Nonlinear Dispersion Relation in Wave Transformation
Institute of Scientific and Technical Information of China (English)
李瑞杰; 严以新; 曹宏生
2003-01-01
A nonlinear dispersion relation is presented to model the nonlinear dispersion of waves over the whole range of possible water depths. It reduces the phase speed over-prediction of both Hedges′ modified relation and Kirby and Dalrymple′s modified relation in the region of 1＜kh＜1.5 for small wave steepness and maintains the monotonicity in phase speed variation for large wave steepness. And it has a simple form. By use of the new nonlinear dispersion relation along with the mild slope equation taking into account weak nonlinearity, a mathematical model of wave transformation is developed and applied to laboratory data. The results show that the model with the new dispersion relation can predict wave transformation over complicated bathymetry satisfactorily.
Dispersive shock waves with nonlocal nonlinearity
Barsi, Christopher; Sun, Can; Fleischer, Jason W
2007-01-01
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
Dispersive shock waves with nonlocal nonlinearity.
Barsi, Christopher; Wan, Wenjie; Sun, Can; Fleischer, Jason W
2007-10-15
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
Nonlinear Dispersion Effect on Wave Transformation
Institute of Scientific and Technical Information of China (English)
LI Ruijie; Dong-Young LEE
2000-01-01
A new nonlinear dispersion relation is given in this paper, which can overcome the limitation of the intermediate minimum value in the dispersion relation proposed by Kirby and Dalrymple (1986), and which has a better approximation to Hedges＇ empirical relation than the modilied relations by Hedges (1987). Kirby and Dahymple (1987) for shallow waters. The new dispersion relation is simple in form. thus it can be used easily in practice. Meanwhile. a general explicil approximalion to the new dispersion rela tion and olher nonlinear dispersion relations is given. By use of the explicit approximation to the new dispersion relation along with the mild slope equation taking inlo account weakly nonlinear effect, a mathematical model is obtained, and it is applied to laboratory data. The results show that the model developed vith the new dispersion relation predicts wave translornation over complicated topography quite well.
Analysis of Wave Nonlinear Dispersion Relation
Institute of Scientific and Technical Information of China (English)
LI Rui-jie; TAO Jian-fu
2005-01-01
The nonlinear dispersion relations and modified relations proposed by Kirby and Hedges have the limitation of intermediate minimum value. To overcome the shortcoming, a new nonlinear dispersion relation is proposed. Based on the summarization and comparison of existing nonlinear dispersion relations, it can be found that the new nonlinear dispersion relation not only keeps the advantages of other nonlinear dispersion relations, but also significantly reduces the relative errors of the nonlinear dispersion relations for a range of the relative water depth of 1＜kh＜1.5 and has sufficient accuracy for practical purposes.
Generalized dispersive wave emission in nonlinear fiber optics.
Webb, K E; Xu, Y Q; Erkintalo, M; Murdoch, S G
2013-01-15
We show that the emission of dispersive waves in nonlinear fiber optics is not limited to soliton-like pulses propagating in the anomalous dispersion regime. We demonstrate, both numerically and experimentally, that pulses propagating in the normal dispersion regime can excite resonant dispersive radiation across the zero-dispersion wavelength into the anomalous regime.
Boundary control of long waves in nonlinear dispersive systems
DEFF Research Database (Denmark)
Hasan, Agus; Foss, Bjarne; Aamo, Ole Morten
2011-01-01
Unidirectional propagation of long waves in nonlinear dispersive systems may be modeled by the Benjamin-Bona-Mahony-Burgers equation, a third order partial differential equation incorporating linear dissipative and dispersive terms, as well as a term covering nonlinear wave phenomena. For higher...... orders of the nonlinearity, the equation may have unstable solitary wave solutions. Although it is a one dimensional problem, achieving a global result for this equation is not trivial due to the nonlinearity and the mixed partial derivative. In this paper, two sets of nonlinear boundary control laws...... that achieve global exponential stability and semi-global exponential stability are derived for both linear and nonlinear cases....
Nearly linear dynamics of nonlinear dispersive waves
Erdogan, M B; Zharnitsky, V
2010-01-01
Dispersive averaging e?ffects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly. Numerical simulations are presented which indicate high accuracy of this approximation. Furthermore, this result is applied to shallow water wave dynamics in the limit of KdV approximation, which is obtained by asymptotic analysis in combination with numerical simulations of KdV.
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...
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 ...
TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The method of the phase plane is emploied to investigate the solitary and periodic traveling waves for a class of nonlinear dispersive partial differential equations.By using the bifurcation theory of dynamical systems to do qualitative analysis,all possible phase portraits in the parametric space for the traveling wave systems are obtained.It can be shown that the existence of a singular straight line in the traveling wave system is the reason why smooth solitary wave solutions converge to solitary cusp wave solution when parameters are varied.The different parameter conditions for the existence of solitary and periodic wave solutions of different kinds are rigorously determined.
A WEAKLY NONLINEAR WATER WAVE MODEL TAKING INTO ACCOUNT DISPERSION OF WAVE PHASE VELOCITY
Institute of Scientific and Technical Information of China (English)
李瑞杰; 李东永
2002-01-01
This paper presents a weakly nonlinear water wave model using a mild slope equation and a new explicit formulation which takes into account dispersion of wave phase velocity, approximates Hedges' (1987) nonlinear dispersion relationship, and accords well with the original empirical formula. Comparison of the calculating results with those obtained from the experimental data and those obtained from linear wave theory showed that the present water wave model considering the dispersion of phase velocity is rational and in good agreement with experiment data.
Viscous Fluid Conduits as a Prototypical Nonlinear Dispersive Wave Platform
Lowman, Nicholas K.
This thesis is devoted to the comprehensive characterization of slowly modulated, nonlinear waves in dispersive media for physically-relevant systems using a threefold approach: analytical, long-time asymptotics, careful numerical simulations, and quantitative laboratory experiments. In particular, we use this interdisciplinary approach to establish a two-fluid, interfacial fluid flow setting known as viscous fluid conduits as an ideal platform for the experimental study of truly one dimensional, unidirectional solitary waves and dispersively regularized shock waves (DSWs). Starting from the full set of fluid equations for mass and linear momentum conservation, we use a multiple-scales, perturbation approach to derive a scalar, nonlinear, dispersive wave equation for the leading order interfacial dynamics of the system. Using a generalized form of the approximate model equation, we use numerical simulations and an analytical, nonlinear wave averaging technique, Whitham-El modulation theory, to derive the key physical features of interacting large amplitude solitary waves and DSWs. We then present the results of quantitative, experimental investigations into large amplitude solitary wave interactions and DSWs. Overtaking interactions of large amplitude solitary waves are shown to exhibit nearly elastic collisions and universal interaction geometries according to the Lax categories for KdV solitons, and to be in excellent agreement with the dynamics described by the approximate asymptotic model. The dispersive shock wave experiments presented here represent the most extensive comparison to date between theory and data of the key wavetrain parameters predicted by modulation theory. We observe strong agreement. Based on the work in this thesis, viscous fluid conduits provide a well-understood, controlled, table-top environment in which to study universal properties of dispersive hydrodynamics. Motivated by the study of wave propagation in the conduit system, we
A Spectral Element Method for Nonlinear and Dispersive Water Waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Bigoni, Daniele; Eskilsson, Claes
The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...... methods is of key interest. We present a high-order general-purpose three-dimensional numerical model solving fully nonlinear and dispersive potential flow equations with a free surface.......The use of flexible mesh discretisation methods are important for simulation of nonlinear wave-structure interactions in offshore and marine settings such as harbour and coastal areas. For real applications, development of efficient models for wave propagation based on unstructured discretisation...
Nonlinear waves in electromigration dispersion in a capillary
Christov, Ivan C
2016-01-01
We construct exact solutions to an unusual nonlinear advection--diffusion equation arising in the study of Taylor--Aris (also known as shear) dispersion due to electroosmotic flow during electromigration in a capillary. An exact reduction to a Darboux equation is found under a traveling-wave anzats. The equilibria of this ordinary differential equation are analyzed, showing that their stability is determined solely by the (dimensionless) wave speed without regard to any (dimensionless) physical parameters. Integral curves, connecting the appropriate equilibria of the Darboux equation that governs traveling waves, are constructed, which in turn are shown to be asymmetric kink solutions ({\\it i.e.}, non-Taylor shocks). Furthermore, it is shown that the governing Darboux equation exhibits bistability, which leads to two coexisting non-negative kink solutions for (dimensionless) wave speeds greater than unity. Finally, we give some remarks on other types of traveling-wave solutions and a discussion of some approx...
Directory of Open Access Journals (Sweden)
Shi Jing
2014-01-01
Full Text Available The solving processes of the homogeneous balance method, Jacobi elliptic function expansion method, fixed point method, and modified mapping method are introduced in this paper. By using four different methods, the exact solutions of nonlinear wave equation of a finite deformation elastic circular rod, Boussinesq equations and dispersive long wave equations are studied. In the discussion, the more physical specifications of these nonlinear equations, have been identified and the results indicated that these methods (especially the fixed point method can be used to solve other similar nonlinear wave equations.
Travelling Wave Solutions in Nonlinear Diffusive and Dispersive Media
Bazeia, D; Raposo, and E.P.
1998-01-01
We investigate the presence of soliton solutions in some classes of nonlinear partial differential equations, namely generalized Korteweg-de Vries-Burgers, Korteveg-de Vries-Huxley, and Korteveg-de Vries-Burgers-Huxley equations, which combine effects of diffusion, dispersion, and nonlinearity. We emphasize the chiral behavior of the travelling solutions, whose velocities are determined by the parameters that define the equation. For some appropriate choices, we show that these equations can be mapped onto equations of motion of relativistic 1+1 dimensional phi^{4} and phi^{6} field theories of real scalar fields. We also study systems of two coupled nonlinear equations of the types mentioned.
Nonlinear wave propagation studies, dispersion modeling, and signal parameters correction
Czech Academy of Sciences Publication Activity Database
Převorovský, Zdeněk
..: ..., 2004, 00. [European Workshop on FP6-AERONEWS /1./. Naples (IT), 13.09.2004-16.09.2004] EU Projects: European Commission(XE) 502927 - AERO-NEWS Institutional research plan: CEZ:AV0Z2076919 Keywords : nodestructive testing * nonlinear elastic wave spectroscopy Subject RIV: BI - Acoustics
Unstructured Spectral Element Model for Dispersive and Nonlinear Wave Propagation
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, Claes; Bigoni, Daniele
2016-01-01
). In the present paper we use a single layer of quadratic (in 2D) and prismatic (in 3D) elements. The model has been stabilized through a combination of over-integration of the Galerkin projections and a mild modal filter. We present numerical tests of nonlinear waves serving as a proof-of-concept validation...
Deterministic and stochastic evolution equations for fully dispersive and weakly nonlinear waves
DEFF Research Database (Denmark)
Eldeberky, Y.; Madsen, Per A.
1999-01-01
This paper presents a new and more accurate set of deterministic evolution equations for the propagation of fully dispersive, weakly nonlinear, irregular, multidirectional waves. The equations are derived directly from the Laplace equation with leading order nonlinearity in the surface boundary c...
Nonlinear Acoustics in a Dispersive Continuum: Random Waves, Radiation Pressure, and Quantum Noise.
