Momani, Shaher
2015-07-01
Building fractional mathematical models for specific phenomena and developing numerical or analytical solutions for these fractional mathematical models are crucial issues in mathematics, physics, and engineering. In this work, a new analytical technique for constructing and predicting solitary pattern solutions of time-fractional dispersive partial differential equations is proposed based on the generalized Taylor series formula and residual error function. The new approach provides solutions in the form of a rapidly convergent series with easily computable components using symbolic computation software. For method evaluation and validation, the proposed technique was applied to three different models and compared with some of the well-known methods. The resultant simulations clearly demonstrate the superiority and potentiality of the proposed technique in terms of the quality performance and accuracy of substructure preservation in the construct, as well as the prediction of solitary pattern solutions for time-fractional dispersive partial differential equations.
Gurbatov, S N; Saichev, A I
2012-01-01
"Waves and Structures in Nonlinear Nondispersive Media: General Theory and Applications to Nonlinear Acoustics” is devoted completely to nonlinear structures. The general theory is given here in parallel with mathematical models. Many concrete examples illustrate the general analysis of Part I. Part II is devoted to applications to nonlinear acoustics, including specific nonlinear models and exact solutions, physical mechanisms of nonlinearity, sawtooth-shaped wave propagation, self-action phenomena, nonlinear resonances and engineering application (medicine, nondestructive testing, geophysics, etc.). This book is designed for graduate and postgraduate students studying the theory of nonlinear waves of various physical nature. It may also be useful as a handbook for engineers and researchers who encounter the necessity of taking nonlinear wave effects into account of their work. Dr. Gurbatov S.N. is the head of Department, and Vice Rector for Research of Nizhny Novgorod State University. Dr. Rudenko O.V. is...
Directory of Open Access Journals (Sweden)
Jia Lin Wu
2013-06-01
Full Text Available In macromolecular self-avoiding random walk, movement of each chain-particle accompanies an instantaneous spin system with de Gennes n = 0 that provides extra energy, extra vacancy volume and relaxation time needed for chain-particles co-movement. Using these additional and instantaneous spin systems not only directly yields the same Brownian motion mode in glass transition (GT and reptation-tube model, but also proves that the entangled chain length corresponding to the Reynolds number in hydrodynamics and the inherent diffusion - delocalization mode of entangled chains, from frozen glass state to melt liquid state, is a chain-size solitary wave with transverse ripplon-like soft wave. Thus, the order parameter of GT is found. The various currently available GT theories, such as Static Replica, Random First-Order Transition, Potential Energy Landscape, Mode-Coupling and Nanoscale Heterogeneity, can be unified using the additional and instantaneous spin system. GT served as an inspiration and continues to serve as the paradigm in the universal random delocalization transitions from disorder to more disorder until turbulence.
Directory of Open Access Journals (Sweden)
Zhang Sheng
2015-01-01
Full Text Available In this paper, Painleve analysis is used to test the Painleve integrability of a forced variable-coefficient extended Korteveg-de Vries equation which can describe the weakly-non-linear long internal solitary waves in the fluid with continuous stratification on density. The obtained results show that the equation is integrable under certain conditions. By virtue of the truncated Painleve expansion, a pair of new exact solutions to the equation is obtained.
Nonlinear drift waves in a dusty plasma with sheared flows
Energy Technology Data Exchange (ETDEWEB)
Vranjes, J. [K.U. Leuven (Belgium). Center for Plasma Astrophysics; Shukla, R.K. [Ruhr-Univ. Bochum (Germany). Inst. fuer Theoretische Physik IV
2002-01-01
Nonlinear properties of dust-modified drift waves and dust-drift waves in a dusty magnetoplasma with equilibrium sheared flows are examined. For this purpose, the relevant nonlinear equations for drift waves are analyzed for various profiles of the perpendicular and parallel plasma flows, and a variety of nonlinear solutions (viz. single and double vortex chains accompanied with zonal flows, tripolar and global vortices), which are driven by nommiform shear flows and nommiform dust density, is presented.
Nonlinear drift waves in a dusty plasma with sheared flows
International Nuclear Information System (INIS)
Vranjes, J.; Shukla, R.K.
2002-01-01
Nonlinear properties of dust-modified drift waves and dust-drift waves in a dusty magnetoplasma with equilibrium sheared flows are examined. For this purpose, the relevant nonlinear equations for drift waves are analyzed for various profiles of the perpendicular and parallel plasma flows, and a variety of nonlinear solutions (viz. single and double vortex chains accompanied with zonal flows, tripolar and global vortices), which are driven by nommiform shear flows and nommiform dust density, is presented
Nonlinear wave beams in a piezo semiconducting layer
International Nuclear Information System (INIS)
Bagdoev, A.G.; Shekoyan, A.V.; Danoyan, Z.N.
1997-01-01
The propagation of quasi-monochromatic nonlinear wave in a piezo semiconducting layer taking into account electron-concentration nonlinearity is considered. For such medium the evolution equations for incoming and reflected waves are derived. Nonlinear Schroedinger equations and solutions for narrow beams are obtained. It is shown that symmetry of incoming and reflected waves does not take place. The focusing of beams is investigated.18 refs
Ma, J. Z. G.; Hirose, A.
2010-05-01
Lower-hybrid (LH) oscillitons reveal one aspect of geocomplexities. They have been observed by rockets and satellites in various regions in geospace. They are extraordinary solitary waves the envelop of which has a relatively longer period, while the amplitude is modulated violently by embedded oscillations of much shorter periods. We employ a two-fluid (electron-ion) slab model in a Cartesian geometry to expose the excitation of LH oscillitons. Relying on a set of self-similar equations, we first produce, as a reference, the well-known three shapes (sinusoidal, sawtooth, and spiky or bipolar) of parallel-propagating ion-acoustic (IA) solitary structures in the absence of electron inertia, along with their Fast Fourier Transform (FFT) power spectra. The study is then expanded to illustrate distorted structures of the IA modes by taking into account all the three components of variables. In this case, the ion-cyclotron (IC) mode comes into play. Furthermore, the electron inertia is incorporated in the equations. It is found that the inertia modulates the coupled IA/IC envelops to produce LH oscillitons. The newly excited structures are characterized by a normal low-frequency IC solitary envelop embedded by high-frequency, small-amplitude LH oscillations which are superimposed upon by higher-frequency but smaller-amplitude IA ingredients. The oscillitons are shown to be sensitive to several input parameters (e.g., the Mach number, the electron-ion mass/temperature ratios, and the electron thermal speed). Interestingly, whenever a LH oscilliton is triggered, there occurs a density cavity the depth of which can reach up to 20% of the background density, along with density humps on both sides of the cavity. Unexpectedly, a mode at much lower frequencies is also found beyond the IC band. Future studies are finally highlighted. The appendices give a general dispersion relation and specific ones of linear modes relevant to all the nonlinear modes encountered in the text.
Modeling the SAR Signature of Nonlinear Internal Waves
National Research Council Canada - National Science Library
Lettvin, Ellen E
2008-01-01
Nonlinear Internal Waves are pervasive globally, particularly in coastal waters. The currents and displacements associated with internal waves influence acoustic propagation and underwater navigation, as well as ocean transport and mixing...
New travelling wave solutions for nonlinear stochastic evolution ...
Indian Academy of Sciences (India)
expansion method to look for travelling wave solutions of nonlinear partial differential equations. It is interesting to mention that, in this method the sign of the parameters can be used to judge the numbers and types of travelling wave solutions.
Nonlinear modulation of ion acoustic waves in a magnetized plasma
International Nuclear Information System (INIS)
Bharuthram, R.; Shukla, P.K.
1987-01-01
The quasistatic plasma slow response to coherent ion acoustic waves in a magnetized plasma is considered. A multidimensional cubic nonlinear Schroedinger equation is derived. It is found that the ion acoustic waves remain modulationally stable against oblique perturbations
Manipulating acoustic wave reflection by a nonlinear elastic metasurface
Guo, Xinxin; Gusev, Vitalyi E.; Bertoldi, Katia; Tournat, Vincent
2018-03-01
The acoustic wave reflection properties of a nonlinear elastic metasurface, derived from resonant nonlinear elastic elements, are theoretically and numerically studied. The metasurface is composed of a two degree-of-freedom mass-spring system with quadratic elastic nonlinearity. The possibility of converting, during the reflection process, most of the fundamental incoming wave energy into the second harmonic wave is shown, both theoretically and numerically, by means of a proper design of the nonlinear metasurface. The theoretical results from the harmonic balance method for a monochromatic source are compared with time domain simulations for a wave packet source. This protocol allows analyzing the dynamics of the nonlinear reflection process in the metasurface as well as exploring the limits of the operating frequency bandwidth. The reported methodology can be applied to a wide variety of nonlinear metasurfaces, thus possibly extending the family of exotic nonlinear reflection processes.
Nonlinear low frequency (LF) waves - Comets and foreshock phenomena
Tsurutani, Bruce T.
1991-01-01
A review is conducted of LF wave nonlinear properties at comets and in the earth's foreshock, engaging such compelling questions as why there are no cometary cyclotron waves, the physical mechanism responsible for 'dispersive whiskers', and the character of a general description of linear waves. Attention is given to the nonlinear properties of LF waves, whose development is illustrated by examples of waves and their features at different distances from the comet, as well as by computer simulation results. Also discussed is a curious wave mode detected from Comet Giacobini-Zinner, both at and upstream of the bow shock/wave.
Effects of vortex-like and non-thermal ion distributions on non-linear dust-acoustic waves
International Nuclear Information System (INIS)
Mamun, A.A.; Cairns, R.A.; Shukla, P.K.
1996-01-01
The effects of vortex-like and non-thermal ion distributions are incorporated in the study of nonlinear dust-acoustic waves in an unmagnetized dusty plasma. It is found that owing to the departure from the Boltzmann ion distribution to a vortex-like phase space distribution, the dynamics of small but finite amplitude dust-acoustic waves is governed by a modified Kortweg endash de Vries equation. The latter admits a stationary dust-acoustic solitary wave solution, which has larger amplitude, smaller width, and higher propagation velocity than that involving adiabatic ions. On the other hand, consideration of a non-thermal ion distribution provides the possibility of coexistence of large amplitude rarefactive as well as compressive dust-acoustic solitary waves, whereas these structures appear independently when the wave amplitudes become infinitely small. The present investigation should help us to understand the salient features of the non-linear dust-acoustic waves that have been observed in a recent numerical simulation study. copyright 1996 American Institute of Physics
Energy Technology Data Exchange (ETDEWEB)
Han Jiuning; He Yonglin; Chen Yan; Zhang Kezhi; Ma Baohong [College of Physics and Electromechanical Engineering, Hexi University, Zhangye 734000 (China)
2013-01-15
By using the model of Cairns et al.[Geophys. Rev. Lett. 22, 2709 (1995)], the head-on collision of cylindrical/spherical ion-acoustic solitary waves in an unmagnetized non-planar plasma consisting of warm adiabatic ions and nonthermally distributed electrons is investigated. The extended Poincare-Lighthill-Kuo perturbation method is used to derive the modified Korteweg-de Vries equations for ion-acoustic solitary waves in this plasma system. The effects of the plasma geometry m, the ion to electron temperature ratio {sigma}, and the nonthermality of the electron distribution {alpha} on the interaction of the colliding solitary waves are studied. It is found that the plasma geometries have a big impact on the phase shifts of solitary waves. Also it is important to note that the phase shifts induced by the collision of compressive and rarefactive solitary waves are very different. We point out that this study is useful to the investigations about the observations of electrostatic solitary structures in astrophysical as well as in experimental plasmas with nonthermal energetic electrons.
International Nuclear Information System (INIS)
Kevrekidis, P.G.; Herring, G.J.; Lafortune, S.; Hoq, Q.E.
2012-01-01
We propose a consideration of the properties of the two-dimensional Ablowitz–Ladik discretization of the ubiquitous nonlinear Schrödinger (NLS) model. We use singularity confinement techniques to suggest that the relevant discretization should not be integrable. More importantly, we identify the prototypical solitary waves of the model and examine their stability, illustrating the remarkable feature that near the continuum limit, this discretization leads to the absence of collapse and complete spectral wave stability, in stark contrast to the standard discretization of the NLS. We also briefly touch upon the three-dimensional case and generalizations of our considerations therein, and also present some more exotic solutions of the model, such as exact line solitons and discrete vortices. -- Highlights: ► The two-dimensional version of the Ablowitz–Ladik discretization of the nonlinear Schrödinger (NLS) equation is considered. ► It is found that near the continuum limit the fundamental discrete soliton is spectrally stable. ► This finding is in sharp contrast with the case of the standard discretization of the NLS equation. ► In the three-dimensional version of the model, the fundamental solitons are unstable. ► Additional waveforms such as exact unstable line solitons and discrete vortices are also touched upon.
Energy Technology Data Exchange (ETDEWEB)
Kevrekidis, P.G., E-mail: kevrekid@gmail.com [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Herring, G.J. [Department of Mathematics and Statistics, Cameron University, Lawton, OK 73505 (United States); Lafortune, S. [Department of Mathematics, College of Charleston, Charleston, SC 29401 (United States); Hoq, Q.E. [Department of Mathematics and Computer Science, Western New England College, Springfield, MA 01119 (United States)
2012-02-06
We propose a consideration of the properties of the two-dimensional Ablowitz–Ladik discretization of the ubiquitous nonlinear Schrödinger (NLS) model. We use singularity confinement techniques to suggest that the relevant discretization should not be integrable. More importantly, we identify the prototypical solitary waves of the model and examine their stability, illustrating the remarkable feature that near the continuum limit, this discretization leads to the absence of collapse and complete spectral wave stability, in stark contrast to the standard discretization of the NLS. We also briefly touch upon the three-dimensional case and generalizations of our considerations therein, and also present some more exotic solutions of the model, such as exact line solitons and discrete vortices. -- Highlights: ► The two-dimensional version of the Ablowitz–Ladik discretization of the nonlinear Schrödinger (NLS) equation is considered. ► It is found that near the continuum limit the fundamental discrete soliton is spectrally stable. ► This finding is in sharp contrast with the case of the standard discretization of the NLS equation. ► In the three-dimensional version of the model, the fundamental solitons are unstable. ► Additional waveforms such as exact unstable line solitons and discrete vortices are also touched upon.