1983-03-01
Karpman , Nonlinear Waves in Dispersive Media, Pergamon Press, New York, 1975, p. 76. 26. R. Beyers, Nonlinear Acoustics, U.S. Government Printing...20301 U. S. Army Research nffice 2 copies Box 12211 Research Triangle Park tlorth Carolina 27709 Defense Technical Information Center 12 copies Cameron
Nonlinear acoustics in a dispersive continuum: Random waves, radiation pressure, and quantum noise
Cabot, M. A.
The nonlinear interaction of sound with sound is studied using dispersive hydrodynamics which derived from a variational principle and the assumption that the internal energy density depends on gradients of the mass density. The attenuation of sound due to nonlinear interaction with a background is calculated and is shown to be sensitive to both the nature of the dispersion and decay bandwidths. The theoretical results are compared to those of low temperature helium experiments. A kinetic equation which described the nonlinear self-inter action of a background is derived. When a Deybe-type cutoff is imposed, a white noise distribution is shown to be a stationary distribution of the kinetic equation. The attenuation and spectrum of decay of a sound wave due to nonlinear interaction with zero point motion is calculated. In one dimension, the dispersive hydrodynamic equations are used to calculate the Langevin and Rayleigh radiation pressures of wave packets and solitary waves.
Three kinds of nonlinear dispersive waves in elastic rods with finite deformation
Institute of Scientific and Technical Information of China (English)
ZHANG Shan-yuan; LIU Zhi-fang
2008-01-01
On the basis of classical linear theory on longitudinal, torsional and flexural waves in thin elastic rods, and taking finite deformation and dispersive effects into consideration, three kinds of nonlinear evolution equations are derived. Qualitative analysis of three kinds of nonlinear equations are presented. It is shown that these equations have homoclinic or heteroclinic orbits on the phase plane, corresponding to solitary wave or shock wave solutions, respectively. Based on the principle of homogeneous balance, these equations are solved with the Jacobi elliptic function expansion method. Results show that existence of solitary wave solution and shock wave solution is possible under certain conditions. These conclusions are consistent with qualitative analysis.
Relativistic regimes for dispersive shock-waves in non-paraxial nonlinear optics
Gentilini, Silvia; Conti, Claudio
2014-01-01
We investigate the effect of non-paraxiality in the dynamics of dispersive shock waves in the defocusing nonlinear Schroedinger equation. We show that the problem can be described in terms of a relativistic particle moving in a potential. Lowest order corrections enhance the wave-breaking and impose a limit to the highest achievable spectrum in an amount experimentally testable.
Optical tsunamis: shoaling of shallow water rogue waves in nonlinear fibers with normal dispersion
Wabnitz, Stefan
2013-01-01
In analogy with ocean waves running up towards the beach, shoaling of prechirped optical pulses may occur in the normal group-velocity dispersion regime of optical fibers. We present exact Riemann wave solutions of the optical shallow water equations and show that they agree remarkably well with the numerical solutions of the nonlinear Schr\\"odinger equation, at least up to the point where a vertical pulse front develops. We also reveal that extreme wave events or optical tsunamis may be generated in dispersion tapered fibers in the presence of higher-order dispersion.
Nonlinear coupling of left and right handed circularly polarized dispersive Alfvén wave
Energy Technology Data Exchange (ETDEWEB)
Sharma, R. P., E-mail: rpsharma@ces.iitd.ac.in; Sharma, Swati, E-mail: swati.sharma704@gmail.com; Gaur, Nidhi, E-mail: nidhiphysics@gmail.com [Centre for Energy Studies, Indian Institute of Technology Delhi, New Delhi 110016 (India)
2014-07-15
The nonlinear phenomena are of prominent interests in understanding the particle acceleration and transportation in the interplanetary space. The ponderomotive nonlinearity causing the filamentation of the parallel propagating circularly polarized dispersive Alfvén wave having a finite frequency may be one of the mechanisms that contribute to the heating of the plasmas. The contribution will be different of the left (L) handed mode, the right (R) handed mode, and the mix mode. The contribution also depends upon the finite frequency of the circularly polarized waves. In the present paper, we have investigated the effect of the nonlinear coupling of the L and R circularly polarized dispersive Alfvén wave on the localized structures formation and the respective power spectra. The dynamical equations are derived in the presence of the ponderomotive nonlinearity of the L and R pumps and then studied semi-analytically as well as numerically. The ponderomotive nonlinearity accounts for the nonlinear coupling between both the modes. In the presence of the adiabatic response of the density fluctuations, the nonlinear dynamical equations satisfy the modified nonlinear Schrödinger equation. The equations thus obtained are solved in solar wind regime to study the coupling effect on localization and the power spectra. The effect of coupling is also studied on Faraday rotation and ellipticity of the wave caused due to the difference in the localization of the left and the right modes with the distance of propagation.
Clack, C
2009-01-01
The nonlinear theory of driven magnetohydrodynamics (MHD) waves in strongly anisotropic and dispersive plasmas, developed for slow resonance by Clack and Ballai [Phys. Plasmas, 15, 2310 (2008)] and Alfv\\'en resonance by Clack \\emph{et al.} [A&A,494, 317 (2009)], is used to study the weakly nonlinear interaction of fast magnetoacoustic (FMA) waves in a one-dimensional planar plasma. The magnetic configuration consists of an inhomogeneous magnetic slab sandwiched between two regions of semi-infinite homogeneous magnetic plasmas. Laterally driven FMA waves penetrate the inhomogeneous slab interacting with the localized slow or Alfv\\'{e}n dissipative layer and are partly reflected, dissipated and transmitted by this region. The nonlinearity parameter defined by Clack and Ballai (2008) is assumed to be small and a regular perturbation method is used to obtain analytical solutions in the slow dissipative layer. The effect of dispersion in the slow dissipative layer is to further decrease the coefficient of ener...
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.
Existence of traveling wave solutions for a nonlinear dissipative-dispersive equation
Institute of Scientific and Technical Information of China (English)
M. B. A. Mansour
2009-01-01
In this paper, we consider a dissipative-dispersive nonlinear equation appliable to many physical phenomena. Using the geometric singular perturbation method based on the theory of dynamical systems, we investigate the existence of its traveling wave solutions with the dissipative terms having sufficiently small coefficients. The results show that the traveling waves exist on a two-dimensional slow manifold in a three-dimensional system of ordinary differential equations (ODEs). Then, we use the Melnikov method to establish the existence of a homoclinic orbit in this manifold corresponding to a solitary wave solution of the equation. Furthermore, we present some numerical computations to show the approximations of such wave orbits.
Zhang, Ya-Ni; Ren, Li-Yong; Gong, Yong-Kang; Li, Xiao-Hui; Wang, Lei-Ran; Sun, Chuan-Dong
2010-06-01
We have proposed a novel type of photonic crystal fiber (PCF) with low dispersion and high nonlinearity for four-wave mixing. This type of fiber is composed of a solid silica core and a cladding with a squeezed hexagonal lattice elliptical airhole along the fiber length. Its dispersion and nonlinearity coefficient are investigated simultaneously by using the full vectorial finite element method. Numerical results show that the proposed highly nonlinear low-dispersion fiber has a total dispersion as low as +/-2.5 ps nm(-1) km(-1) over an ultrabroad wavelength range from 1.43 to 1.8 microm, and the corresponding nonlinearity coefficient and birefringence are about 150 W(-1) km(-1) and 2.5x10(-3) at 1.55 microm, respectively. The proposed PCF with low ultraflattened dispersion, high nonlinearity, and high birefringence can have important application in four-wave mixing.
Zhou, Binbin
2015-01-01
We experimentally observe long-wavelength dispersive waves generation in a BBO crystal. A soliton was formed in normal GVD regime of the crystal by a self-defocusing and negative nonlinearity through phase-mismatched quatradic interaction. Strong temporal pulse compression confirmed the formation of soliton during the pulse propagation inside the crystal. Significant dispersive wave radiation was measured in the anomalous GVD regime of the BBO crystal. With the pump wavelengths from 1.24 to 1.4 $\\mu$m, tunable dispersive waves are generated around 1.9 to 2.2 $\\mu$m. The observed dispersive wave generation is well understood by simulations.
Cauchy problem for a class of nonlinear dispersive wave equations arising in elasto-plastic flow
Zhijian, Yang
2006-01-01
The paper studies the existence, both locally and globally in time, stability, decay estimates and blowup of solutions to the Cauchy problem for a class of nonlinear dispersive wave equations arising in elasto-plastic flow. Under the assumption that the nonlinear term of the equations is of polynomial growth order, say [alpha], it proves that when [alpha]>1, the Cauchy problem admits a unique local solution, which is stable and can be continued to a global solution under rather mild conditions; when [alpha][greater-or-equal, slanted]5 and the initial data is small enough, the Cauchy problem admits a unique global solution and its norm in L1,p(R) decays at the rate for 2
nonlinear term, the local solutions of the Cauchy problem blow up in finite time.
Kartashova, Elena
2013-01-01
In this Letter we study the form of the energy spectrum of Riemann waves in weakly nonlinear non-dispersive media. For quadratic and cubic nonlinearity we demonstrate that the deformation of an Riemann wave over time yields an exponential energy spectrum which turns into power law asymptotic with the slope being approximately -8/3 at the last stage of evolution before breaking. We argue, that this is the universal asymptotic behaviour of Riemann waves in any nonlinear non-dispersive medium at the point of breaking. The results reported in this Letter can be used in various non-dispersive media, e.g. magneto-hydro dynamics, physical oceanography, nonlinear acoustics.
Nonlinear effects related to circularly polarized dispersive Alfvén waves
Sharma, Swati; Gaur, Nidhi; Sharma, R. P.
2016-09-01
In situ measurements of solar wind have strongly implicated its turbulent behavior. The observed power spectra report a breakpoint around length scales of the order of ion scales. As one of the responsible mechanisms for the observed steepening in power spectrum, our approach includes a right circularly polarized dispersive Alfvén wave (DAW) with finite frequency correction which, when subjected to transverse collapse/filamentation instability, may possibly result in steepening of spectrum and progressive transfer of energy from larger scales to smaller scales. We have studied the nonlinear effects associated with coupling of DAW with kinetic Alfvén wave in solar wind at 1 A.U. The formation of localized structures provides a clue about the emergence of turbulence. Numerical simulation is performed to study localization and power spectral density of the field and density fluctuations. The results show steeper spectrum indicating transfer of large scale turbulent energy down to small scales.
Benoit, Michel; Yates, Marissa L.; Raoult, Cécile
2017-04-01
Efficient and accurate numerical models simulating wave propagation are required for a variety of engineering projects including the evaluation of coastal risks, the design of protective coastal structures, and the estimation of the potential for marine renewable energy devices. Nonlinear and dispersive effects are particularly significant in the coastal zone where waves interact with the bottom, the shoreline, and coastal structures. The main challenge in developing a numerical models is finding a compromise between computational efficiency and the required accuracy of the simulated wave field. Here, a potential approach is selected and the (fully nonlinear) water wave problem is formulated using the Euler-Zakharov equations (Zakharov, 1968) describing the temporal evolution of the free surface elevation and velocity potential. The proposed model (Yates and Benoit, 2015) uses a spectral approach in the vertical (i.e. the vertical variation of the potential is approximated by a linear combination of the first NT+1 Chebyshev polynomials, following the work of Tian and Sato (2008)). The Zakharov equations are integrated in time using a fourth-order Runge-Kutta scheme with a constant time step. At each sub-timestep, the Laplace Boundary Value Problem (BVP) is solved to estimate the free surface vertical velocity using the spectral approach, with typical values of NT between 5 to 8 for practical applications. The 1DH version of the code is validated with comparisons to the experimental data set of Becq-Girard et al. (1999), which studied the propagation of irregular waves over a beach profile with a submerged bar. The nonlinear and dispersive capacities of the model are verified with the correct representation of wave-wave interactions, in particular the transfer of energy between different harmonic components during wave propagation (analysis of the transformation of the variance spectrum along the channel). Evolution of wave skewness, asymmetry and kurtosis along the
Herbert, Eric; Mordant, Nicolas; Falcon, Eric
2010-10-01
We report experiments on gravity-capillary wave turbulence on the surface of a fluid. The wave amplitudes are measured simultaneously in time and space by using an optical method. The full space-time power spectrum shows that the wave energy is localized on several branches in the wave-vector-frequency space. The number of branches depends on the power injected within the waves. The measurement of the nonlinear dispersion relation is found to be well described by a law suggesting that the energy transfer mechanisms involved in wave turbulence are restricted not only to purely resonant interaction between nonlinear waves. The power-law scaling of the spatial spectrum and the probability distribution of the wave amplitudes at a given wave number are also measured and compared to the theoretical predictions.