Buffoni, Boris; Groves, Mark D.; Wahlén, Erik
2018-06-01
Fully localised solitary waves are travelling-wave solutions of the three- dimensional gravity-capillary water wave problem which decay to zero in every horizontal spatial direction. Their existence has been predicted on the basis of numerical simulations and model equations (in which context they are usually referred to as `lumps'), and a mathematically rigorous existence theory for strong surface tension (Bond number {β} greater than {1/3}) has recently been given. In this article we present an existence theory for the physically more realistic case {0 point of the reduced functional is found by minimising it over its natural constraint set.
International Nuclear Information System (INIS)
Amour, Rabia; Tribeche, Mouloud
2010-01-01
A first theoretical work is presented to study variable charge dust acoustic solitons within the theoretical framework of the Tsallis statistical mechanics. Our results reveal that the spatial patterns of the variable charge solitary wave are significantly modified by electron nonextensive effects. In particular, it may be noted that for -1 d becomes more negative and the dust grains localization (accumulation) less pronounced. The electrons are locally expelled and pushed out of the region of the soliton's localization. This electron depletion becomes less effective as the electrons evolve far away from their thermal equilibrium. The case q>1 provides qualitatively opposite results: electron nonextensivity makes the solitary structure more spiky. Our results should help in providing a good fit between theoretical and experimental results.
Variational Boussinesq model for strongly nonlinear dispersive waves
Lawrence, C.; Adytia, D.; van Groesen, E.
2018-01-01
For wave tank, coastal and oceanic applications, a fully nonlinear Variational Boussinesq model with optimized dispersion is derived and a simple Finite Element implementation is described. Improving a previous weakly nonlinear version, high waves over flat and varying bottom are shown to be
Nonlinear propagation of short wavelength drift-Alfven waves
DEFF Research Database (Denmark)
Shukla, P. K.; Pecseli, H. L.; Juul Rasmussen, Jens
1986-01-01
Making use of a kinetic ion and a hydrodynamic electron description together with the Maxwell equation, the authors derive a set of nonlinear equations which governs the dynamics of short wavelength ion drift-Alfven waves. It is shown that the nonlinear drift-Alfven waves can propagate as two-dim...
Nonlinear self-modulation of ion-acoustic waves
International Nuclear Information System (INIS)
Ikezi, H.; Schwarzenegger, K.; Simons, A.L.; Ohsawa, Y.; Kamimura, T.
1978-01-01
The nonlinear evolution of an ion-acoustic wave packet is studied. Experimentally, it is found that (i) nonlinear phase modulation develops in the wave packet; (ii) the phase modulation, together with the dispersion effect, causes expansion and breaking of the wave packet; (iii) the ions trapped in the troughs of the wave potential introduce self-phase modulation; and (iv) the ion-acoustic wave is stable with respect to the modulational instability. Computer simulations have reproduced the experimental results. The physical picture and the model equation describing the wave evolution are discussed
Nonlinear waves in bipolar complex viscous astroclouds
Karmakar, P. K.; Haloi, A.
2017-05-01
A theoretical evolutionary model to analyze the dynamics of strongly nonlinear waves in inhomogeneous complex astrophysical viscous clouds on the gravito-electrostatic scales of space and time is procedurally set up. It compositionally consists of warm lighter electrons and ions (Boltzmanian); and cold massive bi-polar dust grains (inertial fluids) alongside vigorous neutral dynamics in quasi-neutral hydrodynamic equilibrium. Application of the Sagdeev pseudo-potential method reduces the inter-coupled structure equations into a pair of intermixed forced Korteweg-de Vries-Burgers (f-KdVB) equations. The force-terms are self-consistently sourced by inhomogeneous gravito-electrostatic interplay. A numerical illustrative shape-analysis based on judicious astronomical parametric platform shows the electrostatic waves evolving as compressive dispersive shock-like eigen-modes. A unique transition from quasi-monotonic to non-monotonic oscillatory compressive shock-like patterns is found to exist. In contrast, the self-gravitational and effective perturbations grow purely as non-monotonic compressive oscillatory shock-like structures with no such transitory features. It is seen that the referral frame velocity acts as amplitude-reducing agent (stabilizing source) for the electrostatic fluctuations solely. A comparison in the prognostic light of various earlier satellite-based observations and in-situ measurements is presented. The paper ends up with synoptic highlights on the main implications and non-trivial applications in the interstellar space and cosmic plasma environments leading to bounded structure formation.
Nonlinear VLF Wave Physics in the Radiation Belts
Crabtree, C. E.; Tejero, E. M.; Ganguli, G.; Mithaiwala, M.; Rudakov, L.; Hospodarsky, G. B.; Kletzing, C.
2014-12-01
Electromagnetic VLF waves, such as whistler mode waves, both control the lifetime of trapped electrons in the radiation belts by pitch-angle scattering and are responsible for the energization of electrons during storms. Traditional approaches to understanding the influence of waves on trapped electrons have assumed that the wave characteristics (frequency spectrum, wave-normal angle distribution, etc.) were both stationary in time and amplitude independent from event to event. In situ data from modern satellite missions, such as the Van Allen probes, are showing that this assumption may not be justified. In addition, recent theoretical results [Crabtree et al. 2012] show that the threshold for nonlinear wave scattering can often be met by naturally occurring VLF waves in the magnetosphere, with wave magnetic fields of the order of 50-100 pT inside the plasmapause. Nonlinear wave scattering (Nonlinear Landau Damping) is an amplitude dependent mechanism that can strongly alter VLF wave propagation [Ganguli et al. 2010], primarily by altering the direction of propagation. Laboratory results have confirmed the dramatic change in propagation direction when the pump wave has sufficient amplitude to exceed the nonlinear threshold [Tejero et al. 2014]. Nonlinear scattering can alter the macroscopic dynamics of waves in the radiation belts leading to the formation of a long-lasting wave-cavity [Crabtree et al. 2012] and, when amplification is present, a multi-pass amplifier [Ganguli et al., 2012]. Such nonlinear wave effects can dramatically reduce electron lifetimes. Nonlinear wave dynamics such as these occur when there are more than one wave present, such a condition necessarily violates the assumption of traditional wave-normal analysis [Santolik et al., 2003] which rely on the plane wave assumption. To investigate nonlinear wave dynamics using modern in situ data we apply the maximum entropy method [Skilling and Bryan, 1984] to solve for the wave distribution function
Wave propagation in elastic medium with heterogeneous quadratic nonlinearity
International Nuclear Information System (INIS)
Tang Guangxin; Jacobs, Laurence J.; Qu Jianmin
2011-01-01
This paper studies the one-dimensional wave propagation in an elastic medium with spatially non-uniform quadratic nonlinearity. Two problems are solved analytically. One is for a time-harmonic wave propagating in a half-space where the displacement is prescribed on the surface of the half-space. It is found that spatial non-uniformity of the material nonlinearity causes backscattering of the second order harmonic, which when combined with the forward propagating waves generates a standing wave in steady-state wave motion. The second problem solved is the reflection from and transmission through a layer of finite thickness embedded in an otherwise linearly elastic medium of infinite extent, where it is assumed that the layer has a spatially non-uniform quadratic nonlinearity. The results show that the transmission coefficient for the second order harmonic is proportional to the spatial average of the nonlinearity across the thickness of the layer, independent of the spatial distribution of the nonlinearity. On the other hand, the coefficient of reflection is proportional to a weighted average of the nonlinearity across the layer thickness. The weight function in this weighted average is related to the propagating phase, thus making the coefficient of reflection dependent on the spatial distribution of the nonlinearity. Finally, the paper concludes with some discussions on how to use the reflected and transmitted second harmonic waves to evaluate the variance and autocorrelation length of nonlinear parameter β when the nonlinearity distribution in the layer is a stochastic process.
International Nuclear Information System (INIS)
Berloff, Natalia G; Roberts, Paul H
2004-01-01
The stability of the axisymmetric solitary waves of the Gross-Pitaevskii (GP) equation is investigated. The implicitly restarted Arnoldi method for banded matrices with shift-invert is used to solve the linearized spectral stability problem. The rarefaction solitary waves on the upper branch of the Jones-Roberts dispersion curve are shown to be unstable to axisymmetric infinitesimal perturbations, whereas the solitary waves on the lower branch and all two-dimensional solitary waves are linearly stable. The growth rates of the instabilities on the upper branch are so small that an arbitrarily specified initial perturbation of a rarefaction wave at first usually evolves towards the upper branch as it acoustically radiates away its excess energy. This is demonstrated through numerical integrations of the GP equation starting from an initial state consisting of an unstable rarefaction wave and random non-axisymmetric noise. The resulting solution evolves towards, and remains for a significant time in the vicinity of, an unperturbed unstable rarefaction wave. It is shown however that, ultimately (or for an initial state extremely close to the upper branch), the solution evolves onto the lower branch or is completely dissipated as sound. It is shown how density depletions in uniform and trapped condensates can generate rarefaction waves, and a simple method is suggested by which such waves can be created in the laboratory
Energy Technology Data Exchange (ETDEWEB)
Berloff, Natalia G [Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA (United Kingdom); Roberts, Paul H [Department of Mathematics, University of California, Los Angeles, CA, 90095 (United States)
2004-11-26
The stability of the axisymmetric solitary waves of the Gross-Pitaevskii (GP) equation is investigated. The implicitly restarted Arnoldi method for banded matrices with shift-invert is used to solve the linearized spectral stability problem. The rarefaction solitary waves on the upper branch of the Jones-Roberts dispersion curve are shown to be unstable to axisymmetric infinitesimal perturbations, whereas the solitary waves on the lower branch and all two-dimensional solitary waves are linearly stable. The growth rates of the instabilities on the upper branch are so small that an arbitrarily specified initial perturbation of a rarefaction wave at first usually evolves towards the upper branch as it acoustically radiates away its excess energy. This is demonstrated through numerical integrations of the GP equation starting from an initial state consisting of an unstable rarefaction wave and random non-axisymmetric noise. The resulting solution evolves towards, and remains for a significant time in the vicinity of, an unperturbed unstable rarefaction wave. It is shown however that, ultimately (or for an initial state extremely close to the upper branch), the solution evolves onto the lower branch or is completely dissipated as sound. It is shown how density depletions in uniform and trapped condensates can generate rarefaction waves, and a simple method is suggested by which such waves can be created in the laboratory.
Nonlinear interaction of waves in an inhomogeneous plasma
International Nuclear Information System (INIS)
Istomin, Ya.N.
1988-01-01
Nonlinear wave processes in a weakly inhomogeneous plasma are considered. A quasilinear equation is derived which takes into account the effect of the waves on resonance particles, provided that the inhomogeneity appreciably affects the nature of the resonance interaction. Three-wave interaction is investigated under the same conditions. As an example, the nonlinear interaction in a relativistic plasma moving along a strong curvilinear magnetic field is considered
International Nuclear Information System (INIS)
Kumar Samanta, Utpal; Saha, Asit; Chatterjee, Prasanta
2013-01-01
Bifurcations of nonlinear propagation of ion acoustic waves (IAWs) in a magnetized plasma whose constituents are cold ions and kappa distributed electron are investigated using a two component plasma model. The standard reductive perturbation technique is used to derive the Zakharov-Kuznetsov (ZK) equation for IAWs. By using the bifurcation theory of planar dynamical systems to this ZK equation, the existence of solitary wave solutions and periodic travelling wave solutions is established. All exact explicit solutions of these travelling waves are determined. The results may have relevance in dense space plasmas
Nonlinear physics of shear Alfvén waves
International Nuclear Information System (INIS)
Zonca, Fulvio; Chen, Liu
2014-01-01
Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These 'nonlinear equilibria' or 'phase-space zonal structures' dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results
Nonlinear physics of shear Alfvén waves
Zonca, Fulvio; Chen, Liu
2014-02-01
Shear Alfvén waves (SAW) play fundamental roles in thermonuclear plasmas of fusion interest, since they are readily excited by energetic particles in the MeV range as well as by the thermal plasma components. Thus, understanding fluctuation induced transport in burning plasmas requires understanding nonlinear SAW physics. There exist two possible routes to nonlinear SAW physics: (i) wave-wave interactions and the resultant spectral energy transfer; (ii) nonlinear wave-particle interactions of SAW instabilities with energetic particles. Within the first route, it is advantageous to understand and describe nonlinear processes in term of proximity of the system to the Alfvénic state, where wave-wave interactions are minimized due to the cancellation of Reynolds and Maxwell stresses. Here, various wave-wave nonlinear dynamics are elucidated in terms of how they break the Alfvénic state. In particular, we discuss the qualitative and quantitative modification of the SAW parametric decay process due to finite ion compressibility and finite ion Larmor radius. We also show that toroidal geometry plays a crucial role in the nonlinear excitation of zonal structures by Alfvén eigenmodes. Within the second route, the coherent nonlinear dynamics of structures in the energetic particle phase space, by which secular resonant particle transport can occur on meso- and macro-scales, must be addressed and understood. These "nonlinear equilibria" or "phase-space zonal structures" dynamically evolve on characteristic (fluctuation induced) turbulent transport time scales, which are generally of the same order of the nonlinear time scale of the underlying fluctuations. In this work, we introduce the general structure of nonlinear Schrödinger equations with complex integro-differential nonlinear terms, which govern these physical processes. To elucidate all these aspects, theoretical analyses are presented together with numerical simulation results.