Mechanical balance laws for fully nonlinear and weakly dispersive water waves
Kalisch, Henrik; Mitsotakis, Dimitrios
2015-01-01
The Serre-Green-Naghdi system is a coupled, fully nonlinear system of dispersive evolution equations which approximates the full water wave problem. The system is an extension of the well known shallow-water system to the situation where the waves are long, but not so long that dispersive effects can be neglected. In the current work, the focus is on deriving mass, momentum and energy densities and fluxes associated with the Serre-Green-Naghdi system. These quantities arise from imposing balance equations of the same asymptotic order as the evolution equations. In the case of an even bed, the conservation equations are satisfied exactly by the solutions of the Serre-Green-Naghdi system. The case of variable bathymetry is more complicated, with mass and momentum conservation satisfied exactly, and energy conservation satisfied only in a global sense. In all cases, the quantities found here reduce correctly to the corresponding counterparts in both the Boussinesq and the shallow-water scaling. One consequence o...
Mechanical balance laws for fully nonlinear and weakly dispersive water waves
Kalisch, Henrik; Khorsand, Zahra; Mitsotakis, Dimitrios
2016-10-01
The Serre-Green-Naghdi system is a coupled, fully nonlinear system of dispersive evolution equations which approximates the full water wave problem. The system is known to describe accurately the wave motion at the surface of an incompressible inviscid fluid in the case when the fluid flow is irrotational and two-dimensional. The system is an extension of the well known shallow-water system to the situation where the waves are long, but not so long that dispersive effects can be neglected. In the current work, the focus is on deriving mass, momentum and energy densities and fluxes associated with the Serre-Green-Naghdi system. These quantities arise from imposing balance equations of the same asymptotic order as the evolution equations. In the case of an even bed, the conservation equations are satisfied exactly by the solutions of the Serre-Green-Naghdi system. The case of variable bathymetry is more complicated, with mass and momentum conservation satisfied exactly, and energy conservation satisfied only in a global sense. In all cases, the quantities found here reduce correctly to the corresponding counterparts in both the Boussinesq and the shallow-water scaling. One consequence of the present analysis is that the energy loss appearing in the shallow-water theory of undular bores is fully compensated by the emergence of oscillations behind the bore front. The situation is analyzed numerically by approximating solutions of the Serre-Green-Naghdi equations using a finite-element discretization coupled with an adaptive Runge-Kutta time integration scheme, and it is found that the energy is indeed conserved nearly to machine precision. As a second application, the shoaling of solitary waves on a plane beach is analyzed. It appears that the Serre-Green-Naghdi equations are capable of predicting both the shape of the free surface and the evolution of kinetic and potential energy with good accuracy in the early stages of shoaling.
Institute of Scientific and Technical Information of China (English)
李志斌; 陈天华
2002-01-01
An algorithm for constructing exact solitary wave solutions and singular solutions for a class of nonlinear dissipative-dispersive system is presented. With the aid of symbolic manipulation system Maple, some explicit solutions are obtained for the system in physically interesting but non-integrable cases.
Koch, Herbert; Vişan, Monica
2014-01-01
The first part of the book provides an introduction to key tools and techniques in dispersive equations: Strichartz estimates, bilinear estimates, modulation and adapted function spaces, with an application to the generalized Korteweg-de Vries equation and the Kadomtsev-Petviashvili equation. The energy-critical nonlinear Schrödinger equation, global solutions to the defocusing problem, and scattering are the focus of the second part. Using this concrete example, it walks the reader through the induction on energy technique, which has become the essential methodology for tackling large data critical problems. This includes refined/inverse Strichartz estimates, the existence and almost periodicity of minimal blow up solutions, and the development of long-time Strichartz inequalities. The third part describes wave and Schrödinger maps. Starting by building heuristics about multilinear estimates, it provides a detailed outline of this very active area of geometric/dispersive PDE. It focuses on concepts and ide...
Larecki, Wieslaw; Banach, Zbigniew
2014-01-01
This paper analyzes the propagation of the waves of weak discontinuity in a phonon gas described by the four-moment maximum entropy phonon hydrodynamics involving a nonlinear isotropic phonon dispersion relation. For the considered hyperbolic equations of phonon gas hydrodynamics, the eigenvalue problem is analyzed and the condition of genuine nonlinearity is discussed. The speed of the wave front propagating into the region in thermal equilibrium is first determined in terms of the integral formula dependent on the phonon dispersion relation and subsequently explicitly calculated for the Dubey dispersion-relation model: |k|=ωc-1(1+bω2). The specification of the parameters c and b for sodium fluoride (NaF) and semimetallic bismuth (Bi) then makes it possible to compare the calculated dependence of the wave-front speed on the sample’s temperature with the empirical relations of Coleman and Newman (1988) describing for NaF and Bi the variation of the second-sound speed with temperature. It is demonstrated that the calculated temperature dependence of the wave-front speed resembles the empirical relation and that the parameters c and b obtained from fitting respectively the empirical relation and the original material parameters of Dubey (1973) are of the same order of magnitude, the difference being in the values of the numerical factors. It is also shown that the calculated temperature dependence is in good agreement with the predictions of Hardy and Jaswal’s theory (Hardy and Jaswal, 1971) on second-sound propagation. This suggests that the nonlinearity of a phonon dispersion relation should be taken into account in the theories aiming at the description of the wave-type phonon heat transport and that the Dubey nonlinear isotropic dispersion-relation model can be very useful for this purpose.
Chow, K K; Shu, C; Lin, Chinlon; Bjarklev, A
2005-10-31
We demonstrate extinction ratio improvement by using pump-modulated four-wave mixing in a dispersion-flattened nonlinear photonic crystal fiber. A 6-dB improvement in the extinction ratio of a degraded return-to-zero signal has been achieved. A power penalty improvement of 3 dB at 10(-9) bit-error-rate level is obtained in the 10 Gb/s bit-error-rate measurements.
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
Using trial equation method, abundant exact envelope traveling wave solutions of high-order dispersive cubic-quintic nonlinear Schrodinger equation, which include envelope soliton solutions, triangular function envelope solutions, and Jacobian elliptic function envelope solutions, are obtained. To our knowledge, all of these results are new.In particular, our proposed method is very simple and can be applied to a lot of similar equations.
DEFF Research Database (Denmark)
Lillieholm, Mads; Galili, Michael; Oxenløwe, Leif Katsuo
2016-01-01
We present a segmented composite HNLF optimised for mitigation of dispersion-fluctuation impairments for broadband pulsed four-wave mixing. The HNLF-segmentation allows for pulsed FWMprocessing of a 13-nm wide input WDM-signal with -4.6-dB conversion efficiency...
Hoefer, Mark A.
This thesis examines nonlinear wave phenomena, in two physical systems: a Bose-Einstein condensate (BEC) and thin film ferromagnets where the magnetization dynamics are excited by the spin momentum transfer (SMT) effect. In the first system, shock waves generated by steep gradients in the BEC wavefunction are shown to be of the disperse type. Asymptotic and averaging methods are used to determine shock speeds and structure in one spatial dimension. These results are compared with multidimensional numerical simulations and experiment showing good, qualitative agreement. In the second system, a model of magnetization dynamics due to SMT is presented. Using this model, nonlinear oscillating modes---nano-oscillators---are found numerically and analytically using perturbative methods. These results compare well with experiment. A Bose-Einstein condensate (BEC) is a quantum fluid that gives rise to interesting shock wave nonlinear dynamics. Experiments depict a BEC that exhibits behavior similar to that of a shock wave in a compressible gas, e.g. traveling fronts with steep gradients. However, the governing Gross-Pitaevskii (GP) equation that describes the mean field of a BEC admits no dissipation hence classical dissipative shock solutions do not explain the phenomena. Instead, wave dynamics with small dispersion is considered and it is shown that this provides a mechanism for the generation of a dispersive shock wave (DSW). Computations with the GP equation are compared to experiment with excellent agreement. A comparison between a canonical 1D dissipative and dispersive shock problem shows significant differences in shock structure and shock front speed. Numerical results associated with laboratory experiments show that three and two-dimensional approximations are in excellent agreement and one dimensional approximations are in qualitative agreement. The interaction of two DSWs is investigated analytically and numerically. Using one dimensional DSW theory it is argued
Directory of Open Access Journals (Sweden)
Paul C. Rivera
2006-01-01
Full Text Available A common approach in modeling the generation and propagation of tsunami is based on the assumption of a kinematic vertical displacement of ocean water that is analogous to the ocean bottom displacement during a submarine earthquake and the use of a non-dispersive long-wave model to simulate its physical transformation as it radiates outward from the source region. In this study, a new generation mechanism and the use of a highly-dispersive wave model to simulate tsunami inception, propagation and transformation are proposed. The new generation model assumes that transient ground motion during the earthquake can accelerate horizontal currents with opposing directions near the fault line whose successive convergence and divergence generate a series of potentially destructive oceanic waves. The new dynamic model incorporates the effects of earthquake moment magnitude, ocean compressibility through the buoyancy frequency, the effects of focal and water depths, and the orientation of ruptured fault line in the tsunami magnitude and directivity.For tsunami wave simulation, the nonlinear momentum-based wave model includes important wave propagation and transformation mechanisms such as refraction, diffraction, shoaling, partial reflection and transmission, back-scattering, frequency dispersion, and resonant wave-wave interaction. Using this model and a coarse-resolution bathymetry, the new mechanism is tested for the Indian Ocean tsunami of December 26, 2004. A new flooding and drying algorithm that consider waves coming from every direction is also proposed for simulation of inundation of low-lying coastal regions.It is shown in the present study that with the proposed generation model, the observed features of the Asian tsunami such as the initial drying of areas east of the source region and the initial flooding of western coasts are correctly simulated. The formation of a series of tsunami waves with periods and lengths comparable to observations
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
By making use of the generalized sine-Gordon equation expansion method, we find cnoidal periodic wave solutions and fundamental bright and dark optical solitarywave solutions for the fourth-order dispersive and the quintic nonlinear Schrodinger equation with self-steepening, and self-frequency shift. Moreover, we discuss the formation conditions of the bright and dark solitary waves.
Explicit Traveling Wave Solutions to Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
Linghai ZHANG
2011-01-01
First of all,some technical tools are developed. Then the author studies explicit traveling wave solutions to nonlinear dispersive wave equations,nonlinear dissipative dispersive wave equations,nonlinear convection equations,nonlinear reaction diffusion equations and nonlinear hyperbolic equations,respectively.