Nonlinear Whistler Wave Physics in the Radiation Belts
Crabtree, Chris
2016-10-01
Wave particle interactions between electrons and whistler waves are a dominant mechanism for controlling the dynamics of energetic electrons in the radiation belts. They are responsible for loss, via pitch-angle scattering of electrons into the loss cone, and energization to millions of electron volts. It has previously been theorized that large amplitude waves on the whistler branch may scatter their wave-vector nonlinearly via nonlinear Landau damping leading to important consequences for the global distribution of whistler wave energy density and hence the energetic electrons. It can dramatically reduce the lifetime of energetic electrons in the radiation belts by increasing the pitch angle scattering rate. The fundamental building block of this theory has now been confirmed through laboratory experiments. Here we report on in situ observations of wave electro-magnetic fields from the EMFISIS instrument on board NASA's Van Allen Probes that show the signatures of nonlinear scattering of whistler waves in the inner radiation belts. In the outer radiation belts, whistler mode chorus is believed to be responsible for the energization of electrons from 10s of Kev to MeV energies. Chorus is characterized by bursty large amplitude whistler mode waves with frequencies that change as a function of time on timescales corresponding to their growth. Theories explaining the chirping have been developed for decades based on electron trapping dynamics in a coherent wave. New high time resolution wave data from the Van Allen probes and advanced spectral techniques are revealing that the wave dynamics is highly structured, with sub-elements consisting of multiple chirping waves with discrete frequency hops between sub-elements. Laboratory experiments with energetic electron beams are currently reproducing the complex frequency vs time dynamics of whistler waves and in addition revealing signatures of wave-wave and beat-wave nonlinear wave-particle interactions. These new data
Nonlinear density waves in a marginally stable gravitating disk
International Nuclear Information System (INIS)
Korchagin, V.I.
1986-01-01
The evolution of short nonlinear density waves in a disk at the stability limit is studied for arbitrary values of the radial wave number k/sub r/. For waves with wave numbers that do not lie at the minimum of the dispersion curve, the behavior of the amplitude is described by a nonlinear parabolic equation; however, stationary soliton solutions cannot exist in such a system since there is no dispersion spreading of a packet. For wave numbers lying at the minimum of the dispersion curve, soliton structures with determined amplitude are possible. In stable gravitating disks and in a disk at the stability limit, two physically different types of soliton can exist
Nonlinear Alfvén Waves in a Vlasov Plasma
DEFF Research Database (Denmark)
Bell, T.F.
1965-01-01
Stationary solutions to the nonlinear Vlasov—Boltzmann equations are considered which represent one-dimensional electromagnetic waves in a hot magnetoplasma. These solutions appear in arbitrary reference frames as circularly polarized, sinusoidal waves of unlimited amplitude, i.e., as nonlinear...... Alfvén waves. Solutions are found implicitly by deriving a set of integral dispersion relations which link the wave characteristics with the particle distribution functions. A physical discussion is given of the way in which the Alfvén waves can trap particles, and it is shown that the presence...
Statistical properties of nonlinear one-dimensional wave fields
Directory of Open Access Journals (Sweden)
D. Chalikov
2005-01-01
Full Text Available A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.
Statistical properties of nonlinear one-dimensional wave fields
Chalikov, D.
2005-06-01
A numerical model for long-term simulation of gravity surface waves is described. The model is designed as a component of a coupled Wave Boundary Layer/Sea Waves model, for investigation of small-scale dynamic and thermodynamic interactions between the ocean and atmosphere. Statistical properties of nonlinear wave fields are investigated on a basis of direct hydrodynamical modeling of 1-D potential periodic surface waves. The method is based on a nonstationary conformal surface-following coordinate transformation; this approach reduces the principal equations of potential waves to two simple evolutionary equations for the elevation and the velocity potential on the surface. The numerical scheme is based on a Fourier transform method. High accuracy was confirmed by validation of the nonstationary model against known solutions, and by comparison between the results obtained with different resolutions in the horizontal. The scheme allows reproduction of the propagation of steep Stokes waves for thousands of periods with very high accuracy. The method here developed is applied to simulation of the evolution of wave fields with large number of modes for many periods of dominant waves. The statistical characteristics of nonlinear wave fields for waves of different steepness were investigated: spectra, curtosis and skewness, dispersion relation, life time. The prime result is that wave field may be presented as a superposition of linear waves is valid only for small amplitudes. It is shown as well, that nonlinear wave fields are rather a superposition of Stokes waves not linear waves. Potential flow, free surface, conformal mapping, numerical modeling of waves, gravity waves, Stokes waves, breaking waves, freak waves, wind-wave interaction.
Approximate Stream Function wavemaker theory for highly non-linear waves in wave flumes
DEFF Research Database (Denmark)
Zhang, H.W.; Schäffer, Hemming Andreas
2007-01-01
An approximate Stream Function wavemaker theory for highly non-linear regular waves in flumes is presented. This theory is based on an ad hoe unified wave-generation method that combines linear fully dispersive wavemaker theory and wave generation for non-linear shallow water waves. This is done...... by applying a dispersion correction to the paddle position obtained for non-linear long waves. The method is validated by a number of wave flume experiments while comparing with results of linear wavemaker theory, second-order wavemaker theory and Cnoidal wavemaker theory within its range of application....
Nonlinear interaction of the surface waves at a plasma boundary
International Nuclear Information System (INIS)
Dolgopolov, V.V.; El-Naggar, I.A.; Hussein, A.M.; Khalil, Sh.M.
1976-01-01
Amplitudes of electromagnetic waves with combination frequencies, radiating from the plasma boundary due to nonlinear interaction of the surface waves, have been found. Previous papers on this subject did not take into account that the tangential components of the electric field of waves with combination frequencies were discontinuous at the plasma boundary. (Auth.)
Nonlinear Scattering of VLF Waves in the Radiation Belts
Crabtree, Chris; Rudakov, Leonid; Ganguli, Guru; Mithaiwala, Manish
2014-10-01
Electromagnetic VLF waves, such as whistler mode waves, control the lifetime of trapped electrons in the radiation belts by pitch-angle scattering. Since the pitch-angle scattering rate is a strong function of the wave properties, a solid understanding of VLF wave sources and propagation in the magnetosphere is critical to accurately calculate electron lifetimes. Nonlinear scattering (Nonlinear Landau Damping) is a mechanism that can strongly alter VLF wave propagation [Ganguli et al. 2010], primarily by altering the direction of propagation, and has not been accounted for in previous models of radiation belt dynamics. Laboratory results have confirmed the dramatic change in propagation direction when the pump wave has sufficient amplitude to exceed the nonlinear threshold [Tejero et al. 2014]. Recent results show that the threshold for nonlinear scattering can often be met by naturally occurring VLF waves in the magnetosphere, with wave magnetic fields of the order of 50-100 pT inside the plasmapause. Nonlinear scattering can then dramatically alter the macroscopic dynamics of waves in the radiation belts leading to the formation of a long-lasting wave-cavity [Crabtree et al. 2012] and, when amplification is present, a multi-pass amplifier [Ganguli et al. 2012]. By considering these effects, the lifetimes of electrons can be dramatically reduced. This work is supported by the Naval Research Laboratory base program.
Energy Technology Data Exchange (ETDEWEB)
Singh, S. V.; Devanandhan, S.; Lakhina, G. S. [Indian Institute of Geomagnetism, Navi Mumbai (India); Bharuthram, R. [University of the Western Cape, Bellville (South Africa)
2013-01-15
Obliquely propagating ion-acoustic soliatry waves are examined in a magnetized plasma composed of kappa distributed electrons and fluid ions with finite temperature. The Sagdeev potential approach is used to study the properties of finite amplitude solitary waves. Using a quasi-neutrality condition, it is possible to reduce the set of equations to a single equation (energy integral equation), which describes the evolution of ion-acoustic solitary waves in magnetized plasmas. The temperature of warm ions affects the speed, amplitude, width, and pulse duration of solitons. Both the critical and the upper Mach numbers are increased by an increase in the ion temperature. The ion-acoustic soliton amplitude increases with the increase in superthermality of electrons. For auroral plasma parameters, the model predicts the soliton speed, amplitude, width, and pulse duration, respectively, to be in the range of (28.7-31.8) km/s, (0.18-20.1) mV/m; (590-167) m, and (20.5-5.25) ms, which are in good agreement with Viking observations.
Khater, Mostafa M. A.; Seadawy, Aly R.; Lu, Dianchen
2018-03-01
In this research, we investigate one of the most popular model in nature and also industrial which is the pressure equation of bubbly liquids with examination for viscosity and heat transfer which has many application in nature and engineering. Understanding the physical meaning of exact and solitary traveling wave solutions for this equation gives the researchers in this field a great clear vision of the pressure waves in a mixture liquid and gas bubbles taking into consideration the viscosity of liquid and the heat transfer and also dynamics of contrast agents in the blood flow at ultrasonic researches. To achieve our goal, we apply three different methods which are extended tanh-function method, extended simple equation method and a new auxiliary equation method on this equation. We obtained exact and solitary traveling wave solutions and we also discuss the similarity and difference between these three method and make a comparison between results that we obtained with another results that obtained with the different researchers using different methods. All of these results and discussion explained the fact that our new auxiliary equation method is considered to be the most general, powerful and the most result-oriented. These kinds of solutions and discussion allow for the understanding of the phenomenon and its intrinsic properties as well as the ease of way of application and its applicability to other phenomena.
The effect of dust size distribution on the damping of the solitary waves in a dusty plasma
International Nuclear Information System (INIS)
Yang, Xue; Xu, Yan-Xia; Qi, Xin; Wang, Cang-Long; Duan, Wen-Shan; Yang, Lei
2013-01-01
The effect of the dust size distribution on the damping rate of the solitary wave in a dusty plasma is investigated in the present paper. It is found that the damping rate increases as either the mean radius of dust grains increases or as the total number density of the dust grains increases. The damping rate is less for usual dusty plasma (about which the number density of the smaller dust grains is larger than that of the larger dust grains) than that of the unusual dusty plasma (about which the number density of the larger dust grains is larger than that of the smaller dust grains)
Generation of Caustics and Rogue Waves from Nonlinear Instability.
Safari, Akbar; Fickler, Robert; Padgett, Miles J; Boyd, Robert W
2017-11-17
Caustics are phenomena in which nature concentrates the energy of waves and may exhibit rogue-type behavior. Although they are known mostly in optics, caustics are intrinsic to all wave phenomena. As we demonstrate in this Letter, the formation of caustics and consequently rogue events in linear systems requires strong phase fluctuations. We show that nonlinear phase shifts can generate sharp caustics from even small fluctuations. Moreover, in that the wave amplitude increases dramatically in caustics, nonlinearity is usually inevitable. We perform an experiment in an optical system with Kerr nonlinearity, simulate the results based on the nonlinear Schrödinger equation, and achieve perfect agreement. As the same theoretical framework is used to describe other wave systems such as large-scale water waves, our results may also aid the understanding of ocean phenomena.
Nonlinear dynamics of resonant electrons interacting with coherent Langmuir waves
Tobita, Miwa; Omura, Yoshiharu
2018-03-01
We study the nonlinear dynamics of resonant particles interacting with coherent waves in space plasmas. Magnetospheric plasma waves such as whistler-mode chorus, electromagnetic ion cyclotron waves, and hiss emissions contain coherent wave structures with various discrete frequencies. Although these waves are electromagnetic, their interaction with resonant particles can be approximated by equations of motion for a charged particle in a one-dimensional electrostatic wave. The equations are expressed in the form of nonlinear pendulum equations. We perform test particle simulations of electrons in an electrostatic model with Langmuir waves and a non-oscillatory electric field. We solve equations of motion and study the dynamics of particles with different values of inhomogeneity factor S defined as a ratio of the non-oscillatory electric field intensity to the wave amplitude. The simulation results demonstrate deceleration/acceleration, thermalization, and trapping of particles through resonance with a single wave, two waves, and multiple waves. For two-wave and multiple-wave cases, we describe the wave-particle interaction as either coherent or incoherent based on the probability of nonlinear trapping.
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Rasmussen, Kim
1996-01-01
in an exponentially decreasing width of the solution in the long-time limit. We also find that a sufficiently large noise variance may cause an initially localized distribution to spread instead of contracting, and that the critical variance necessary to cause dispersion will for small damping be the same......We study the effect of adding noise and nonlinear damping in the two-dimensional nonlinear Schrodinger equation (NLS). Using a collective approach, we find that for initial conditions where total collapse occurs in the unperturbed NLS, the presence of the damping term will instead...
Inelastic collision of two solitons for generalized BBM equation with cubic nonlinearity
Directory of Open Access Journals (Sweden)
Jingdong Wei
2015-06-01
Full Text Available We study the inelastic collision of two solitary waves of different velocities for the generalized Benjamin-Bona-Mahony (BBM equation with cubic nonlinearity. It shows that one solitary wave is smaller than the other one in the H^1(R energy space. We explore the sharp estimates of the nonzero residue due to the collision, and prove the inelastic collision of two solitary waves and nonexistence of a pure 2-soliton solution.
Nonlinear acoustic waves in micro-inhomogeneous solids
Nazarov, Veniamin
2014-01-01
Nonlinear Acoustic Waves in Micro-inhomogeneous Solids covers the broad and dynamic branch of nonlinear acoustics, presenting a wide variety of different phenomena from both experimental and theoretical perspectives. The introductory chapters, written in the style of graduate-level textbook, present a review of the main achievements of classic nonlinear acoustics of homogeneous media. This enables readers to gain insight into nonlinear wave processes in homogeneous and micro-inhomogeneous solids and compare it within the framework of the book. The subsequent eight chapters covering: Physical m
Nonlinear evolution equations for waves in random media
International Nuclear Information System (INIS)
Pelinovsky, E.; Talipova, T.
1994-01-01
The scope of this paper is to highlight the main ideas of asymptotical methods applying in modern approaches of description of nonlinear wave propagation in random media. We start with the discussion of the classical conception of ''mean field''. Then an exactly solvable model describing nonlinear wave propagation in the medium with fluctuating parameters is considered in order to demonstrate that the ''mean field'' method is not correct. We develop new asymptotic procedures of obtaining the nonlinear evolution equations for the wave fields in random media. (author). 16 refs
Some remarks on coherent nonlinear coupling of waves in plasmas
International Nuclear Information System (INIS)
Wilhelmsson, H.
1976-01-01
The analysis of nonlinear processes in plasma physics has given rise to a basic set of coupled equations. These equations describe the coherent nonlinear evolution of plasma waves. In this paper various possibilities of analysing these equations are discussed and inherent difficulties in the description of nonlinear interactions between different types of waves are pointed out. Specific examples of stimulated excitation of waves are considered. These are the parametric excitation of hybrid resonances in hot magnetized multi-ion component plasma and laser-plasma interactions. (B.D.)