Huang, N. E.; Tung, C.-C.
1977-01-01
The influence of the directional distribution of wave energy on the dispersion relation is calculated numerically using various directional wave spectrum models. The results indicate that the dispersion relation varies both as a function of the directional energy distribution and the direction of propagation of the wave component under consideration. Furthermore, both the mean deviation and the random scatter from the linear approximation increase as the energy spreading decreases. Limited observational data are compared with the theoretical results. The agreement is favorable.
Xia, Ya-Rong; Xin, Xiang-Peng; Zhang, Shun-Li
2017-01-01
This paper mainly discusses the (2+1)-dimensional modified dispersive water-wave (MDWW) system which will be proved nonlinear self-adjointness. This property is applied to construct conservation laws corresponding to the symmetries of the system. Moreover, via the truncated Painlevé analysis and consistent tanh-function expansion (CTE) method, the soliton-cnoidal periodic wave interaction solutions and corresponding images will be eventually achieved. Supported by National Natural Science Foundation of China under Grant Nos. 11371293, 11505090, the Natural Science Foundation of Shaanxi Province under Grant No. 2014JM2-1009, Research Award Foundation for Outstanding Young Scientists of Shandong Province under Grant No. BS2015SF009 and the Science and Technology Innovation Foundation of Xi’an under Grant No. CYX1531WL41
Directory of Open Access Journals (Sweden)
Jing Yin
2015-07-01
Full Text Available A total variation diminishing-weighted average flux (TVD-WAF-based hybrid numerical scheme for the enhanced version of nonlinearly dispersive Boussinesq-type equations was developed. The one-dimensional governing equations were rewritten in the conservative form and then discretized on a uniform grid. The finite volume method was used to discretize the flux term while the remaining terms were approximated with the finite difference method. The second-order TVD-WAF method was employed in conjunction with the Harten-Lax-van Leer (HLL Riemann solver to calculate the numerical flux, and the variables at the cell interface for the local Riemann problem were reconstructed via the fourth-order monotone upstream-centered scheme for conservation laws (MUSCL. The time marching scheme based on the third-order TVD Runge-Kutta method was used to obtain numerical solutions. The model was validated through a series of numerical tests, in which wave breaking and a moving shoreline were treated. The good agreement between the computed results, documented analytical solutions, and experimental data demonstrates the correct discretization of the governing equations and high accuracy of the proposed scheme, and also conforms the advantages of the proposed shock-capturing scheme for the enhanced version of the Boussinesq model, including the convenience in the treatment of wave breaking and moving shorelines and without the need for a numerical filter.
DEFF Research Database (Denmark)
Bigoni, Daniele; Engsig-Karup, Allan Peter; Eskilsson, Claes
2016-01-01
of the evolution of waves. The model is analyzed using random sampling techniques and nonintrusive methods based on generalized polynomial chaos (PC). These methods allow us to accurately and efficiently estimate the probability distribution of the solution and require only the computation of the solution...... at different points in the parameter space, allowing for the reuse of existing simulation software. The choice of the applied methods is driven by the number of uncertain input parameters and by the fact that finding the solution of the considered model is computationally intensive. We revisit experimental...
Multi-symplectic structure of fully-nonlinear weakly-dispersive internal gravity waves
Clamond, Didier
2016-01-01
In this short communication we present the multi-symplectic structure for the two-layer Serre-Green-Naghdi equations describing the evolution of large amplitude internal gravity long waves. We consider only a two-layer stratification with rigid bottom and lid for simplicity, generalisations to several layers being straightforward. This multi-symplectic formulation allows the application of various multi-symplectic integrators (such as Euler or Preissman box schemes) that preserve exactly the multi-symplecticity at the discrete level.
Multi-symplectic structure of fully nonlinear weakly dispersive internal gravity waves
Clamond, Didier; Dutykh, Denys
2016-08-01
In this short communication, we present the multi-symplectic structure for the two-layer Serre-Green-Naghdi equations describing the evolution of large amplitude internal gravity water waves when both layers are shallow. We consider only a two-layer stratification with rigid bottom and lid for simplicity, generalisations to several layers being conceivable. This multi-symplectic formulation allows the application of various multi-symplectic integrators (such as Euler or Preissman box schemes) that preserve exactly the multi-symplecticity at the discrete level.
Finite volume schemes for dispersive wave propagation and runup
Dutykh, Denys; Katsaounis, Theodoros; Mitsotakis, Dimitrios
2011-04-01
Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the method to bidirectional nonlinear, dispersive wave propagation in one space dimension. Special emphasis is given to important nonlinear phenomena such as solitary waves interactions, dispersive shock wave formation and the runup of breaking and non-breaking long waves.
Finite volume schemes for dispersive wave propagation and runup
Dutykh, Denys; Mitsotakis, Dimitrios
2010-01-01
Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus mainly on the application of the method to bidirectional nonlinear, dispersive wave propagation in one space dimension. Special emphasis is given to important nonlinear phenomena such as solitary waves interactions, dispersive shock wave formation and the runup of breaking and non-breaking long waves.
Richoux, Olivier; Hardy, Jean
2009-01-01
This paper presents an application of time-frequency methods to characterize the dispersion of acoustic waves travelling in a one-dimensional periodic or disordered lattice made up of Helmholtz resonators connected to a cylindrical tube. These methods allow (1) to evaluate the velocity of the wave energy when the input signal is an acoustic pulse ; (2) to display the evolution of the spectral content of the transient signal ; (3) to show the role of the localized nonlinearities on the propagation .i.e the emergence of higher harmonics. The main result of this paper is that the time-frequency methods point out how the nonlinearities break the localization of the waves and/or the filter effects of the lattice.
Nonlinear Electron Waves in Strongly Magnetized Plasmas
DEFF Research Database (Denmark)
Pécseli, Hans; Juul Rasmussen, Jens
1980-01-01
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.......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...
Hui, Zhan-Qiang; Zhang, Jian-Guo
2012-05-01
We propose the use of cross-phase modulation (XPM) and four-wave mixing (FWM) in dispersion-flattened highly nonlinear photonic crystal fibers (HNL-PCFs) to implement the functionalities of wavelength conversion, simultaneous time demultiplexing and wavelength multicasting in optical time-division multiplexing (OTDM) systems. The experiments on wavelength conversion at 80 Gbit s-1and OTDM demultiplexing from 80 to 10 Gbit s-1 with wavelength multicasting of two channels are successfully demonstrated to validate the proposed scheme, which are carried out by using two segments of dispersion-flattened HNL-PCFs with lengths of 100 and 50 m, respectively. Moreover, the bit error rate (BER) performance is also measured. The results show that our designed system can achieve a power penalty of less than 4.6 dB for two multicasting channels with a 24 nm wavelength span at the BER of 10-9 when compared with the 10 Gbit/s back-to-back measurement. The proposed system is transparent to bit rate since only an ultrafast third-order nonlinear effect is used. The resulting configuration is compact, robust and reliable, benefiting from the use of dispersion-flattened HNL-PCFs with short lengths. This also makes the proposed system more flexible in the operational wavelengths than those based on dispersion-shifted fibers and traditional highly nonlinear fibers. The work was supported in part by the CAS/SAFEA International Partnership Program for Creative Research Teams.
Electric characterization of a nonlinear dispersive transmission line
Energy Technology Data Exchange (ETDEWEB)
Ferreira, E.S.; Ricotta, R.M. [Faculdade de Tecnologia de Sao Paulo (FATEC-SP), SP (Brazil)], Emails: ferreira@fatecsp.br, regina@fatecsp.br
2009-07-01
A preliminary study of electrical soliton propagation in a nonlinear dispersion electrical line is presented. This is probably the simplest system that allows the observation of such waves whose main characteristic is the perfect balance of nonlinear and dispersive aspects. (author)
Arshad, M.; Seadawy, Aly R.; Lu, Dianchen
2017-08-01
The higher-order nonlinear Schrödinger equation (NLSE) with fourth-order dispersion, cubic-quintic terms, self-steepening and nonlinear dispersive terms describes the propagation of extremely short pulses in optical fibers. In this paper, the elliptic function, bright and dark solitons and solitary wave solutions of higher-order NLSE are constructed by employing a modified extended direct algebraic method, which has important applications in applied mathematics and physics. Furthermore, we also present the formation conditions of the bright and dark solitons for this equation. The modulation instability is utilized to discuss the stability of these solutions, which shows that all solutions are exact and stable. Many other higher-order nonlinear evolution equations arising in applied sciences can also be solved by this powerful, effective and reliable method.
Shock waves in dispersive Eulerian fluids
Hoefer, M A
2013-01-01
The long time behavior of an initial step resulting in a dispersive shock wave (DSW) for the one-dimensional isentropic Euler equations regularized by generic, third order dispersion is considered by use of Whitham averaging. Under modest assumptions, the jump conditions (DSW locus and speeds) for admissible, weak DSWs are characterized and found to depend only upon the sign of dispersion (convex or concave) and a general pressure law. Two mechanisms leading to the breakdown of this simple wave DSW theory for sufficiently large jumps are identified: a change in the sign of dispersion, leading to gradient catastrophe in the modulation equations, and the loss of genuine nonlinearity in the modulation equations. Large amplitude DSWs are constructed for several particular dispersive fluids with differing pressure laws modeled by the generalized nonlinear Schr\\"{o}dinger equation. These include superfluids (Bose-Einstein condensates and ultracold Fermions) and "optical fluids". Estimates of breaking times for smoo...
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...
Introduction to nonlinear dispersive equations
Linares, Felipe
2015-01-01
This textbook introduces the well-posedness theory for initial-value problems of nonlinear, dispersive partial differential equations, with special focus on two key models, the Korteweg–de Vries equation and the nonlinear Schrödinger equation. A concise and self-contained treatment of background material (the Fourier transform, interpolation theory, Sobolev spaces, and the linear Schrödinger equation) prepares the reader to understand the main topics covered: the initial-value problem for the nonlinear Schrödinger equation and the generalized Korteweg–de Vries equation, properties of their solutions, and a survey of general classes of nonlinear dispersive equations of physical and mathematical significance. Each chapter ends with an expert account of recent developments and open problems, as well as exercises. The final chapter gives a detailed exposition of local well-posedness for the nonlinear Schrödinger equation, taking the reader to the forefront of recent research. The second edition of Introdu...
DEFF Research Database (Denmark)
Zhou, Binbin; Guo, Hairun; Bache, Morten
2015-01-01
and without critical phase-matching requirements. Pumping a bulk quadratic nonlinear crystal (unpoled LiNbO3 cut for noncritical phase-mismatched interaction) with sub-mJ near-IR 50-fs pulses, tunable and broadband (∼ 1,000 cm−1) mid-IR pulses around 3.0 μm are generated with excellent spatio-temporal pulse...... quality, having up to 10.5 μJ energy (6.3% conversion). The mid-IR pulses are dispersive waves phase-matched to near-IR self-defocusing solitons created by the induced self-defocusing cascaded nonlinearity. This process is filament-free and the input pulse energy can therefore be scaled arbitrarily...
DEFF Research Database (Denmark)
Zhou, Binbin; Guo, Hairun; Bache, Morten
2015-01-01
and without critical phase-matching requirements. Pumping a bulk quadratic nonlinear crystal (unpoled LiNbO3 cut for noncritical phase-mismatched interaction) with sub-mJ near-IR 50-fs pulses, tunable and broadband (∼ 1,000 cm−1) mid-IR pulses around 3.0 μm are generated with excellent spatio-temporal pulse...... quality, having up to 10.5 μJ energy (6.3% conversion). The mid-IR pulses are dispersive waves phase-matched to near-IR self-defocusing solitons created by the induced self-defocusing cascaded nonlinearity. This process is filament-free and the input pulse energy can therefore be scaled arbitrarily...... by using large-aperture crystals. The technique can readily be implemented with other crystals and laser wavelengths, and can therefore potentially replace current ultrafast frequency-conversion processes to the mid-IR....
DEFF Research Database (Denmark)
Andersen, Peter Andreas; Tokle, Torger; Geng, Yan
2005-01-01
by the gain bandwidth of erbium-doped fiber amplifiers, are obtained in only 50-m dispersion-flattened HNL-PCF with nonlinear coefficient equal to 11 W-1·km-1. This experiment demonstrates the potential of four-wave mixing in HNL-PCF as a modulation format and bit rate transparent wavelength conversion......Wavelength conversion of a 40-Gb/s return-to-zero differential phase-shift keying signal is demonstrated in a highly nonlinear photonic crystal fiber (HNL-PCF) for the first time. A conversion efficiency of -20 dB for a pump power of 23 dBm and a conversion bandwidth of 31 nm, essentially limited...
Dispersive internal long wave models
Energy Technology Data Exchange (ETDEWEB)
Camassa, R.; Choi, W.; Holm, D.D. [Los Alamos National Lab., NM (United States); Levermore, C.D.; Lvov, Y. [Univ. of Arizona, Tucson, AZ (United States)
1998-11-01
This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at Los Alamos National Laboratory (LANL). This work is a joint analytical and numerical study of internal dispersive water wave propagation in a stratified two-layer fluid, a problem that has important geophysical fluid dynamics applications. Two-layer models can capture the main density-dependent effects because they can support, unlike homogeneous fluid models, the observed large amplitude internal wave motion at the interface between layers. The authors have derived new model equations using multiscale asymptotics in combination with the method they have developed for vertically averaging velocity and vorticity fields across fluid layers within the original Euler equations. The authors have found new exact conservation laws for layer-mean vorticity that have exact counterparts in the models. With this approach, they have derived a class of equations that retain the full nonlinearity of the original Euler equations while preserving the simplicity of known weakly nonlinear models, thus providing the theoretical foundation for experimental results so far unexplained.
Nonlinear wave interactions in quantum magnetoplasmas
Shukla, P K; Marklund, M; Stenflo, L
2006-01-01
Nonlinear interactions involving electrostatic upper-hybrid (UH), ion-cyclotron (IC), lower-hybrid (LH), and Alfven waves in quantum magnetoplasmas are considered. For this purpose, the quantum hydrodynamical equations are used to derive the governing equations for nonlinearly coupled UH, IC, LH, and Alfven waves. The equations are then Fourier analyzed to obtain nonlinear dispersion relations, which admit both decay and modulational instabilities of the UH waves at quantum scales. The growth rates of the instabilities are presented. They can be useful in applications of our work to diagnostics in laboratory and astrophysical settings.
Directory of Open Access Journals (Sweden)
L. S. Konev
2015-09-01
Full Text Available Numerical method for calculation of forward and backward waves of intense few-cycle laser pulses propagating in an optical waveguide with dispersion and cubic nonlinearity of electronic and electronic-vibration nature is described. Simulations made with the implemented algorithm show that accounting for Raman nonlinearity does not lead to qualitative changes in behavior of the backward wave. Speaking about quantitative changes, the increase of efficiency of energy transfer from the forward wave to the backward wave is observed. Presented method can be also used to simulate interaction of counterpropagating pulses.
Improved fiber nonlinearity mitigation in dispersion managed optical OFDM links
Tamilarasan, Ilavarasan; Saminathan, Brindha; Murugappan, Meenakshi
2017-02-01
Fiber nonlinearity is seen as a capacity limiting factor in OFDM based dispersion managed links since the Four Wave Mixing effects become enhanced due to the high PAPR. In this paper, the authors have compared the linear and nonlinear PAPR reduction techniques for fiber nonlinearity mitigation in OFDM based dispersion managed links. In the existing optical systems, linear transform techniques such as SLM and PTS have been implemented to reduce nonlinear effects. In the proposed study, superior performance of the L2-by-3 nonlinear transform technique is demonstrated for PAPR reduction to mitigate fiber nonlinearities. The performance evaluation is carried out by interfacing multiple simulators. The results of both linear and nonlinear transform techniques have been compared and the results show that nonlinear transform technique outperforms the linear transform in terms of nonlinearity mitigation and improved BER performance.
Wave-equation dispersion inversion
Li, Jing
2016-12-08
We present the theory for wave-equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. The dispersion curves are obtained from Rayleigh waves recorded by vertical-component geophones. Similar to wave-equation traveltime tomography, the complicated surface wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the phase-velocity and frequency domains. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2-D or 3-D S-wave velocity models. This procedure, denoted as wave-equation dispersion inversion (WD), does not require the assumption of a layered model and is significantly less prone to the cycle-skipping problems of full waveform inversion. The synthetic and field data examples demonstrate that WD can approximately reconstruct the S-wave velocity distributions in laterally heterogeneous media if the dispersion curves can be identified and picked. The WD method is easily extended to anisotropic data and the inversion of dispersion curves associated with Love waves.
A method for generating highly nonlinear periodic waves in physical wave basins
DEFF Research Database (Denmark)
Zhang, Haiwen; Schäffer, Hemming A.; Bingham, Harry B.
2006-01-01
This abstract describes a new method for generating nonlinear waves of constant form in physical wave basins. The idea is to combine fully dispersive linear wavemaker theory with nonlinear shallow water wave generation theory; and use an exact nonlinear theory as the target. We refer to the metho...... as an ad-hoc unified wave generation theory, since there is no rigorous analysis behind the idea which is simply justified by the improved results obtained for the practical generation of steady nonlinear waves....
A NUMERICAL METHOD FOR NONLINEAR WATER WAVES
Institute of Scientific and Technical Information of China (English)
ZHAO Xi-zeng; SUN Zhao-chen; LIANG Shu-xiu; HU Chang-hong
2009-01-01
This article presents a numerical method for modeling nonlinear water waves based on the High Order Spectral (HOS) method proposed by Dommermuth and Yue and West et al., involving Taylor expansion of the Dirichlet problem and the Fast Fourier Transform (FFT) algorithm. The validation and efficiency of the numerical scheme is illustrated by a number of case studies on wave and wave train configuration including the evolution of fifth-order Stokes waves, wave dispersive focusing and the instability of Stokes wave with finite slope. The results agree well with those obtained by other studies.
A Boussinesq model with alleviated nonlinearity and dispersion
Institute of Scientific and Technical Information of China (English)
ZHANG Dian-xin; TAO Jian-hua
2008-01-01
The classical Boussinesq equation is a weakly nonlinear and weakly dispersive equation, which has been widely applied to simulate wave propagation in off-coast shallow waters. A new form of the Boussinesq model for an uneven bottoms is derived in this paper. In the new model, nonlinearity is reduced without increasing the order of the highest derivative in the differential equations. Dispersion relationship of the model is improved to the order of Pade (2,2) by adjusting a parameter in the model based on the long wave approximation. Analysis of the linear dispersion, linear shoaling and nonlinearity of the present model shows that the performances in terms of nonlinearity, dispersion and shoaling of this model are improved. Numerical results obtained with the present model are in agreement with experimental data.
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...
Nonlinear surface waves in photonic hypercrystals
Ali, Munazza Zulfiqar
2017-08-01
Photonic crystals and hyperbolic metamaterials are merged to give the concept of photonic hypercrystals. It combines the properties of its two constituents to give rise to novel phenomena. Here the propagation of Transverse Magnetic waves at the interface between a nonlinear dielectric material and a photonic hypercrystal is studied and the corresponding dispersion relation is derived using the uniaxial parallel approximation. Both dielectric and metallic photonic hypercrystals are studied and it is found that nonlinearity limits the infinite divergence of wave vectors of the surface waves. These states exist in the frequency region where the linear surface waves do not exist. It is also shown that the nonlinearity can be used to engineer the group velocity of the resulting surface wave.
Ultrabroadband dispersive radiation by spatiotemporal oscillation of multimode waves
Wright, Logan G; Christodoulides, Demetrios N; Wise, Frank W
2015-01-01
Despite the abundance and importance of three-dimensional systems, relatively little progress has been made on spatiotemporal nonlinear optical waves compared to time-only or space-only systems. Here we study radiation emitted by three-dimensionally evolving nonlinear optical waves in multimode fiber. Spatiotemporal oscillations of solitons in the fiber generate multimode dispersive wave sidebands over an ultrabroadband spectral range. This work suggests routes to multipurpose sources of coherent electromagnetic waves, with unprecedented wavelength coverage.
Single-mode dispersive waves and soliton microcomb dynamics
Yi, Xu; Yang, Qi-Fan; Zhang, Xueyue; Yang, Ki Youl; Li, Xinbai; Vahala, Kerry
2017-03-01
Dissipative Kerr solitons are self-sustaining optical wavepackets in resonators. They use the Kerr nonlinearity to both compensate dispersion and offset optical loss. Besides providing insights into nonlinear resonator physics, they can be applied in frequency metrology, precision clocks, and spectroscopy. Like other optical solitons, the dissipative Kerr soliton can radiate power as a dispersive wave through a process that is the optical analogue of Cherenkov radiation. Dispersive waves typically consist of an ensemble of optical modes. Here, a limiting case is studied in which the dispersive wave is concentrated into a single cavity mode. In this limit, its interaction with the soliton induces hysteresis behaviour in the soliton's spectral and temporal properties. Also, an operating point of enhanced repetition-rate stability occurs through balance of dispersive-wave recoil and Raman-induced soliton-self-frequency shift. The single-mode dispersive wave can therefore provide quiet states of soliton comb operation useful in many applications.
Soliton trapping of dispersive waves in photonic crystal fiber with two zero dispersive wavelengths.
Wang, Weibin; Yang, Hua; Tang, Pinghua; Zhao, Chujun; Gao, Jing
2013-05-06
Based on the generalized nonlinear Schrödinger equation, we present a numerical study of trapping of dispersive waves by solitons during supercontinuum generation in photonic crystal fibers pumped with femtosecond pulses in the anomalous dispersion region. Numerical simulation results show that the generated supercontinuum is bounded by two branches of dispersive waves, namely blue-shifted dispersive waves (B-DWs) and red-shifted dispersive waves (R-DWs). We find a novel phenomenon that not only B-DWs but also R-DWs can be trapped by solitons across the zero-dispersion wavelength when the group-velocity matching between the soliton and the dispersive wave is satisfied, which may led to the generation of new spectral components via mixing of solitons and dispersive waves. Mixing of solitons with dispersive waves has been shown to play an important role in shaping not only the edge of the supercontinuum, but also its central part around the higher zero-dispersion wavelength. Further, we show that the phenomenon of soliton trapping of dispersive waves in photonic crystal fibers with two zero-dispersion wavelengths has a very close relationship with pumping power and the interval between two zero-dispersion wavelengths. In order to clearly display the evolution of soliton trapping of dispersive waves, the spectrogram of output pulses is observed using cross-correlation frequency-resolved optical gating technique (XFROG).