Interaction of solitary pulses in single mode optical fibres | Usman ...
African Journals Online (AJOL)
Two solitary waves launched, by way of incidence, into an optical fibre from a single pulse if the pulses are in-phase as understood from results of inverse scattering transform method applied to the cubic nonlinear Schrödinger equations, (CNLSE\\'s). The single CNLSE is then understood to describe evolution of coupled ...
Electron non-linearities in Langmuir waves with application to beat-wave experiments
International Nuclear Information System (INIS)
Bell, A.R.; Gibbon, P.
1988-01-01
Non-linear Langmuir waves are examined in the context of the beat-wave accelerator. With a background of immobile ions the waves in one dimension are subject to the relativistic non-linearity of Rosenbluth, M.N. and Liu, C.S., Phys. Rev. Lett., 1972, 29, 701. In two or three dimensions, other electron non-linearities occur which involve electric and magnetic fields. The quasi-linear equations for these non-linearities are developed and solved numerically in a geometry representative of laser-driven beat waves. (author)
Rogue and shock waves in nonlinear dispersive media
Resitori, Stefania; Baronio, Fabio
2016-01-01
This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists ...
Effect of Forcing Function on Nonlinear Acoustic Standing Waves
Finkheiner, Joshua R.; Li, Xiao-Fan; Raman, Ganesh; Daniels, Chris; Steinetz, Bruce
2003-01-01
Nonlinear acoustic standing waves of high amplitude have been demonstrated by utilizing the effects of resonator shape to prevent the pressure waves from entering saturation. Experimentally, nonlinear acoustic standing waves have been generated by shaking an entire resonating cavity. While this promotes more efficient energy transfer than a piston-driven resonator, it also introduces complicated structural dynamics into the system. Experiments have shown that these dynamics result in resonator forcing functions comprised of a sum of several Fourier modes. However, previous numerical studies of the acoustics generated within the resonator assumed simple sinusoidal waves as the driving force. Using a previously developed numerical code, this paper demonstrates the effects of using a forcing function constructed with a series of harmonic sinusoidal waves on resonating cavities. From these results, a method will be demonstrated which allows the direct numerical analysis of experimentally generated nonlinear acoustic waves in resonators driven by harmonic forcing functions.
Nonlinear electrostatic ion-acoustic "oscilliton" waves driven by charge non-neutrality effects
Directory of Open Access Journals (Sweden)
J. Z. G. Ma
2011-01-01
Full Text Available Nonlinear "oscilliton" structures features a low-frequency (LF solitary envelope, the amplitude of which is modulated violently by superimposed high-frequency (HF oscillations. We have studied the charge non-neutrality effects on the excitation of electrostatic ion-acoustic (IA oscillitons. A two-fluid, warm plasma model is employed, and a set of nonlinear self-similar equations is solved in a cylindrical geometry. Under charge-neutrality conditions, three conventional IA structures (namely, sinusoidal, sawtooth, and spicky/bipolar are obtained. By contrast, under charge non-neutrality conditions, oscilliton structures are excited, where the LF envelope is in the sound-wave (SW mode, while the HF ingredients include the IA mode and the ion-Langmiur (IL mode. The amplitudes of the SW wave are violently modulated by the IA oscillations, whereas the upward sides of the IA amplitudes are modulated by the IL oscillations of smaller amplitudes, and the downward sides are modulated by hybrid IA/IL oscillations. The nonlinear oscillitons are found to be dependent not only upon the input parameters (e.g., the Mach number, the Debye length, and the initial temperature of particles, but on initial conditions as well.
DEFF Research Database (Denmark)
Christiansen, Peter Leth; Gaididei, Yuri Borisovich; Johansson, M.
1998-01-01
The dynamics of discrete two-dimensional nonlinear Schrodinger models with long-range dispersive interactions is investigated. In particular, we focus on the cases where the dispersion arises from a dipole-dipole interaction, assuming the dipole moments at each lattice site to be aligned either...
Nonlinear periodic waves in dusty plasma with variable dust charge
International Nuclear Information System (INIS)
Yadav, Lakhan Lal; Bharuthram, R.
2002-01-01
Using the reductive perturbation method, we present a theory of nonlinear periodic waves, viz. the cnoidal waves, in a dusty plasma consisting of electrons, ions, and cold dust grains with charge fluctuations, which in the limiting case reduce to dust acoustic solitons. It is found that the frequency of the dust acoustic cnoidal wave increases with its amplitude. The dust charge fluctuations are found to affect the characteristics of the cnoidal waves
Nonlinear spin wave coupling in adjacent magnonic crystals
Energy Technology Data Exchange (ETDEWEB)
Sadovnikov, A. V., E-mail: sadovnikovav@gmail.com; Nikitov, S. A. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation); Kotel' nikov Institute of Radioengineering and Electronics, Russian Academy of Sciences, Moscow 125009 (Russian Federation); Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E. [Laboratory “Metamaterials,” Saratov State University, Saratov 410012 (Russian Federation)
2016-07-25
We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.
Nonlinear spin wave coupling in adjacent magnonic crystals
International Nuclear Information System (INIS)
Sadovnikov, A. V.; Nikitov, S. A.; Beginin, E. N.; Morozova, M. A.; Sharaevskii, Yu. P.; Grishin, S. V.; Sheshukova, S. E.
2016-01-01
We have experimentally studied the coupling of spin waves in the adjacent magnonic crystals. Space- and time-resolved Brillouin light-scattering spectroscopy is used to demonstrate the frequency and intensity dependent spin-wave energy exchange between the side-coupled magnonic crystals. The experiments and the numerical simulation of spin wave propagation in the coupled periodic structures show that the nonlinear phase shift of spin wave in the adjacent magnonic crystals leads to the nonlinear switching regime at the frequencies near the forbidden magnonic gap. The proposed side-coupled magnonic crystals represent a significant advance towards the all-magnonic signal processing in the integrated magnonic circuits.
Evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations
Zhang, Linghai
2017-10-01
The main purposes of this paper are to accomplish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear system of reaction diffusion equations ut =uxx + α [ βH (u - θ) - u ] - w, wt = ε (u - γw) and to establish the existence, stability, instability and bifurcation of the nonlinear waves of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ], under different conditions on the model constants. To establish the bifurcation for the system, we will study the existence and instability of a standing pulse solution if 0 1; the existence and instability of two standing wave fronts if 2 (1 + αγ) θ = αβγ and 0 traveling wave front as well as the existence and instability of a standing pulse solution if 0 traveling wave front as well as the existence and instability of an upside down standing pulse solution if 0 traveling wave back of the nonlinear scalar reaction diffusion equation ut =uxx + α [ βH (u - θ) - u ] -w0, where w0 = α (β - 2 θ) > 0 is a positive constant, if 0 motivation to study the existence, stability, instability and bifurcations of the nonlinear waves is to study the existence and stability/instability of infinitely many fast/slow multiple traveling pulse solutions of the nonlinear system of reaction diffusion equations. The existence and stability of infinitely many fast multiple traveling pulse solutions are of great interests in mathematical neuroscience.
Qualitative aspects of nonlinear wave motion: Complexity and simplicity
International Nuclear Information System (INIS)
Engelbrecht, J.
1993-01-01
The nonlinear wave processes possess many qualitative properties which cannot be described by linear theories. In this presentation, an attempt is made to systematize the main aspects of this fascinating area. The sources of nonlinearities are analyzed in order to understand why and how the nonlinear mathematical models are formulated. The technique of evolution equations is discussed then as a main mathematical tool to separate multiwave processes into single waves. The evolution equations give concise but in many cases sufficient description of wave processes in solids permitting to analyze spectral changes, phase changes and velocities, coupling of waves, and interaction of nonlinearities with other physical effects of the same order. Several new problems are listed. Knowing the reasons, the seemingly complex problems can be effectively analyzed. 61 refs
Nonlinear surface waves at ferrite-metamaterial waveguide structure
Hissi, Nour El Houda; Mokhtari, Bouchra; Eddeqaqi, Noureddine Cherkaoui; Shabat, Mohammed Musa; Atangana, Jacques
2016-09-01
A new ferrite slab made of a metamaterial (MTM), surrounded by a nonlinear cover cladding and a ferrite substrate, was shown to support unusual types of electromagnetic surface waves. We impose the boundary conditions to derive the dispersion relation and others necessary to formulate the proposed structure. We analyse the dispersion properties of the nonlinear surface waves and we calculate the associated propagation index and the film-cover interface nonlinearity. In the calculation, several sets of the permeability of the MTM are considered. Results show that the waves behaviour depends on the values of the permeability of the MTM, the thickness of the waveguide and the film-cover interface nonlinearity. It is also shown that the use of the singular solutions to the electric field equation allows to identify several new properties of surface waves which do not exist in conventional waveguide.
Tribeche, Mouloud; Mayout, Saliha
2016-07-01
The combined effects of ionization, ion loss and electron suprathermality on dust ion- acoustic solitary waves in a collisional dusty plasma are examined. Carrying out a small but finite amplitude analysis, a damped Korteweg- de Vries (dK-- dV) equation is derived. The damping term decreases with the increase of the spectral index and saturates for Maxwellian electrons. Choosing typical plasma parameters, the analytical approximate solution of the dK- dV equation is numerically analyzed. We first neglect the ionization and ion loss effects and account only for collisions to estimate the relative importance between these damping terms which can act concurrently. Interestingly, we found that as the suprathermal character of the electrons becomes important, the strength of the collisions related dissipation becomes more important and causes the DIA solitary wave amplitude to decay more rapidly. Moreover, the collisional damping may largely prevail over the ionization and ion loss related damping. The latter becomes more effective as the electrons evolve far away from their thermal equilibrium. Our results complement and provide new insights into previously published work on this problem.
International Nuclear Information System (INIS)
Inc, Mustafa
2007-01-01
In this paper, the nonlinear dispersive Zakharov-Kuznetsov ZK(m, n, k) equations are solved exactly by using the Adomian decomposition method. The two special cases, ZK(2, 2, 2) and ZK(3, 3, 3), are chosen to illustrate the concrete scheme of the decomposition method in ZK(m, n, k) equations. General formulas for the solutions of ZK(m, n, k) equations are established
Nonlinear Electromagnetic Waves and Spherical Arc-Polarized Waves in Space Plasmas
Tsurutani, B.; Ho, Christian M.; Arballo, John K.; Lakhina, Gurbax S.; Glassmeier, Karl-Heinz; Neubauer, Fritz M.
1997-01-01
We review observations of nonlinear plasma waves detected by interplanetary spacecraft. For this paper we will focus primarily on the phase-steepened properties of such waves. Plasma waves at comet Giacobini-Zinner measured by the International Cometary Explorer (ICE), at comets Halley and Grigg-Skjellerup measured by Giotto, and interplanetary Alfven waves measured by Ulysses, will be discussed and intercompared.
Optical rogue waves and soliton turbulence in nonlinear fibre optics
DEFF Research Database (Denmark)
Genty, G.; Dudley, J. M.; de Sterke, C. M.
2009-01-01
We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required.......We examine optical rogue wave generation in nonlinear fibre propagation in terms of soliton turbulence. We show that higher-order dispersion is sufficient to generate localized rogue soliton structures, and Raman scattering effects are not required....
On Maximally Dissipative Shock Waves in Nonlinear Elasticity
Knowles, James K.
2010-01-01
Shock waves in nonlinearly elastic solids are, in general, dissipative. We study the following question: among all plane shock waves that can propagate with a given speed in a given one-dimensional nonlinearly elastic bar, which one—if any—maximizes the rate of dissipation? We find that the answer to this question depends strongly on the qualitative nature of the stress-strain relation characteristic of the given material. When maximally dissipative shocks do occur, they propagate according t...
DEFF Research Database (Denmark)
Guo, Hairun; Zeng, Xianglong; Zhou, Binbin
2013-01-01
We interpret the purely spectral forward Maxwell equation with up to third-order induced polarizations for pulse propagation and interactions in quadratic nonlinear crystals. The interpreted equation, also named the nonlinear wave equation in the frequency domain, includes quadratic and cubic...... nonlinearities, delayed Raman effects, and anisotropic nonlinearities. The full potential of this wave equation is demonstrated by investigating simulations of solitons generated in the process of ultrafast cascaded second-harmonic generation. We show that a balance in the soliton delay can be achieved due...
Green function formalism for nonlinear acoustic waves in layered media
International Nuclear Information System (INIS)
Lobo, A.; Tsoy, E.; De Sterke, C.M.
2000-01-01
Full text: The applications of acoustic waves in identifying defects in adhesive bonds between metallic plates have received little attention at high intensities where the media respond nonlinearly. However, the effects of reduced bond strength are more distinct in the nonlinear response of the structure. Here we assume a weak nonlinearity acting as a small perturbation, thereby reducing the problem to a linear one. This enables us to develop a specialized Green function formalism for calculating acoustic fields in layered media
Defocusing regimes of nonlinear waves in media with negative dispersion
DEFF Research Database (Denmark)
Bergé, L.; Kuznetsov, E.A.; Juul Rasmussen, J.
1996-01-01
Defocusing regimes of quasimonochromatic waves governed by a nonlinear Schrodinger equation with mixed-sign dispersion are investigated. For a power-law nonlinearity, we show that localized solutions to this equation defined at the so-called critical dimension cannot collapse in finite time...
Exact travelling wave solutions for some important nonlinear
Indian Academy of Sciences (India)
The two-dimensional nonlinear physical models and coupled nonlinear systems such as Maccari equations, Higgs equations and Schrödinger–KdV equations have been widely applied in many branches of physics. So, finding exact travelling wave solutions of such equations are very helpful in the theories and numerical ...
New travelling wave solutions for nonlinear stochastic evolution
Indian Academy of Sciences (India)
The nonlinear stochastic evolution equations have a wide range of applications in physics, chemistry, biology, economics and finance from various points of view. In this paper, the (′/)-expansion method is implemented for obtaining new travelling wave solutions of the nonlinear (2 + 1)-dimensional stochastic ...