Zhou, B B; Bache, M
2014-01-01
Generating energetic femtosecond mid-IR pulses is crucial for ultrafast spectroscopy, and currently relies on parametric processes that, while efficient, are also complex. Here we experimentally show a simple alternative that uses a single pump wavelength without any pump synchronization and without critical phase-matching requirements. Pumping a bulk quadratic nonlinear crystal (unpoled LiNbO$_3$ cut for noncritical phase-mismatched interaction) with sub-mJ near-IR 50-fs pulses, tunable and broadband ($\\sim 1,000$ cm$^{-1}$) mid-IR pulses around $3.0~\\mu\\rm m$ are generated with excellent spatio-temporal pulse quality, having up to 10.5 $\\mu$J energy (6.3% conversion). The mid-IR pulses are dispersive waves phase-matched to near-IR self-defocusing solitons created by the induced self-defocusing cascaded nonlinearity. This process is filament-free and the input pulse energy can therefore be scaled arbitrarily by using large-aperture crystals. The technique can readily be implemented with other crystals and la...
DEFF Research Database (Denmark)
Pedersen, Martin Erland Vestergaard; Cheng, Ji; Xu, Chris
2013-01-01
An improved version of the generalized nonlinear Schrödinger equation is derived, which takes into account the correct dispersion of the transverse field distribution. The new improved version of the generalized nonlinear Schrödinger equation is verified to give the same results as the standard...
Nonlinear dispersion effects in elastic plates: numerical modelling and validation
Kijanka, Piotr; Radecki, Rafal; Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2017-04-01
Nonlinear features of elastic wave propagation have attracted significant attention recently. The particular interest herein relates to complex wave-structure interactions, which provide potential new opportunities for feature discovery and identification in a variety of applications. Due to significant complexity associated with wave propagation in nonlinear media, numerical modeling and simulations are employed to facilitate design and development of new measurement, monitoring and characterization systems. However, since very high spatio- temporal accuracy of numerical models is required, it is critical to evaluate their spectral properties and tune discretization parameters for compromise between accuracy and calculation time. Moreover, nonlinearities in structures give rise to various effects that are not present in linear systems, e.g. wave-wave interactions, higher harmonics generation, synchronism and | recently reported | shifts to dispersion characteristics. This paper discusses local computational model based on a new HYBRID approach for wave propagation in nonlinear media. The proposed approach combines advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE). The methods are investigated in the context of their accuracy for predicting nonlinear wavefields, in particular shifts to dispersion characteristics for finite amplitude waves and secondary wavefields. The results are validated against Finite Element (FE) calculations for guided waves in copper plate. Critical modes i.e., modes determining accuracy of a model at given excitation frequency - are identified and guidelines for numerical model parameters are proposed.
Dispersive shock waves and modulation theory
El, G. A.; Hoefer, M. A.
2016-10-01
There is growing physical and mathematical interest in the hydrodynamics of dissipationless/dispersive media. Since G.B. Whitham's seminal publication fifty years ago that ushered in the mathematical study of dispersive hydrodynamics, there has been a significant body of work in this area. However, there has been no comprehensive survey of the field of dispersive hydrodynamics. Utilizing Whitham's averaging theory as the primary mathematical tool, we review the rich mathematical developments over the past fifty years with an emphasis on physical applications. The fundamental, large scale, coherent excitation in dispersive hydrodynamic systems is an expanding, oscillatory dispersive shock wave or DSW. Both the macroscopic and microscopic properties of DSWs are analyzed in detail within the context of the universal, integrable, and foundational models for uni-directional (Korteweg-de Vries equation) and bi-directional (Nonlinear Schrödinger equation) dispersive hydrodynamics. A DSW fitting procedure that does not rely upon integrable structure yet reveals important macroscopic DSW properties is described. DSW theory is then applied to a number of physical applications: superfluids, nonlinear optics, geophysics, and fluid dynamics. Finally, we survey some of the more recent developments including non-classical DSWs, DSW interactions, DSWs in perturbed and inhomogeneous environments, and two-dimensional, oblique DSWs.
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....
Longitudinal nonlinear wave propagation through soft tissue.
Valdez, M; Balachandran, B
2013-04-01
In this paper, wave propagation through soft tissue is investigated. A primary aim of this investigation is to gain a fundamental understanding of the influence of soft tissue nonlinear material properties on the propagation characteristics of stress waves generated by transient loadings. Here, for computational modeling purposes, the soft tissue is modeled as a nonlinear visco-hyperelastic material, the geometry is assumed to be one-dimensional rod geometry, and uniaxial propagation of longitudinal waves is considered. By using the linearized model, a basic understanding of the characteristics of wave propagation is developed through the dispersion relation and in terms of the propagation speed and attenuation. In addition, it is illustrated as to how the linear system can be used to predict brain tissue material parameters through the use of available experimental ultrasonic attenuation curves. Furthermore, frequency thresholds for wave propagation along internal structures, such as axons in the white matter of the brain, are obtained through the linear analysis. With the nonlinear material model, the authors analyze cases in which one of the ends of the rods is fixed and the other end is subjected to a loading. Two variants of the nonlinear model are analyzed and the associated predictions are compared with the predictions of the corresponding linear model. The numerical results illustrate that one of the imprints of the nonlinearity on the wave propagation phenomenon is the steepening of the wave front, leading to jump-like variations in the stress wave profiles. This phenomenon is a consequence of the dependence of the local wave speed on the local deformation of the material. As per the predictions of the nonlinear material model, compressive waves in the structure travel faster than tensile waves. Furthermore, it is found that wave pulses with large amplitudes and small elapsed times are attenuated over shorter spans. This feature is due to the elevated
Dynamics of Nonlinear Waves on Bounded Domains
Maliborski, Maciej
2016-01-01
This thesis is concerned with dynamics of conservative nonlinear waves on bounded domains. In general, there are two scenarios of evolution. Either the solution behaves in an oscillatory, quasiperiodic manner or the nonlinear effects cause the energy to concentrate on smaller scales leading to a turbulent behaviour. Which of these two possibilities occurs depends on a model and the initial conditions. In the quasiperiodic scenario there exist very special time-periodic solutions. They result for a delicate balance between dispersion and nonlinear interaction. The main body of this dissertation is concerned with construction (by means of perturbative and numerical methods) of time-periodic solutions for various nonlinear wave equations on bounded domains. While turbulence is mainly associated with hydrodynamics, recent research in General Relativity has also revealed turbulent phenomena. Numerical studies of a self-gravitating massless scalar field in spherical symmetry gave evidence that anti-de Sitter space ...
Panda, Nishant; Dawson, Clint; Zhang, Yao; Kennedy, Andrew B.; Westerink, Joannes J.; Donahue, Aaron S.
2014-09-01
A local discontinuous Galerkin method for Boussinesq-Green-Naghdi equations is presented and validated against experimental results for wave transformation over a submerged shoal. Currently Green-Naghdi equations have many variants. In this paper a numerical method in one dimension is presented for the Green-Naghdi equations based on rotational characteristics in the velocity field. Stability criterion is also established for the linearized Green-Naghdi equations for both the analytical problem and the numerical method. Verification is done against a linearized standing wave problem in flat bathymetry and h, p (denoted by K in this paper) error rates are plotted. Validation plots show good agreement of the numerical results with the experimental ones.
Single-mode dispersive waves and soliton microcomb dynamics
Yi, Xu; Zhang, Xueyue; Yang, Ki Youl; Vahala, Kerry
2016-01-01
Dissipative Kerr solitons are self-sustaining optical wavepackets in resonators. They use the Kerr nonlinearity to both compensate dispersion and to offset optical loss. Besides providing insights into nonlinear resonator physics, they can be applied in frequency metrology, precision clocks, and spectroscopy. Like other optical solitons, the dissipative Kerr soliton can radiate power in the form of a dispersive wave through a process that is the optical analogue of Cherenkov radiation. Dispersive waves typically consist of an ensemble of optical modes. A limiting case is demonstrated in which the dispersive wave is concentrated into a single cavity mode. In this limit, its interaction with the soliton is shown to induce bistable behavior in the spectral and temporal properties of the soliton. Also, an operating point of enhanced repetition-rate stability is predicted and observed. The single-mode dispersive wave can therefore provide quiet states of soliton comb operation useful in many applications.
A nonlinear RDF model for waves propagating in shallow water
Institute of Scientific and Technical Information of China (English)
王厚杰; 杨作升; 李瑞杰; 张军
2001-01-01
In this paper, a composite explicit nonlinear dispersion relation is presented with reference to Stokes 2nd order dispersion relation and the empirical relation of Hedges. The explicit dispersion relation has such advantages that it can smoothly match the Stokes relation in deep and intermediate water and Hedgs’s relation in shallow water. As an explicit formula, it separates the nonlinear term from the linear dispersion relation. Therefore it is convenient to obtain the numerical solution of nonlinear dispersion relation. The present formula is combined with the modified mild-slope equation including nonlinear effect to make a Refraction-Diffraction (RDF) model for wave propagating in shallow water. This nonlinear model is verified over a complicated topography with two submerged elliptical shoals resting on a slope beach. The computation results compared with those obtained from linear model show that at present the nonlinear RDF model can predict the nonlinear characteristics and the combined refracti
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......, it is the universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...
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...
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....
New explicit exact solutions to a nonlinear dispersive-dissipative equation
Institute of Scientific and Technical Information of China (English)
Naranmandula; Wang Ke-Xie
2004-01-01
Using the first-integral method, we obtain a series of new explicit exact solutions such as exponential function solutions, triangular function solutions, singular solitary wave solution and kink solitary wave solution of a nonlinear dispersive-dissipative equation, which describes weak nonlinear ion-acoustic waves in plasma consisting of cold ions and warm electrons.
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.
DEFF Research Database (Denmark)
Chow, K.K.; Shu, Chester; Lin, Chinlon;
2006-01-01
All optical wavelength multicasting at 4 x 10 Gb/s with extinction ratio enhancement has been demonstrated based on pump-modulated four-wave mixing in a nonlinear photonic crystal fiber. We show that the input signal wavelength can simultaneously convert to four different wavelengths, with a power...
Dispersive shock waves in nematic liquid crystals
Smyth, Noel F.
2016-10-01
The propagation of coherent light with an initial step intensity profile in a nematic liquid crystal is studied using modulation theory. The propagation of light in a nematic liquid crystal is governed by a coupled system consisting of a nonlinear Schrödinger equation for the light beam and an elliptic equation for the medium response. In general, the intensity step breaks up into a dispersive shock wave, or undular bore, and an expansion fan. In the experimental parameter regime for which the nematic response is highly nonlocal, this nematic bore is found to differ substantially from the standard defocusing nonlinear Schrödinger equation structure due to the effect of the nonlocality of the nematic medium. It is found that the undular bore is of Korteweg-de Vries equation-type, consisting of bright waves, rather than of nonlinear Schrödinger equation-type, consisting of dark waves. In addition, ahead of this Korteweg-de Vries bore there can be a uniform wavetrain with a short front which brings the solution down to the initial level ahead. It is found that this uniform wavetrain does not exist if the initial jump is below a critical value. Analytical solutions for the various parts of the nematic bore are found, with emphasis on the role of the nonlocality of the nematic medium in shaping this structure. Excellent agreement between full numerical solutions of the governing nematicon equations and these analytical solutions is found.
Properties of Nonlinear Dynamo Waves
Tobias, S. M.
1997-01-01
Dynamo theory offers the most promising explanation of the generation of the sun's magnetic cycle. Mean field electrodynamics has provided the platform for linear and nonlinear models of solar dynamos. However, the nonlinearities included are (necessarily) arbitrarily imposed in these models. This paper conducts a systematic survey of the role of nonlinearities in the dynamo process, by considering the behaviour of dynamo waves in the nonlinear regime. It is demonstrated that only by considering realistic nonlinearities that are non-local in space and time can modulation of the basic dynamo wave he achieved. Moreover, this modulation is greatest when there is a large separation of timescales provided by including a low magnetic Prandtl number in the equation for the velocity perturbations.
Nonlinear wave-wave interactions and wedge waves
Institute of Scientific and Technical Information of China (English)
Ray Q.Lin; Will Perrie
2005-01-01
A tetrad mechanism for exciting long waves,for example edge waves,is described based on nonlinear resonant wave-wave interactions.In this mechanism,resonant interactions pass energy to an edge wave,from the three participating gravity waves.The estimated action flux into the edge wave can be orders of magnitude greater than the transfer fluxes derived from other competing mechanisms,such as triad interactions.Moreover,the numerical results show that the actual transfer rates into the edge wave from the three participating gravity waves are two-to three- orders of magnitude greater than bottom friction.
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...... of a constantly maintained pump wave is derived and a general dispersion relation describing the modulation of the high frequency wave due to different low frequency responses is obtained. Particular attention is devoted to a purely growing modulation. The relative importance of the ponderomotive force...
Extended models of nonlinear waves in liquid with gas bubbles
Kudryashov, Nikolay A
2016-01-01
In this work we generalize the models for nonlinear waves in a gas--liquid mixture taking into account an interphase heat transfer, a surface tension and a weak liquid compressibility simultaneously at the derivation of the equations for nonlinear waves. We also take into consideration high order terms with respect to the small parameter. Two new nonlinear differential equations are derived for long weakly nonlinear waves in a liquid with gas bubbles by the reductive perturbation method considering both high order terms with respect to the small parameter and the above mentioned physical properties. One of these equations is the perturbation of the Burgers equation and corresponds to main influence of dissipation on nonlinear waves propagation. The other equation is the perturbation of the Burgers--Korteweg--de Vries equation and corresponds to main influence of dispersion on nonlinear waves propagation.
Observation of Dispersive Shock Waves, Solitons, and Their Interactions in Viscous Fluid Conduits.
Maiden, Michelle D; Lowman, Nicholas K; Anderson, Dalton V; Schubert, Marika E; Hoefer, Mark A
2016-04-29
Dispersive shock waves and solitons are fundamental nonlinear excitations in dispersive media, but dispersive shock wave studies to date have been severely constrained. Here, we report on a novel dispersive hydrodynamic test bed: the effectively frictionless dynamics of interfacial waves between two high viscosity contrast, miscible, low Reynolds number Stokes fluids. This scenario is realized by injecting from below a lighter, viscous fluid into a column filled with high viscosity fluid. The injected fluid forms a deformable pipe whose diameter is proportional to the injection rate, enabling precise control over the generation of symmetric interfacial waves. Buoyancy drives nonlinear interfacial self-steepening, while normal stresses give rise to the dispersion of interfacial waves. Extremely slow mass diffusion and mass conservation imply that the interfacial waves are effectively dissipationless. This enables high fidelity observations of large amplitude dispersive shock waves in this spatially extended system, found to agree quantitatively with a nonlinear wave averaging theory. Furthermore, several highly coherent phenomena are investigated including dispersive shock wave backflow, the refraction or absorption of solitons by dispersive shock waves, and the multiphase merging of two dispersive shock waves. The complex, coherent, nonlinear mixing of dispersive shock waves and solitons observed here are universal features of dissipationless, dispersive hydrodynamic flows.
Reconstruction of nonlinear wave propagation
Fleischer, Jason W; Barsi, Christopher; Wan, Wenjie
2013-04-23
Disclosed are systems and methods for characterizing a nonlinear propagation environment by numerically propagating a measured output waveform resulting from a known input waveform. The numerical propagation reconstructs the input waveform, and in the process, the nonlinear environment is characterized. In certain embodiments, knowledge of the characterized nonlinear environment facilitates determination of an unknown input based on a measured output. Similarly, knowledge of the characterized nonlinear environment also facilitates formation of a desired output based on a configurable input. In both situations, the input thus characterized and the output thus obtained include features that would normally be lost in linear propagations. Such features can include evanescent waves and peripheral waves, such that an image thus obtained are inherently wide-angle, farfield form of microscopy.
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...
Institute of Scientific and Technical Information of China (English)
WANG Qi; CHEN Yong; ZHANG Hong-Qing
2005-01-01
In this work we devise an algebraic method to uniformly construct rational form solitary wave solutions and Jacobi and Weierstrass doubly periodic wave solutions of physical interest for nonlinear evolution equations. With the aid of symbolic computation, we apply the proposed method to solving the (1+1)-dimensional dispersive long wave equation and explicitly construct a series of exact solutions which include the rational form solitary wave solutions and elliptic doubly periodic wave solutions as special cases.
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 resonance a stationary state arise consisting of multiple oscillating shock waves. Off resonance driving leads to a nearly linear oscillating ground state but superimposed by bursts of a fast oscillating shock wave. Based on a travelling wave ansatz for the fluid velocity potential with an added 2'nd order...... 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....
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...
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 universality and robustness of the main models with respect to perturbations that developped the field. This is true for both continuous and discrete equations. In this volume we keep this broad view and draw new perspectives for nonlinear waves in complex systems. In particular we address energy flow...... in Fourier space and equipartition, the role of inhomogeneities and complex geometry and the importance of coupled systems....
Institute of Scientific and Technical Information of China (English)
Yan Wang; Qing Wang; Wei Zhang; Xiaoming Liu; Jiangde Peng
2005-01-01
@@ A broadband multiwavelength Raman fiber ring laser (RFRL) covering the whole C-band at room temperature are presented. The effect of the intracavity highly nonlinear dispersion-shifted fiber on broadening and flattening the output spectrum envelope is discussed and experimentally demonstrated. More than 45-dB extinction-ratio multiwavelength output from 1527.76 to 1566.86 nm with 100-GHz channel spacing and 2.1-dB power ripple has been achieved by carefully controlling the individual powers of three pump lasers.
Optical dispersive shock waves in defocusing colloidal media
An, X.; Marchant, T. R.; Smyth, N. F.
2017-03-01
The propagation of an optical dispersive shock wave, generated from a jump discontinuity in light intensity, in a defocusing colloidal medium is analysed. The equations governing nonlinear light propagation in a colloidal medium consist of a nonlinear Schrödinger equation for the beam and an algebraic equation for the medium response. In the limit of low light intensity, these equations reduce to a perturbed higher order nonlinear Schrödinger equation. Solutions for the leading and trailing edges of the colloidal dispersive shock wave are found using modulation theory. This is done for both the perturbed nonlinear Schrödinger equation and the full colloid equations for arbitrary light intensity. These results are compared with numerical solutions of the colloid equations.
Databases of surface wave dispersion
Directory of Open Access Journals (Sweden)
L. Boschi
2005-06-01
Full Text Available Observations of seismic surface waves provide the most important constraint on the elastic properties of the Earths lithosphere and upper mantle. Two databases of fundamental mode surface wave dispersion were recently compiled and published by groups at Harvard (Ekström et al., 1997 and Utrecht/Oxford (Trampert and Woodhouse, 1995, 2001, and later employed in 3-d global tomographic studies. Although based on similar sets of seismic records, the two databases show some significant discrepancies. We derive phase velocity maps from both, and compare them to quantify the discrepancies and assess the relative quality of the data; in this endeavour, we take careful account of the effects of regularization and parametrization. At short periods, where Love waves are mostly sensitive to crustal structure and thickness, we refer our comparison to a map of the Earths crust derived from independent data. On the assumption that second-order effects like seismic anisotropy and scattering can be neglected, we find the measurements of Ekström et al. (1997 of better quality; those of Trampert and Woodhouse (2001 result in phase velocity maps of much higher spatial frequency and, accordingly, more difficult to explain and justify geophysically. The discrepancy is partly explained by the more conservative a priori selection of data implemented by Ekström et al. (1997. Nevertheless, it becomes more significant with decreasing period, which indicates that it could also be traced to the different measurement techniques employed by the authors.
Nonlinear electron acoustic waves in presence of shear magnetic field
Energy Technology Data Exchange (ETDEWEB)
Dutta, Manjistha; Khan, Manoranjan [Department of Instrumentation Science, Jadavpur University, Kolkata 700 032 (India); Ghosh, Samiran [Department of Applied Mathematics, University of Calcutta 92, Acharya Prafulla Chandra Road, Kolkata 700 009 (India); Chakrabarti, Nikhil [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064 (India)
2013-12-15
Nonlinear electron acoustic waves are studied in a quasineutral plasma in the presence of a variable magnetic field. The fluid model is used to describe the dynamics of two temperature electron species in a stationary positively charged ion background. Linear analysis of the governing equations manifests dispersion relation of electron magneto sonic wave. Whereas, nonlinear wave dynamics is being investigated by introducing Lagrangian variable method in long wavelength limit. It is shown from finite amplitude analysis that the nonlinear wave characteristics are well depicted by KdV equation. The wave dispersion arising in quasineutral plasma is induced by transverse magnetic field component. The results are discussed in the context of plasma of Earth's magnetosphere.
Hopf Bifurcation in a Nonlinear Wave System
Institute of Scientific and Technical Information of China (English)
HE Kai-Fen
2004-01-01
@@ Bifurcation behaviour of a nonlinear wave system is studied by utilizing the data in solving the nonlinear wave equation. By shifting to the steady wave frame and taking into account the Doppler effect, the nonlinear wave can be transformed into a set of coupled oscillators with its (stable or unstable) steady wave as the fixed point.It is found that in the chosen parameter regime, both mode amplitudes and phases of the wave can bifurcate to limit cycles attributed to the Hopf instability. It is emphasized that the investigation is carried out in a pure nonlinear wave framework, and the method can be used for the further exploring routes to turbulence.
Wave equation with concentrated nonlinearities
Noja, Diego; Posilicano, Andrea
2004-01-01
In this paper we address the problem of wave dynamics in presence of concentrated nonlinearities. Given a vector field $V$ on an open subset of $\\CO^n$ and a discrete set $Y\\subset\\RE^3$ with $n$ elements, we define a nonlinear operator $\\Delta_{V,Y}$ on $L^2(\\RE^3)$ which coincides with the free Laplacian when restricted to regular functions vanishing at $Y$, and which reduces to the usual Laplacian with point interactions placed at $Y$ when $V$ is linear and is represented by an Hermitean m...
New multi-soliton solutions and travelling wave solutions of the dispersive long-wave equations
Institute of Scientific and Technical Information of China (English)
张解放; 郭冠平; 吴锋民
2002-01-01
Using the extended homogeneous balance method, the (1+1)-dimensional dispersive Iong-wave equations have been solved. Starting from the homogeneous balance method, we have obtained a nonlinear transformation for simplifying a dispersive long-wave equation into a linear partial differential equation. Usually, we can obtain only a type of soliton-like solution. In this paper, we have further found some new multi-soliton solutions and exact travelling solutions of the dispersive long-wave equations from the linear partial equation.
Stationary one-dimensional dispersive shock waves
Kartashov, Yaroslav V
2011-01-01
We address shock waves generated upon the interaction of tilted plane waves with negative refractive index defect in defocusing media with linear gain and two-photon absorption. We found that in contrast to conservative media where one-dimensional dispersive shock waves usually exist only as nonstationary objects expanding away from defect or generating beam, the competition between gain and two-photon absorption in dissipative medium results in the formation of localized stationary dispersive shock waves, whose transverse extent may considerably exceed that of the refractive index defect. One-dimensional dispersive shock waves are stable if the defect strength does not exceed certain critical value.