Stability of nonlinear waves and patterns and related topics
Ghazaryan, Anna; Lafortune, Stephane; Manukian, Vahagn
2018-04-01
Periodic and localized travelling waves such as wave trains, pulses, fronts and patterns of more complex structure often occur in natural and experimentally built systems. In mathematics, these objects are realized as solutions of nonlinear partial differential equations. The existence, dynamic properties and bifurcations of those solutions are of interest. In particular, their stability is important for applications, as the waves that are observable are usually stable. When the waves are unstable, further investigation is warranted of the way the instability is exhibited, i.e. the nature of the instability, and also coherent structures that appear as a result of an instability of travelling waves. A variety of analytical, numerical and hybrid techniques are used to study travelling waves and their properties. This article is part of the theme issue `Stability of nonlinear waves and patterns and related topics'.
International Nuclear Information System (INIS)
Mirzade, Fikret Kh.
2005-01-01
The propagation of longitudinal strain wave in a plate with quadratic nonlinearity of elastic continuum was studied in the context of a model that takes into account the joint dynamics of elastic displacements in the medium and the concentration of the nonequilibrium laser-induced point defects. The input equations of the problem are reformulated in terms of only the total displacements of the medium points. In this case, the presence of structural defects manifests itself in the emergence of a delayed response of the system to the propagation of the strain-related perturbations, which is characteristic of media with relaxation or memory. The model equations describing the nonlinear displacement wave were derived with allowance made for the values of the relaxation parameter. The influence of the generation and relaxation of lattice defects on the propagation of this wave was analyzed. It is shown that, for short relaxation times of defects, the strain can propagate in the form of shock fronts. In the case of longer relaxation times, shock waves do not form and the strain wave propagates only in the form of solitary waves or a train of solitons. The contributions of the finiteness of the defect-recombination rate to linear and nonlinear elastic modulus, and spatial dispersion are determined
Lamb Wave Technique for Ultrasonic Nonlinear Characterization in Elastic Plates
International Nuclear Information System (INIS)
Lee, Tae Hun; Kim, Chung Seok; Jhang, Kyung Young
2010-01-01
Since the acoustic nonlinearity is sensitive to the minute variation of material properties, the nonlinear ultrasonic technique(NUT) has been considered as a promising method to evaluate the material degradation or fatigue. However, there are certain limitations to apply the conventional NUT using the bulk wave to thin plates. In case of plates, the use of Lamb wave can be considered, however, the propagation characteristics of Lamb wave are completely different with the bulk wave, and thus the separate study for the nonlinearity of Lamb wave is required. For this work, this paper analyzed first the conditions of mode pair suitable for the practical application as well as for the cumulative propagation of quadratic harmonic frequency and summarized the result in for conditions: phase matching, non-zero power flux, group velocity matching, and non-zero out-of-plane displacement. Experimental results in aluminum plates showed that the amplitude of the secondary Lamb wave and nonlinear parameter grew up with increasing propagation distance at the mode pair satisfying the above all conditions and that the ration of nonlinear parameters measured in Al6061-T6 and Al1100-H15 was closed to the ratio of the absolute nonlinear parameters
International Nuclear Information System (INIS)
Shang Yadong
2008-01-01
The extended hyperbolic functions method for nonlinear wave equations is presented. Based on this method, we obtain a multiple exact explicit solutions for the nonlinear evolution equations which describe the resonance interaction between the long wave and the short wave. The solutions obtained in this paper include (a) the solitary wave solutions of bell-type for S and L, (b) the solitary wave solutions of kink-type for S and bell-type for L, (c) the solitary wave solutions of a compound of the bell-type and the kink-type for S and L, (d) the singular travelling wave solutions, (e) periodic travelling wave solutions of triangle function types, and solitary wave solutions of rational function types. The variety of structure to the exact solutions of the long-short wave equation is illustrated. The methods presented here can also be used to obtain exact solutions of nonlinear wave equations in n dimensions
Exact Solutions for Nonlinear Differential Difference Equations in Mathematical Physics
Directory of Open Access Journals (Sweden)
Khaled A. Gepreel
2013-01-01
Full Text Available We modified the truncated expansion method to construct the exact solutions for some nonlinear differential difference equations in mathematical physics via the general lattice equation, the discrete nonlinear Schrodinger with a saturable nonlinearity, the quintic discrete nonlinear Schrodinger equation, and the relativistic Toda lattice system. Also, we put a rational solitary wave function method to find the rational solitary wave solutions for some nonlinear differential difference equations. The proposed methods are more effective and powerful to obtain the exact solutions for nonlinear difference differential equations.
Propagation of nonlinear ion acoustic wave with generation of long-wavelength waves
International Nuclear Information System (INIS)
Ohsawa, Yukiharu; Kamimura, Tetsuo
1978-01-01
The nonlinear propagation of the wave packet of an ion acoustic wave with wavenumber k 0 asymptotically equals k sub(De) (the electron Debye wavenumber) is investigated by computer simulations. From the wave packet of the ion acoustic wave, waves with long wavelengths are observed to be produced within a few periods for the amplitude oscillation of the original wave packet. These waves are generated in the region where the original wave packet exists. Their characteristic wavelength is of the order of the length of the wave packet, and their propagation velocity is almost equal to the ion acoustic speed. The long-wavelength waves thus produced strongly affect the nonlinear evolution of the original wave packet. (auth.)
Grammatico, Sara; Scalzulli, Emilia; Petrucci, Maria Teresa
2017-01-01
Solitary plasmacytoma is a rare disease characterized by a localized proliferation of neoplastic monoclonal plasma cells, without evidence of systemic disease. It can be subdivided into solitary bone plasmacytoma, if the lesion originates in bone, or solitary extramedullary plasmacytoma, if the lesion involves a soft tissue. Incidence of solitary bone plasmacytoma is higher than solitary extramedullary plasmacytoma. Also prognosis is different: even if both forms respond well to treatment, ov...
Symbolic computation of nonlinear wave interactions on MACSYMA
International Nuclear Information System (INIS)
Bers, A.; Kulp, J.L.; Karney, C.F.F.
1976-01-01
In this paper the use of a large symbolic computation system - MACSYMA - in determining approximate analytic expressions for the nonlinear coupling of waves in an anisotropic plasma is described. MACSYMA was used to implement the solutions of a fluid plasma model nonlinear partial differential equations by perturbation expansions and subsequent iterative analytic computations. By interacting with the details of the symbolic computation, the physical processes responsible for particular nonlinear wave interactions could be uncovered and appropriate approximations introduced so as to simplify the final analytic result. Details of the MACSYMA system and its use are discussed and illustrated. (Auth.)
Nonlinear pattern formation of Faraday waves
Binks, D.J.; Water, van de W.
1997-01-01
A cascade of surface wave patterns with increasing rotational symmetry ranging from simple square to tenfold quasiperiodic is observed for Faraday waves. The experiment concerns the excitation of subharmonic standing surface waves by oscillating vertical acceleration. Our observation agrees with the
International Nuclear Information System (INIS)
Esfandyari-Kalejahi, A.; Akbari-Moghanjoughi, M.; Mehdipoor, M.
2009-01-01
Ion-acoustic (IA) solitary waves are investigated in a magnetized three-component plasma consisting of cold ions, isothermal hot electrons, and positrons. The basic set of fluid equations is reduced to the Korteweg de Vries equation using the standard reductive perturbation (multiple-scale) technique. Theoretical and numerical analyses confirm significant effects of the presence of positrons and the dependence of the electron to positron temperature ratio on the amplitude and the width of IA solitary waves. It is shown that the rarefactive and compressive IA solitary excitations can propagate when the propagation angle θ satisfies 0≤θ 0 , whereas their width depends strictly on B 0 . The numerical analysis has been done based on the typical numerical data from a pulsar magnetosphere.
Nonlinear waves in electron–positron–ion plasmas including charge ...
Indian Academy of Sciences (India)
2017-01-04
Jan 4, 2017 ... The introduction of the Poisson equation increased the Mach number required to generate the waveforms but the driving electric field E0 was reduced. The results are compared with satellite observations. Keywords. Nonlinear waves; low frequency; ion-acoustic waves. PACS Nos 52.35.Qz; 52.35.Fp; 52.35 ...
Droghei, R.; Falcini, F.; Casalbore, D.; Martorelli, E.; Mosetti, R.; Sannino, G.; Santoleri, R.; Chiocci, F. L.
2016-11-01
Subaqueous, asymmetric sand waves are typically observed in marine channel/canyon systems, tidal environments, and continental slopes exposed to strong currents, where they are formed by current shear resulting from a dominant unidirectional flow. However, sand-wave fields may be readily observed in marine environments where no such current exists; the physical processes driving their formation are enigmatic or not well understood. We propose that internal solitary waves (ISWs) induced by tides can produce an effective, unidirectional boundary “current” that forms asymmetric sand waves. We test this idea by examining a sand-wave field off the Messina Strait, where we hypothesize that ISWs formed at the interface between intermediate and surface waters are refracted by topography. Hence, we argue that the deflected pattern (i.e., the depth-dependent orientation) of the sand-wave field is due to refraction of such ISWs. Combining field observations and numerical modelling, we show that ISWs can account for three key features: ISWs produce fluid velocities capable of mobilizing bottom sediments; the predicted refraction pattern resulting from the interaction of ISWs with bottom topography matches the observed deflection of the sand waves; and predicted migration rates of sand waves match empirical estimates. This work shows how ISWs may contribute to sculpting the structure of continental margins and it represents a promising link between the geological and oceanographic communities.
Shen, Yujia; Wen, Zichao; Yan, Zhenya; Hang, Chao
2018-04-01
We study the three-wave interaction that couples an electromagnetic pump wave to two frequency down-converted daughter waves in a quadratic optical crystal and P T -symmetric potentials. P T symmetric potentials are shown to modulate stably nonlinear modes in two kinds of three-wave interaction models. The first one is a spatially extended three-wave interaction system with odd gain-and-loss distribution in the channel. Modulated by the P T -symmetric single-well or multi-well Scarf-II potentials, the system is numerically shown to possess stable soliton solutions. Via adiabatical change of system parameters, numerical simulations for the excitation and evolution of nonlinear modes are also performed. The second one is a combination of P T -symmetric models which are coupled via three-wave interactions. Families of nonlinear modes are found with some particular choices of parameters. Stable and unstable nonlinear modes are shown in distinct families by means of numerical simulations. These results will be useful to further investigate nonlinear modes in three-wave interaction models.
Directional nonlinear guided wave mixing: Case study of counter-propagating shear horizontal waves
Hasanian, Mostafa; Lissenden, Cliff J.
2018-04-01
While much nonlinear ultrasonics research has been conducted on higher harmonic generation, wave mixing provides the potential for sensitive measurements of incipient damage unencumbered by instrumentation nonlinearity. Studies of nonlinear ultrasonic wave mixing, both collinear and noncollinear, for bulk waves have shown the robust capability of wave mixing for early damage detection. One merit of bulk wave mixing lies in their non-dispersive nature, but guided waves enable inspection of otherwise inaccessible material and a variety of mixing options. Co-directional guided wave mixing was studied previously, but arbitrary direction guided wave mixing has not been addressed until recently. Wave vector analysis is applied to study variable mixing angles to find wave mode triplets (two primary waves and a secondary wave) resulting in the phase matching condition. As a case study, counter-propagating Shear Horizontal (SH) guided wave mixing is analyzed. SH wave interactions generate a secondary Lamb wave mode that is readily receivable. Reception of the secondary Lamb wave mode is compared for an angle beam transducer, an air coupled transducer, and a laser Doppler vibrometer (LDV). Results from the angle beam and air coupled transducers are quite consistent, while the LDV measurement is plagued by variability issues.
Nonlinear frequency shift of finite-amplitude electrostatic surface waves
International Nuclear Information System (INIS)
Stenflo, L.
1989-01-01
The problem concerning the appropriate form for the nonlinear frequency shift arising from slow density modulations of electrostatic surface waves in a semi-infinite unmagnetized plasma is reconsidered. The spatial dependence of the wave amplitude normal to the surface is kept general in order to allow for possible nonlinear attenuation behaviour of the surface waves. It is found that if the frequency shift is expressed as a function of the density and its gradient then the result is identical with that of Zhelyazkov, I. Proceedings International Conference on Plasma Physics, Kiev, 1987, Vol. 2, p. 694, who assumed a linear exponential attenuation behaviour. (author)
Soliton Steering by Longitudinal Modulation of the Nonlinearity in Waveguide Arrays
Assanto, Gaetano; Cisneros, Luis A.; Minzoni, Antonmaria A.; Skuse, Benjamin D.; Smyth, Noel F.; Worthy, Annette L.
2010-01-01
We show how discrete solitary waves in one and two-dimensional waveguide arrays can be steered across the lattice via the introduction of a longitudinal periodic modulation of the nonlinear response. Through parametric energy transfer from the modulation to the solitary wave, the latter can increase its width and overcome the Peierls-Nabarro potential to propagate freely.
Nonlinear periodic space-charge waves in plasma
International Nuclear Information System (INIS)
Kovalev, V. A.
2009-01-01
A solution is obtained in the form of coupled nonlinear periodic space-charge waves propagating in a magnetoactive plasma. The wave spectrum in the vicinity of the critical point, where the number of harmonics increases substantially, is found to fall with harmonic number as ∝ s -1/3 . Periodic space-charge waves are invoked to explain the zebra pattern in the radio emission from solar flares.
Modelization of highly nonlinear waves in coastal regions
Gouin, Maïté; Ducrozet, Guillaume; Ferrant, Pierre
2015-04-01
The proposed work deals with the development of a highly non-linear model for water wave propagation in coastal regions. The accurate modelization of surface gravity waves is of major interest in ocean engineering, especially in the field of marine renewable energy. These marine structures are intended to be settled in coastal regions where the effect of variable bathymetry may be significant on local wave conditions. This study presents a numerical model for the wave propagation with complex bathymetry. It is based on High-Order Spectral (HOS) method, initially limited to the propagation of non-linear wave fields over flat bottom. Such a model has been developed and validated at the LHEEA Lab. (Ecole Centrale Nantes) over the past few years and the current developments will enlarge its application range. This new numerical model will keep the interesting numerical properties of the original pseudo-spectral approach (convergence, efficiency with the use of FFTs, …) and enable the possibility to propagate highly non-linear wave fields over long time and large distance. Different validations will be provided in addition to the presentation of the method. At first, Bragg reflection will be studied with the proposed approach. If the Bragg condition is satisfied, the reflected wave generated by a sinusoidal bottom patch should be amplified as a result of resonant quadratic interactions between incident wave and bottom. Comparisons will be provided with experiments and reference solutions. Then, the method will be used to consider the transformation of a non-linear monochromatic wave as it propagates up and over a submerged bar. As the waves travel up the front slope of the bar, it steepens and high harmonics are generated due to non-linear interactions. Comparisons with experimental data will be provided. The different test cases will assess the accuracy and efficiency of the method proposed.
Nonlinear dust-ion-acoustic waves in a multi-ion plasma with ...
Indian Academy of Sciences (India)
The basic features of such dust-ion-acoustic solitary and shock waves have been ... ion plasmas because of its vital role in understanding different types of ... cannot support the usual ion-acoustic waves, but can support the DIA waves of ...
New, A. L.; Magalhaes, J. M.; da Silva, J. C. B.
2013-09-01
Energetic Internal Solitary Waves (ISWs) were recently discovered radiating from the central region of the Mascarene Plateau in the south-western Indian Ocean (da Silva et al., 2011). SAR imagery revealed the two-dimensional structure of the waves which propagated for several hundred kilometres in deep water both to the east and west of a sill, located near 12.5°S, 61°E between the Saya de Malha and Nazareth banks. These waves were presumed to originate from the disintegration of a large lee wave formed on the western side of the sill at the time of maximum barotropic flow to the west. In the present paper we focus instead on ISWs propagating in the shallow water above the Saya da Malha (SM) bank (to the north of the sill), rather than on those propagating in deep water (here denominated as type-I or -II waves if propagating to the west or east respectively). Analysis of an extended SAR image dataset reveals strong sea surface signatures of complex patterns of ISWs propagating over the SM bank arising from different sources. We identify three distinct types of waves, and propose suitable generation mechanisms for them using synergy from different remotely sensed datasets, together with analyses of linear phase speeds (resulting from local stratification and bathymetry). In particular, we find a family of ISWs (termed here A-type waves) which results from the disintegration of a lee wave which forms on the western slopes of SM. We also identify two further wave trains (B- and C-type waves) which we suggest result from refraction of the deep water type-I and -II waves onto the SM bank. Therefore, both B- and C-type waves can be considered to result from the same generation source as the type-I and -II waves. Finally, we consider the implications of the ISWs for mixing and biological production over the SM bank, and provide direct evidence, from ocean colour satellite images, of enhanced surface chlorophyll over a shallow topographic feature on the bank, which is
Nonlinear excitation of geodesic acoustic modes by drift waves
International Nuclear Information System (INIS)
Chakrabarti, N.; Singh, R.; Kaw, P. K.; Guzdar, P. N.
2007-01-01
In this paper, two mode-coupling analyses for the nonlinear excitation of the geodesic acoustic modes (GAMs) in tokamak plasmas by drift waves are presented. The first approach is a coherent parametric process, which leads to a three-wave resonant interaction. This investigation allows for the drift waves and the GAMs to have comparable scales. The second approach uses the wave-kinetic equations for the drift waves, which then couples to the GAMs. This requires that the GAM scale length be large compared to the wave packet associated with the drift waves. The resonance conditions for these two cases lead to specific predictions of the radial wave number of the excited GAMs
Nonlinear Waves on Stochastic Support: Calcium Waves in Astrocyte Syncytia
Jung, P.; Cornell-Bell, A. H.
Astrocyte-signaling has been observed in cell cultures and brain slices in the form of Calcium waves. Their functional relevance for neuronal communication, brain functions and diseases is, however, not understood. In this paper, the propagation of intercellular calcium waves is modeled in terms of waves in excitable media on a stochastic support. We utilize a novel method to decompose the spatiotemporal patterns into space-time clusters (wave fragments). Based on this cluster decomposition, a statistical description of wave patterns is developed.
Alfven wave resonances and flow induced by nonlinear Alfven waves in a stratified atmosphere
International Nuclear Information System (INIS)
Stark, B. A.; Musielak, Z. E.; Suess, S. T.
1996-01-01
A nonlinear, time-dependent, ideal MHD code has been developed and used to compute the flow induced by nonlinear Alfven waves propagating in an isothermal, stratified, plane-parallel atmosphere. The code is based on characteristic equations solved in a Lagrangian frame. Results show that resonance behavior of Alfven waves exists in the presence of a continuous density gradient and that the waves with periods corresponding to resonant peaks exert considerably more force on the medium than off-resonance periods. If only off-peak periods are considered, the relationship between the wave period and induced longitudinal velocity shows that short period WKB waves push more on the background medium than longer period, non-WKB, waves. The results also show the development of the longitudinal waves induced by finite amplitude Alfven waves. Wave energy transferred to the longitudinal mode may provide a source of localized heating
Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report
International Nuclear Information System (INIS)
Tataronis, J. A.
2004-01-01
This program treats theoretically low frequency linear and nonlinear wave processes in magnetized plasmas. A primary objective has been to evaluate the effectiveness of MHD waves to heat plasma and drive current in toroidal configurations. The research covers the following topics: (1) the existence and properties of the MHD continua in plasma equilibria without spatial symmetry; (2) low frequency nonresonant current drive and nonlinear Alfven wave effects; and (3) nonlinear electron acceleration by rf and random plasma waves. Results have contributed to the fundamental knowledge base of MHD activity in symmetric and asymmetric toroidal plasmas. Among the accomplishments of this research effort, the following are highlighted: Identification of the MHD continuum mode singularities in toroidal geometry. Derivation of a third order ordinary differential equation that governs nonlinear current drive in the singular layers of the Alfven continuum modes in axisymmetric toroidal geometry. Bounded solutions of this ODE implies a net average current parallel to the toroidal equilibrium magnetic field. Discovery of a new unstable continuum of the linearized MHD equation in axially periodic circular plasma cylinders with shear and incompressibility. This continuum, which we named ''accumulation continuum'' and which is related to ballooning modes, arises as discrete unstable eigenfrequency accumulate on the imaginary frequency axis in the limit of large mode numbers. Development of techniques to control nonlinear electron acceleration through the action of multiple coherent and random plasmas waves. Two important elements of this program aye student participation and student training in plasma theory
Constrained non-linear waves for offshore wind turbine design
International Nuclear Information System (INIS)
Rainey, P J; Camp, T R
2007-01-01
Advancements have been made in the modelling of extreme wave loading in the offshore environment. We give an overview of wave models used at present, and their relative merits. We describe a method for embedding existing non-linear solutions for large, regular wave kinematics into linear, irregular seas. Although similar methods have been used before, the new technique is shown to offer advances in computational practicality, repeatability, and accuracy. NewWave theory has been used to constrain the linear simulation, allowing best possible fit with the large non-linear wave. GH Bladed was used to compare the effect of these models on a generic 5 MW turbine mounted on a tripod support structure
International Nuclear Information System (INIS)
Li Shi-You; Zhang Shi-Feng; Cai Hong; Deng Xiao-Hua
2012-01-01
Analysis on the spatial structure of electrostatic solitary waves (ESWs) along the plasma sheet boundary layer (PSBL) near an on-going magnetic reconnection X-line is performed. Most of the ESWs in the PSBL of R3 region near reconnection X-line are propagating earthwards away from the reconnecting site. An analysis of their spatial structure shows that, when ESWs propagate along the ambient field in the PSBL, outwards from the magnetic reconnection X-line, their amplitude will finally attenuate and thus the electron hole will fade away but their spatial scale remains unchanged. However, the spatial structure of propagating ESWs evolves from 1-D-like to 2-D-like though totally in a 1-D structure. (geophysics, astronomy, and astrophysics)
Li, S. Y.; Zhang, S. F.; Cai, H.; Chen, X. Q.; Deng, X. H.
2013-06-01
In this paper, we report the observations and statistical characteristics of tripolar electrostatic solitary waves (ESWs) along the plasma sheet boundary layer near the magnetic reconnection X line in the near-Earth magnetotail. Within reconnection diffusion region, the tripolar ESWs are ample and are continuously observed during one burst interval (8.75 s) of the Geotail/WaveForm Capture in the neutral plasma sheet where β > 1 on 10:20 UT, 2 February 1996. The tripolar ESW is suggested to be one kind of steady-going solitary structure. More than 200 waveforms with clear tripolar characteristics are differentiated for statistical analysis, and result shows that (1) their amplitude is within 100->500 μV/m, with an average amplitude of about 254 μV/m; (2) the pulse width of the tripolar ESWs is 0.5-1.0 ms, with an average value of about 0.75 ms; (3) it is asymmetrical in both the amplitude and pulse width of the tripolar ESWs: most part of the tripolar ESWs (about 76.5%) are asymmetrical in the amplitude of one hump and the other one, and more than 75% (about 177 amount the 236 waveforms) of the tripolar ESWs are asymmetrical in the time duration of the two humps in the waveform; (4) most of the tripolar ESWs are with the potential humps of 10-60 mV, small ratio of them with potential humps larger than 100 mV. The tripolar ESWs with net potential drop of about 10-50 mV can be interpreted as "weak" double layers. The possible generation mechanism of tripolar ESWs and their role in reconnection are discussed by studying the particle distribution during which the tripolar ESWs are continuously observed. The observation of tripolar ESWs presents evidence of complex structure of electron holes within the reconnection diffusion region and is helpful to the understanding of the energy release process of reconnection.
Nonlinear response and bistability of driven ion acoustic waves
Akbari-Moghanjoughi, M.
2017-08-01
The hydrodynamic model is used to obtain a generalized pseudoforce equation through which the nonlinear response of periodically driven ion acoustic waves is studied in an electron-ion plasma with isothermal and adiabatic ion fluids. The pseudotime series, corresponding to different driving frequencies, indicates that nonlinearity effects appear more strongly for smaller frequency values. The existence of extra harmonic resonances in the nonlinear amplitude spectrum is a clear indication of the interaction of an external force with harmonic components of the nonlinear ion acoustic waves. It is shown that many plasma parameters significantly and differently affect the nonlinear resonance spectrum of ion acoustic excitations. A heuristic but accurate model for the foldover effect is used which quite satisfactorily predicts the bistability of driven plasma oscillations. It is remarked that the characteristic resonance peak of isothermal ion plasma oscillations appears at lower frequencies but is stronger compared to that of adiabatic ions. Comparison of the exact numerical results for fully nonlinear and approximate (weakly nonlinear) models indicates that a weakly nonlinear model exaggerates the hysteresis and jump phenomenon for higher values of the external force amplitude.
Energy Technology Data Exchange (ETDEWEB)
Torello, David [GW Woodruff School of Mechanical Engineering, Georgia Tech (United States); Kim, Jin-Yeon [School of Civil and Environmental Engineering, Georgia Tech (United States); Qu, Jianmin [Department of Civil and Environmental Engineering, Northwestern University (United States); Jacobs, Laurence J. [School of Civil and Environmental Engineering, Georgia Tech and GW Woodruff School of Mechanical Engineering, Georgia Tech (United States)
2015-03-31
This research considers the effects of diffraction, attenuation, and the nonlinearity of generating sources on measurements of nonlinear ultrasonic Rayleigh wave propagation. A new theoretical framework for correcting measurements made with air-coupled and contact piezoelectric receivers for the aforementioned effects is provided based on analytical models and experimental considerations. A method for extracting the nonlinearity parameter β{sub 11} is proposed based on a nonlinear least squares curve-fitting algorithm that is tailored for Rayleigh wave measurements. Quantitative experiments are conducted to confirm the predictions for the nonlinearity of the piezoelectric source and to demonstrate the effectiveness of the curve-fitting procedure. These experiments are conducted on aluminum 2024 and 7075 specimens and a β{sub 11}{sup 7075}/β{sub 11}{sup 2024} measure of 1.363 agrees well with previous literature and earlier work.
Analytical and numerical investigation of nonlinear internal gravity waves
Directory of Open Access Journals (Sweden)
S. P. Kshevetskii
2001-01-01
Full Text Available The propagation of long, weakly nonlinear internal waves in a stratified gas is studied. Hydrodynamic equations for an ideal fluid with the perfect gas law describe the atmospheric gas behaviour. If we neglect the term Ͽ dw/dt (product of the density and vertical acceleration, we come to a so-called quasistatic model, while we name the full hydro-dynamic model as a nonquasistatic one. Both quasistatic and nonquasistatic models are used for wave simulation and the models are compared among themselves. It is shown that a smooth classical solution of a nonlinear quasistatic problem does not exist for all t because a gradient catastrophe of non-linear internal waves occurs. To overcome this difficulty, we search for the solution of the quasistatic problem in terms of a generalised function theory as a limit of special regularised equations containing some additional dissipation term when the dissipation factor vanishes. It is shown that such solutions of the quasistatic problem qualitatively differ from solutions of a nonquasistatic nature. It is explained by the fact that in a nonquasistatic model the vertical acceleration term plays the role of a regularizator with respect to a quasistatic model, while the solution qualitatively depends on the regularizator used. The numerical models are compared with some analytical results. Within the framework of the analytical model, any internal wave is described as a system of wave modes; each wave mode interacts with others due to equation non-linearity. In the principal order of a perturbation theory, each wave mode is described by some equation of a KdV type. The analytical model reveals that, in a nonquasistatic model, an internal wave should disintegrate into solitons. The time of wave disintegration into solitons, the scales and amount of solitons generated are important characteristics of the non-linear process; they are found with the help of analytical and numerical investigations. Satisfactory
Nonlinear wave chaos: statistics of second harmonic fields.
Zhou, Min; Ott, Edward; Antonsen, Thomas M; Anlage, Steven M
2017-10-01
Concepts from the field of wave chaos have been shown to successfully predict the statistical properties of linear electromagnetic fields in electrically large enclosures. The Random Coupling Model (RCM) describes these properties by incorporating both universal features described by Random Matrix Theory and the system-specific features of particular system realizations. In an effort to extend this approach to the nonlinear domain, we add an active nonlinear frequency-doubling circuit to an otherwise linear wave chaotic system, and we measure the statistical properties of the resulting second harmonic fields. We develop an RCM-based model of this system as two linear chaotic cavities coupled by means of a nonlinear transfer function. The harmonic field strengths are predicted to be the product of two statistical quantities and the nonlinearity characteristics. Statistical results from measurement-based calculation, RCM-based simulation, and direct experimental measurements are compared and show good agreement over many decades of power.
Computer simulations on the nonlinear frequency shift and nonlinear modulation of ion-acoustic waves
International Nuclear Information System (INIS)
Ohsawa, Yukiharu; Kamimura, Tetsuo.
1976-11-01
The nonlinear behavior of ion-acoustic waves with rather short wave-length, k lambda sub(De) asymptotically equals 1, is investigated by computer sumulations. It is observed that the nonlinear frequency shift is negative and is proportional to square root of the initial wave amplitude when the amplitude is not too large. This proportionality breaks down and the frequency shift can become positive (for large Te/Ti), when (n tilde sub(i)/n 0 )sup(1/2)>0.25, where n tilde sub(i) is the ion density perturbation and n 0 the average plasma density. Nonlinear modulation of the wave-packet is clearly seen; however, modulational instability was not observed. The importance of the effects of trapped ions to these phenomena is emphasized. (auth.)
Nonlinear wave particle interaction in the Earth's foreshock
Mazelle, C.; LeQueau, D.; Meziane, K.; Lin, R. P.; Parks, G.; Reme, H.; Sanderson, T.; Lepping, R. P.
1997-01-01
The possibility that ion beams could provide a free energy source for driving an ion/ion instability responsible for the ULF wave occurrence is investigated. For this, the wave dispersion relation with the observed parameters is solved. Secondly, it is shown that the ring-like distributions could then be produced by a coherent nonlinear wave-particle interaction. It tends to trap the ions into narrow cells in velocity space centered around a well-defined pitch-angle, directly related to the saturation wave amplitude in the analytical theory. The theoretical predictions with the observations are compared.
Nonlinear transient waves in coupled phase oscillators with inertia.
Jörg, David J
2015-05-01
Like the inertia of a physical body describes its tendency to resist changes of its state of motion, inertia of an oscillator describes its tendency to resist changes of its frequency. Here, we show that finite inertia of individual oscillators enables nonlinear phase waves in spatially extended coupled systems. Using a discrete model of coupled phase oscillators with inertia, we investigate these wave phenomena numerically, complemented by a continuum approximation that permits the analytical description of the key features of wave propagation in the long-wavelength limit. The ability to exhibit traveling waves is a generic feature of systems with finite inertia and is independent of the details of the coupling function.
Nonlinear modulation of torsional waves in elastic rod. [Instability
Energy Technology Data Exchange (ETDEWEB)
Hirao, M; Sugimoto, N [Osaka Univ., Toyonaka (Japan). Faculty of Engineering Science
1977-06-01
Nonlinear Schroedinger equation, which describes the nonlinear modulation of dispersive torsional waves in an elastic rod of circular cross-section, is derived by the derivative expansion method. It is found, for the lowest dispersive mode, that the modulational instability occurs except in the range of the carrier wavenumber, 2.799
Nonlinear approximation with general wave packets
DEFF Research Database (Denmark)
Borup, Lasse; Nielsen, Morten
2005-01-01
We study nonlinear approximation in the Triebel-Lizorkin spaces with dictionaries formed by dilating and translating one single function g. A general Jackson inequality is derived for best m-term approximation with such dictionaries. In some special cases where g has a special structure, a complete...
On the Stochastic Wave Equation with Nonlinear Damping
International Nuclear Information System (INIS)
Kim, Jong Uhn
2008-01-01
We discuss an initial boundary value problem for the stochastic wave equation with nonlinear damping. We establish the existence and uniqueness of a solution. Our method for the existence of pathwise solutions consists of regularization of the equation and data, the Galerkin approximation and an elementary measure-theoretic argument. We also prove the existence of an invariant measure when the equation has pure nonlinear damping
Ganguli, G.; Crabtree, C. E.; Rudakov, L.; Mithaiwala, M.
2014-12-01
Velocity ring instabilities are a common naturally occuring magnetospheric phenomenon that can also be generated by man made ionospheric experiments. These instabilities are known to generate lower-hybrid waves, which generally cannot propagte out of the source region. However, nonlinear wave physics can convert these linearly driven electrostatic lower-hybrid waves into electromagnetic waves that can escape the source region. These nonlinearly generated waves can be an important source of VLF turbulence that controls the trapped electron lifetime in the radiation belts. We develop numerical solutions to the wave-kinetic equation in a periodic box including the effects of nonlinear (NL) scattering (nonlinear Landau damping) of Lower-hybrid waves giving the evolution of the wave-spectra in wavenumber space. Simultaneously we solve the particle diffusion equation of both the background plasma particles and the ring ions, due to both linear and nonlinear Landau resonances. At initial times for cold ring ions, an electrostatic beam mode is excited, while the kinetic mode is stable. As the instability progresses the ring ions heat, the beam mode is stabilized, and the kinetic mode destabilizes. When the amplitude of the waves becomes sufficient the lower-hybrid waves are scattered (by either nearly unmagnetized ions or magnetized electrons) into electromagnetic magnetosonic waves [Ganguli et al 2010]. The effect of NL scattering is to limit the amplitude of the waves, slowing down the quasilinear relaxation time and ultimately allowing more energy from the ring to be liberated into waves [Mithaiwala et al. 2011]. The effects of convection out of the instability region are modeled, additionally limiting the amplitude of the waves, allowing further energy to be liberated from the ring [Scales et al., 2012]. Results are compared to recent 3D PIC simulations [Winske and Duaghton 2012].
Nonlinearly driven oscillations in the gyrotron traveling-wave amplifier
International Nuclear Information System (INIS)
Chiu, C. C.; Pao, K. F.; Yan, Y. C.; Chu, K. R.; Barnett, L. R.; Luhmann, N. C. Jr.
2008-01-01
By delivering unprecedented power and gain, the gyrotron traveling-wave amplifier (gyro-TWT) offers great promise for advanced millimeter wave radars. However, the underlying physics of this complex nonlinear system is yet to be fully elucidated. Here, we report a new phenomenon in the form of nonlinearly driven oscillations. A zero-drive stable gyro-TWT is shown to be susceptible to a considerably reduced dynamic range at the band edge, followed by a sudden transition into driven oscillations and then a hysteresis effect. An analysis of this unexpected behavior and its physical interpretation are presented.
Propagation of Quasi-plane Nonlinear Waves in Tubes
Directory of Open Access Journals (Sweden)
P. Koníček
2002-01-01
Full Text Available This paper deals with possibilities of using the generalized Burgers equation and the KZK equation to describe nonlinear waves in circular ducts. A new method for calculating of diffraction effects taking into account boundary layer effects is described. The results of numerical solutions of the model equations are compared. Finally, the limits of validity of the used model equations are discussed with respect to boundary conditions and the radius of the circular duct. The limits of applicability of the KZK equation and the GBE equation for describing nonlinear waves in tubes are discussed.
International Nuclear Information System (INIS)
El Naggar, I.A.; Hussein, A.M.; Khalil, Sh.M.
1992-09-01
Electromagnetic waves radiated with combination frequencies from a semi-bounded plasma due to nonlinear interaction of radiation with surface wave (both of P-polarization) has been investigated. Waves are radiated both into vacuum and plasma are found to be P-polarized. We take into consideration the continuity at the plasma boundary of the tangential components of the electric field of the waves. The case of normal incidence of radiation and rarefield plasma layer is also studied. (author). 7 refs
Nonlinear steady-state coupling of LH waves
International Nuclear Information System (INIS)
Ko, K.; Krapchev, V.B.
1981-02-01
The coupling of lower hybrid waves at the plasma edge by a two waveguide array with self-consistent density modulation is solved numerically. For a linear density profile, the governing nonlinear Klein-Gordon equation for the electric field can be written as a system of nonlinearly modified Airy equations in Fourier k/sub z/-space. Numerical solutions to the nonlinear system satisfying radiation condition are obtained. Spectra broadening and modifications to resonance cone trajectories are observed with increase of incident power
Nonlinear reflection of shock shear waves in soft elastic media.
Pinton, Gianmarco; Coulouvrat, François; Gennisson, Jean-Luc; Tanter, Mickaël
2010-02-01
For fluids, the theoretical investigation of shock wave reflection has a good agreement with experiments when the incident shock Mach number is large. But when it is small, theory predicts that Mach reflections are physically unrealistic, which contradicts experimental evidence. This von Neumann paradox is investigated for shear shock waves in soft elastic solids with theory and simulations. The nonlinear elastic wave equation is approximated by a paraxial wave equation with a cubic nonlinear term. This equation is solved numerically with finite differences and the Godunov scheme. Three reflection regimes are observed. Theory is developed for shock propagation by applying the Rankine-Hugoniot relations and entropic constraints. A characteristic parameter relating diffraction and non-linearity is introduced and its theoretical values are shown to match numerical observations. The numerical solution is then applied to von Neumann reflection, where curved reflected and Mach shocks are observed. Finally, the case of weak von Neumann reflection, where there is no reflected shock, is examined. The smooth but non-monotonic transition between these three reflection regimes, from linear Snell-Descartes to perfect grazing case, provides a solution to the acoustical von Neumann paradox for the shear wave equation. This transition is similar to the quadratic non-linearity in fluids.
Nonlinear Wave Mixing Technique for Nondestructive Assessment of Infrastructure Materials
Ju, Taeho
To operate safely, structures and components need to be inspected or monitored either periodically or in real time for potential failure. For this purpose, ultrasonic nondestructive evaluation (NDE) techniques have been used extensively. Most of these ultrasonic NDE techniques utilize only the linear behavior of the ultrasound. These linear techniques are effective in detecting discontinuities in materials such as cracks, voids, interfaces, inclusions, etc. However, in many engineering materials, it is the accumulation of microdamage that leads to degradation and eventual failure of a component. Unfortunately, it is difficult for linear ultrasonic NDE techniques to characterize or quantify such damage. On the other hand, the acoustic nonlinearity parameter (ANLP) of a material is often positively correlated with such damage in a material. Thus, nonlinear ultrasonic NDE methods have been used in recently years to characterize cumulative damage such as fatigue in metallic materials, aging in polymeric materials, and degradation of cement-based materials due to chemical reactions. In this thesis, we focus on developing a suit of novel nonlinear ultrasonic NDE techniques based on the interactions of nonlinear ultrasonic waves, namely wave mixing. First, a noncollinear wave mixing technique is developed to detect localized damage in a homogeneous material by using a pair of noncollinear a longitudinal wave (L-wave) and a shear wave (S-wave). This pair of incident waves make it possible to conduct NDE from a single side of the component, a condition that is often encountered in practical applications. The proposed noncollinear wave mixing technique is verified experimentally by carrying out measurements on aluminum alloy (AA 6061) samples. Numerical simulations using the Finite Element Method (FEM) are also conducted to further demonstrate the potential of the proposed technique to detect localized damage in structural components. Second, the aforementioned nonlinear
Nonlinear wave equations, formation of singularities
John, Fritz
1990-01-01
This is the second volume in the University Lecture Series, designed to make more widely available some of the outstanding lectures presented in various institutions around the country. Each year at Lehigh University, a distinguished mathematical scientist presents the Pitcher Lectures in the Mathematical Sciences. This volume contains the Pitcher lectures presented by Fritz John in April 1989. The lectures deal with existence in the large of solutions of initial value problems for nonlinear hyperbolic partial differential equations. As is typical with nonlinear problems, there are many results and few general conclusions in this extensive subject, so the author restricts himself to a small portion of the field, in which it is possible to discern some general patterns. Presenting an exposition of recent research in this area, the author examines the way in which solutions can, even with small and very smooth initial data, "blow up" after a finite time. For various types of quasi-linear equations, this time de...
A general theory of two-wave mixing in nonlinear media
DEFF Research Database (Denmark)
Chi, Mingjun; Huignard, Jean-Pierre; Petersen, Paul Michael
2009-01-01
A general theory of two-wave mixing in nonlinear media is presented. Assuming a gain (or absorption) grating and a refractive index grating are generated because of the nonlinear process in a nonlinear medium, the coupled-wave equations of two-wave mixing are derived based on the Maxwell’s wave e...
Closed form solutions of two time fractional nonlinear wave equations
Directory of Open Access Journals (Sweden)
M. Ali Akbar
2018-06-01
Full Text Available In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G′/G-expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics. Keywords: Traveling wave solution, Soliton, Generalized (G′/G-expansion method, Time fractional Duffing equation, Time fractional Riccati equation
Experimental observation of azimuthal shock waves on nonlinear acoustical vortices
International Nuclear Information System (INIS)
Brunet, Thomas; Thomas, Jean-Louis; Marchiano, Regis; Coulouvrat, Francois
2009-01-01
Thanks to a new focused array of piezoelectric transducers, experimental results are reported here to evidence helical acoustical shock waves resulting from the nonlinear propagation of acoustical vortices (AVs). These shock waves have a three-dimensional spiral shape, from which both the longitudinal and azimuthal components are studied. The inverse filter technique used to synthesize AVs allows various parameters to be varied, especially the topological charge which is the key parameter describing screw dislocations. Firstly, an analysis of the longitudinal modes in the frequency domain reveals a wide cascade of harmonics (up to the 60th order) leading to the formation of the shock waves. Then, an original measurement in the transverse plane exhibits azimuthal behaviour which has never been observed until now for acoustical shock waves. Finally, these new experimental results suggest interesting potential applications of nonlinear effects in terms of acoustics spanners in order to manipulate small objects.
Mathematical Methods in Wave Propagation: Part 2--Non-Linear Wave Front Analysis
Jeffrey, Alan
1971-01-01
The paper presents applications and methods of analysis for non-linear hyperbolic partial differential equations. The paper is concluded by an account of wave front analysis as applied to the piston problem of gas dynamics. (JG)
On the pressure field of nonlinear standing water waves
Schwartz, L. W.
1980-01-01
The pressure field produced by two dimensional nonlinear time and space periodic standing waves was calculated as a series expansion in the wave height. The high order series was summed by the use of Pade approximants. Calculations included the pressure variation at great depth, which was considered to be a likely cause of microseismic activity, and the pressure distribution on a vertical barrier or breakwater.
Some nonlinear processes relevant to the beat wave accelerator
International Nuclear Information System (INIS)
Bingham, R.; Mori, W.B.
1985-03-01
The beat wave accelerator depends on the generation of a large amplitude plasma wave with a phase velocity close to the velocity of light c. The plasma wave (ωsub(p), ksub(p)) is generated by beating colinear laser beams (ω 1 , k 1 ) and (ω 2 ,k 2 ) with ωsub(p) = ω 1 -ω 2 , ksub(p) = k 1 -k 2 . Since the process involves both large amplitude transverse and longitudinal waves, various nonlinear instabilities associated with either wave may occur. The object of the article is to discuss some of the processes that may compete with the beat wave generation listing their threshold and growth rate. (author)
On the so called rogue waves in nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Y. Charles Li
2016-04-01
Full Text Available The mechanism of a rogue water wave is still unknown. One popular conjecture is that the Peregrine wave solution of the nonlinear Schrodinger equation (NLS provides a mechanism. A Peregrine wave solution can be obtained by taking the infinite spatial period limit to the homoclinic solutions. In this article, from the perspective of the phase space structure of these homoclinic orbits in the infinite dimensional phase space where the NLS defines a dynamical system, we examine the observability of these homoclinic orbits (and their approximations. Our conclusion is that these approximate homoclinic orbits are the most observable solutions, and they should correspond to the most common deep ocean waves rather than the rare rogue waves. We also discuss other possibilities for the mechanism of a rogue wave: rough dependence on initial data or finite time blow up.
Wave propagation in non-linear media
Broer, L.J.F.
1965-01-01
The problem of the propagation of electromagnetic waves through solids is essentially one of interaction between light quanta and matter. The most fundamental and general treatment of this subject is therefore undoubtedly based on the quantummechanical theory of this interaction. Nevertheless, a
Periodic solutions for one dimensional wave equation with bounded nonlinearity
Ji, Shuguan
2018-05-01
This paper is concerned with the periodic solutions for the one dimensional nonlinear wave equation with either constant or variable coefficients. The constant coefficient model corresponds to the classical wave equation, while the variable coefficient model arises from the forced vibrations of a nonhomogeneous string and the propagation of seismic waves in nonisotropic media. For finding the periodic solutions of variable coefficient wave equation, it is usually required that the coefficient u (x) satisfies ess infηu (x) > 0 with ηu (x) = 1/2 u″/u - 1/4 (u‧/u)2, which actually excludes the classical constant coefficient model. For the case ηu (x) = 0, it is indicated to remain an open problem by Barbu and Pavel (1997) [6]. In this work, for the periods having the form T = 2p-1/q (p , q are positive integers) and some types of boundary value conditions, we find some fundamental properties for the wave operator with either constant or variable coefficients. Based on these properties, we obtain the existence of periodic solutions when the nonlinearity is monotone and bounded. Such nonlinearity may cross multiple eigenvalues of the corresponding wave operator. In particular, we do not require the condition ess infηu (x) > 0.
Parameter spaces for linear and nonlinear whistler-mode waves
International Nuclear Information System (INIS)
Summers, Danny; Tang, Rongxin; Omura, Yoshiharu; Lee, Dong-Hun
2013-01-01
We examine the growth of magnetospheric whistler-mode waves which comprises a linear growth phase followed by a nonlinear growth phase. We construct time-profiles for the wave amplitude that smoothly match at the transition between linear and nonlinear wave growth. This matching procedure can only take place over a limited “matching region” in (N h /N 0 ,A T )-space, where A T is the electron thermal anisotropy, N h is the hot (energetic) electron number density, and N 0 is the cold (background) electron number density. We construct this matching region and determine how the matching wave amplitude varies throughout the region. Further, we specify a boundary in (N h /N 0 ,A T )-space that separates a region where only linear chorus wave growth can occur from the region in which fully nonlinear chorus growth is possible. We expect that this boundary should prove of practical use in performing computationally expensive full-scale particle simulations, and in interpreting experimental wave data
Optical rogue waves generation in a nonlinear metamaterial
Onana Essama, Bedel Giscard; Atangana, Jacques; Biya-Motto, Frederick; Mokhtari, Bouchra; Cherkaoui Eddeqaqi, Noureddine; Kofane, Timoleon Crepin
2014-11-01
We investigate the behavior of electromagnetic wave which propagates in a metamaterial for negative index regime. The optical pulse propagation is described by the nonlinear Schrödinger equation with cubic-quintic nonlinearities, second- and third-order dispersion effects. The behavior obtained for negative index regime is compared to that observed for positive index regime. The characterization of electromagnetic wave uses some pulse parameters obtained analytically and called collective coordinates such as amplitude, temporal position, width, chirp, frequency shift and phase. Six frequency ranges have been pointed out where a numerical evolution of collective coordinates and their stability are studied under a typical example to verify our analysis. It appears that a robust soliton due to a perfect compensation process between second-order dispersion and cubic-nonlinearity is presented at each frequency range for both negative and positive index regimes. Thereafter, the stability of the soliton pulse and physical conditions leading to optical rogue waves generation are discussed at each frequency range for both regimes, when third-order dispersion and quintic-nonlinearity come into play. We have demonstrated that collective coordinates give much useful information on external and internal behavior of rogue events. Firstly, we determine at what distance begins the internal excitation leading to rogue waves. Secondly, what kind of internal modification and how it modifies the system in order to build-up rogue events. These results lead to a best comprehension of the mechanism of rogue waves generation. So, it clearly appears that the rogue wave behavior strongly depends on nonlinearity strength of distortion, frequency and regime considered.
Directory of Open Access Journals (Sweden)
Papari Das
2018-01-01
Full Text Available A nonextensive nonthermal magnetized viscoelastic astrofluid, compositionally containing nonthermal electrons and ions together with massive polarized dust micro-spherical grains of variable electric charge, is allowed to endure weakly nonlinear perturbation around its equilibrium. The nonextensivity originating from the large-scale non-local effects is included via the Tsallis thermo-statistical distribution laws describing the lighter species. Assuming the equilibrium as a homogeneous hydrostatic one, the dust polarization effects are incorporated via the conventional homogeneous polarization force law. The perturbed fluid model evolves as a unique conjugate pair of coupled extended Korteweg-de Vries (e-KdV equations. A constructed numerical tapestry shows the collective excitations of a new pair of distinct classes of nonlinear mode structures in new parametric space. The first family indicates periodic electrostatic compressive eigenmodes in the form of soliton-chains. Likewise, the second one reveals gravitational rarefactive solitary patterns. Their microphysical multi-parametric dependencies of the eigen-patterns are illustratively analyzed and bolstered. The paper ends up with some promising implications and applications in the astro-cosmo-plasmic context of wave-induced accretive triggering processes responsible for gravitationally bounded (gravito-condensed astro-structure formation, such as stellesimals, planetsimals, etc.
Das, Papari; Karmakar, Pralay Kumar
2018-01-01
A nonextensive nonthermal magnetized viscoelastic astrofluid, compositionally containing nonthermal electrons and ions together with massive polarized dust micro-spherical grains of variable electric charge, is allowed to endure weakly nonlinear perturbation around its equilibrium. The nonextensivity originating from the large-scale non-local effects is included via the Tsallis thermo-statistical distribution laws describing the lighter species. Assuming the equilibrium as a homogeneous hydrostatic one, the dust polarization effects are incorporated via the conventional homogeneous polarization force law. The perturbed fluid model evolves as a unique conjugate pair of coupled extended Korteweg-de Vries (e-KdV) equations. A constructed numerical tapestry shows the collective excitations of a new pair of distinct classes of nonlinear mode structures in new parametric space. The first family indicates periodic electrostatic compressive eigenmodes in the form of soliton-chains. Likewise, the second one reveals gravitational rarefactive solitary patterns. Their microphysical multi-parametric dependencies of the eigen-patterns are illustratively analyzed and bolstered. The paper ends up with some promising implications and applications in the astro-cosmo-plasmic context of wave-induced accretive triggering processes responsible for gravitationally bounded (gravito-condensed) astro-structure formation, such as stellesimals, planetsimals, etc.
Nonlinear Bloch waves in metallic photonic band-gap filaments
International Nuclear Information System (INIS)
Kaso, Artan; John, Sajeev
2007-01-01
We demonstrate the occurrence of nonlinear Bloch waves in metallic photonic crystals (PCs). These periodically structured filaments are characterized by an isolated optical pass band below an effective plasma gap. The pass band occurs in a frequency range where the metallic filament exhibits a negative, frequency-dependent dielectric function and absorption loss. The metallic losses are counterbalanced by gain in two models of inhomogeneously broadened nonlinear oscillators. In the first model, we consider close-packed quantum dots that fill the void regions of a two-dimensional (2D) metallic PC, and whose inhomogeneously broadened emission spectrum spans the original optical pass band of the bare filament. In the second model, we consider thin (10-50 nm) layers of inhomogeneously broadened two-level resonators, with large dipole oscillator strength, that cover the interior surfaces of 2D metallic (silver and tungsten) PCs. These may arise from localized surface plasmon resonances due to small metal particles or an otherwise rough metal surface. For simplicity, we treat electromagnetic modes with electric field perpendicular to the plane of metal periodicity. In both models, a pumping threshold of the resonators is found, above which periodic nonlinear solutions of Maxwell's equations with purely real frequency within the optical pass band emerge. These nonlinear Bloch waves exhibit a laserlike input pumping to output amplitude characteristic. For strong surface resonances, these nonlinear waves may play a role in light emission from a hot tungsten (suitably microstructured) filament
Nonlinear Bloch waves in metallic photonic band-gap filaments
Kaso, Artan; John, Sajeev
2007-11-01
We demonstrate the occurrence of nonlinear Bloch waves in metallic photonic crystals (PCs). These periodically structured filaments are characterized by an isolated optical pass band below an effective plasma gap. The pass band occurs in a frequency range where the metallic filament exhibits a negative, frequency-dependent dielectric function and absorption loss. The metallic losses are counterbalanced by gain in two models of inhomogeneously broadened nonlinear oscillators. In the first model, we consider close-packed quantum dots that fill the void regions of a two-dimensional (2D) metallic PC, and whose inhomogeneously broadened emission spectrum spans the original optical pass band of the bare filament. In the second model, we consider thin (10 50 nm) layers of inhomogeneously broadened two-level resonators, with large dipole oscillator strength, that cover the interior surfaces of 2D metallic (silver and tungsten) PCs. These may arise from localized surface plasmon resonances due to small metal particles or an otherwise rough metal surface. For simplicity, we treat electromagnetic modes with electric field perpendicular to the plane of metal periodicity. In both models, a pumping threshold of the resonators is found, above which periodic nonlinear solutions of Maxwell’s equations with purely real frequency within the optical pass band emerge. These nonlinear Bloch waves exhibit a laserlike input pumping to output amplitude characteristic. For strong surface resonances, these nonlinear waves may play a role in light emission from a hot tungsten (suitably microstructured) filament.
Simulations of nonlinear continuous wave pressure fields in FOCUS
Zhao, Xiaofeng; Hamilton, Mark F.; McGough, Robert J.
2017-03-01
The Khokhlov - Zabolotskaya - Kuznetsov (KZK) equation is a parabolic approximation to the Westervelt equation that models the effects of diffraction, attenuation, and nonlinearity. Although the KZK equation is only valid in the far field of the paraxial region for mildly focused or unfocused transducers, the KZK equation is widely applied in medical ultrasound simulations. For a continuous wave input, the KZK equation is effectively modeled by the Bergen Code [J. Berntsen, Numerical Calculations of Finite Amplitude Sound Beams, in M. F. Hamilton and D. T. Blackstock, editors, Frontiers of Nonlinear Acoustics: Proceedings of 12th ISNA, Elsevier, 1990], which is a finite difference model that utilizes operator splitting. Similar C++ routines have been developed for FOCUS, the `Fast Object-Oriented C++ Ultrasound Simulator' (http://www.egr.msu.edu/˜fultras-web) to calculate nonlinear pressure fields generated by axisymmetric flat circular and spherically focused ultrasound transducers. This new routine complements an existing FOCUS program that models nonlinear ultrasound propagation with the angular spectrum approach [P. T. Christopher and K. J. Parker, J. Acoust. Soc. Am. 90, 488-499 (1991)]. Results obtained from these two nonlinear ultrasound simulation approaches are evaluated and compared for continuous wave linear simulations. The simulation results match closely in the farfield of the paraxial region, but the results differ in the nearfield. The nonlinear pressure field generated by a spherically focused transducer with a peak surface pressure of 0.2MPa radiating in a lossy medium with β = 3.5 is simulated, and the computation times are also evaluated. The nonlinear simulation results demonstrate acceptable agreement in the focal zone. These two related nonlinear simulation approaches are now included with FOCUS to enable convenient simulations of nonlinear pressure fields on desktop and laptop computers.
Waves in nonlinear pre-stressed materials
Schneider, Wilhelm; Saccomandi, G
2007-01-01
The papers in this book provide a unique state-of-the-art multidisciplinary overview on the subject of waves in pre-stressed materials through the interaction of several topics, ranging from the mathematical modelling of incremental material response (elastic and inelastic), to the analysis of the governing differential equations and boundary-value problems, and to computational methods for the solution to these problems, with particular reference to industrial, geophysical, and biomechanical applications. A complete view on the title subject is proposed, including: The basic and fundamental theoretical issues (mechanical modelling, exact solutions, asymptotic methods, numerical treatment); A unified introduction to wave propagation (small on large and large on large); A look toward classical (such as geophysics and the mechanics of rubber-like solids) and emergent (such as biomechanics) applications.