Nonlinear propagation and control of acoustic waves in phononic superlattices
Jiménez, Noé; Picó, Rubén; García-Raffi, Lluís M; Sánchez-Morcillo, Víctor J
2015-01-01
The propagation of intense acoustic waves in a one-dimensional phononic crystal is studied. The medium consists in a structured fluid, formed by a periodic array of fluid layers with alternating linear acoustic properties and quadratic nonlinearity coefficient. The spacing between layers is of the order of the wavelength, therefore Bragg effects such as band-gaps appear. We show that the interplay between strong dispersion and nonlinearity leads to new scenarios of wave propagation. The classical waveform distortion process typical of intense acoustic waves in homogeneous media can be strongly altered when nonlinearly generated harmonics lie inside or close to band gaps. This allows the possibility of engineer a medium in order to get a particular waveform. Examples of this include the design of media with effective (e.g. cubic) nonlinearities, or extremely linear media (where distortion can be cancelled). The presented ideas open a way towards the control of acoustic wave propagation in nonlinear regime.
Exact solitary wave solutions of nonlinear wave equations
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The hyperbolic function method for nonlinear wave equations ispresented. In support of a computer algebra system, many exact solitary wave solutions of a class of nonlinear wave equations are obtained via the method. The method is based on the fact that the solitary wave solutions are essentially of a localized nature. Writing the solitary wave solutions of a nonlinear wave equation as the polynomials of hyperbolic functions, the nonlinear wave equation can be changed into a nonlinear system of algebraic equations. The system can be solved via Wu Elimination or Grbner base method. The exact solitary wave solutions of the nonlinear wave equation are obtained including many new exact solitary wave solutions.
Shear Flow Dispersion Under Wave and Current
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The longitudinal dispersion of solute in open channel flow with short period progressive waves is investigated. The waves induce second order drift velocity in the direction of propagation and enhance the mixing process in concurrent direction. The 1-D wave-period-averaged dispersion equation is derived and an expression for the wave-current induced longitudinal dispersion coefficient (WCLDC) is proposed based on Fischer's expression (1979) for dispersion in unidirectional flow. The result shows that the effect of waves on dispersion is mainly due to the cross-sectional variation of the drift velocity. Furthermore, to obtain a more practical expression of the WCLDC, the longitudinal dispersion coefficient due to Seo and Cheong (1998) is modified to incluee the effect of drift velocity. Laboratory experiments have been conducted to verify the proposed expression. The experimental results, together with dimensional analysis, show that the wave effect can be reflected by the ratio between the wave amplitude and wave period. A comparative study between the cases with and without waves demonstrates that the magnitude of the longitudinal dispersion coefficient is increased under the presence of waves.
QT dispersion and P wave dispersion in patients with fibromyalgia.
Yolbaş, Servet; Yıldırım, Ahmet; Düzenci, Deccane; Karakaya, Bülent; Dağlı, Mustafa Necati; Koca, Süleyman Serdar
2016-12-01
Fibromyalgia (FM) is a chronic disease characterized by widespread pain. Somatic complaints associated with the cardiovascular system, such as chest pain and palpitations, are frequently seen in FM patients. P and QT dispersions are simple and inexpensive measurements reflecting the regional heterogeneity of atrial and ventricular repolarization, respectively. QT dispersion can cause serious ventricular arrhythmias. The aim of the present study was to evaluate QT dispersion and P wave dispersion in patients with FM. The study involved 48 FM patients who fulfilled the established criteria and 32 healthy controls (HC). A standard 12-lead electrocardiogram was performed on all participants. QT dispersion was defined as the difference between the longest and the shortest QT intervals. Similarly, the differences between the shortest and longest P waves were defined as P wave dispersion. The QT dispersion and corrected QT dispersion were shorter in the FM group compared with the HC group (pdispersion value, there was no significant difference between the FM and HC groups (p=0.088). Longer QT and P wave dispersions are not problems in patients with FM. Therefore, it may be concluded that fibromyalgia does not include an increased risk of atrial and/or ventricular arrhythmias.
Nonlinear Alfvén wave dynamics in plasmas
Energy Technology Data Exchange (ETDEWEB)
Sarkar, Anwesa; Chakrabarti, Nikhil [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064 (India); Schamel, Hans [Theoretical Physics, University of Bayreuth, D-95440 Bayreuth (Germany)
2015-07-15
Nonlinear Alfvén wave dynamics is presented using Lagrangian fluid approach in a compressible collisional magnetized plasma. In the framework of two fluid dynamics, finite electron inertia is shown to serve as a dispersive effect acting against the convective nonlinearity. In a moving frame, the Alfvén wave can, therefore, form an arbitrarily strong amplitude solitary wave structure due to the balance between nonlinearity and dispersion. Weak amplitude Alfvén waves are shown to be governed by a modified KdV equation, which extends for finite dissipation to a mKdV-Burgers equation. These equations have well known solutions. Next, we have analyzed the fourth order nonlinear Alfvén wave system of equations both numerically and by approximation method. The results indicate a collapse of the density and magnetic field irrespective of the presence of dispersion. The wave magnetic field, however, appears to be less singular showing collapse only when the dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas and are expected to be of special importance in the astrophysical context of magnetic star formation.
Nonlinear Alfvén wave dynamics in plasmas
Sarkar, Anwesa; Chakrabarti, Nikhil; Schamel, Hans
2015-07-01
Nonlinear Alfvén wave dynamics is presented using Lagrangian fluid approach in a compressible collisional magnetized plasma. In the framework of two fluid dynamics, finite electron inertia is shown to serve as a dispersive effect acting against the convective nonlinearity. In a moving frame, the Alfvén wave can, therefore, form an arbitrarily strong amplitude solitary wave structure due to the balance between nonlinearity and dispersion. Weak amplitude Alfvén waves are shown to be governed by a modified KdV equation, which extends for finite dissipation to a mKdV-Burgers equation. These equations have well known solutions. Next, we have analyzed the fourth order nonlinear Alfvén wave system of equations both numerically and by approximation method. The results indicate a collapse of the density and magnetic field irrespective of the presence of dispersion. The wave magnetic field, however, appears to be less singular showing collapse only when the dispersive effects are negligible. These results may contribute to our understanding of the generation of strongly localized magnetic fields (and currents) in plasmas and are expected to be of special importance in the astrophysical context of magnetic star formation.
Exact Wave Solutions for the High-order Dispersive Nonlinear Schr odinger Equation%高阶色散非线性薛定谔方程的精确波解
Institute of Scientific and Technical Information of China (English)
施业琼; 韩松
2009-01-01
利用行波约化方法,研究了用于描述飞秒光脉冲传输的高阶色散非线性薛定谔方程.通过借助一个新的高阶辅助方程的解,取得了该方程不同类型的包络型的孤波解、扭结波解、周期波解及奇异波解.%By using the traveling wave reduction method, a new auxiliary differential equation and its solutions are used to construct the exact traveling wave solutions, some new exact solutions for the high-order dispersive nonlinear Schrodinger equation are obtained which include bell profile solutions, kink profile solutions, triangular periodic solutions and singular solutions. This equation is used to describe the propagation of femtosecond optical pulses in fibers.
Hamiltonian theory of nonlinear waves in planetary rings
Stewart, G. R.
1987-01-01
The derivation of a Hamiltonian field theory for nonlinear density waves in Saturn's rings is discussed. Starting with a Hamiltonian for a discrete system of gravitating streamlines, an averaged Hamiltonian is obtained by successive applications of Lie transforms. The transformation may be carried out to any desired order in q, where q is the nonlinearity parameter defined in the work of Shu, et al (1985) and Borderies et al (1985). Subsequent application of the Wentzel-Kramer-Brillouin Method approximation yields an asymptotic field Hamiltonian. Both the nonlinear dispersion relation and the wave action transport equation are easily derived from the corresponding Lagrangian by the standard variational principle.
Non-classical dispersive shock waves in shallow water
Sprenger, Patrick; Hoefer, Mark
2016-11-01
A classical model for shallow water waves with strong surface tension is the Kawahara equation, which is the Korteweg-de Vries (KdV) including a fifth order derivative term. A particular problem of interest to these types of equations is step initial data, known as the Riemann problem, which results in a shock in finite time. Unlike classical shock waves, where a discontinuity is resolved by dissipation, the dispersive regularization results in the discontinuity resolved as a dispersive shock wave (DSW). When parameter choices result in non-convex dispersion, three distinct dynamic regimes are observed that can be characterized solely by the amplitude of the initial step. For small jumps, a perturbed KdV DSW with positive polarity and orientation is generated, accompanied by small amplitude radiation from an embedded solitary wave leading edge, termed a radiating DSW. For moderate jumps, a crossover regime is observed with waves propagating forward and backward from the sharp transition region. For sufficiently large jumps, a new type of DSW is observed we term a translating DSW were a partial, non-monotonic, negative solitary wave at the trailing edge is connected to an interior nonlinear periodic wave and exhibits features common to both dissipative and dispersive shock waves.
Dispersion managed solitons in the presence of saturated nonlinearity
Hundertmark, Dirk; Lee, Young-Ran; Ried, Tobias; Zharnitsky, Vadim
2017-10-01
The averaged dispersion managed nonlinear Schrödinger equation with saturated nonlinearity is considered. It is shown that under rather general assumptions on the saturated nonlinearity, the ground state solution corresponding to the dispersion managed soliton can be found for both zero residual dispersion and positive residual dispersion. The same applies to diffraction management solitons, which are a discrete version describing certain waveguide arrays.
Institute of Scientific and Technical Information of China (English)
Xiao Li; Zhang Wei; Huang Yi-Dong; Peng Jiang-De
2008-01-01
High nonlinear microstructure fibre (HNMF) is preferred in nonlinear fibre optics, especially in the applications of optical parametric effects, due to its high optical nonlinear coefficient. However, polarization dependent dispersion will impact the nonlinear optical parametric process in HNMFs. In this paper, modulation instability (MI) method is used to measure the polarization dependent dispersion of a piece of commercial HNMF, including the group velocity dispersion, the dispersion slope, the fourth-order dispersion and group birefringence. It also experimentally demonstrates the impact of the polarization dependent dispersion on the continuous wave supercontinuum (SC) generation. On one axis MI sidebands with symmetric frequency dctunings are generated, while on the other axis with larger MI frequency detuning, SC is generated by soliton self-frequency shift.
Standing waves for discrete nonlinear Schrodinger equations
Ming Jia
2016-01-01
The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. By using critical point theory, we establish some new sufficient conditions on the existence results of standing waves for the discrete nonlinear Schrodinger equations. We give an appropriate example to illustrate the conclusion obtained.
Parametric interaction and intensification of nonlinear Kelvin waves
Novotryasov, Vadim
2008-01-01
Observational evidence is presented for nonlinear interaction between mesoscale internal Kelvin waves at the tidal -- $\\omega_t$ or the inertial -- $\\omega_i$ frequency and oscillations of synoptic -- $\\Omega $ frequency of the background coastal current of Japan/East Sea. Enhanced coastal currents at the sum -- $\\omega_+ $ and dif -- $\\omega_-$ frequencies: $\\omega_\\pm =\\omega_{t,i}\\pm \\Omega$ have properties of propagating Kelvin waves suggesting permanent energy exchange from the synoptic band to the mesoscale $\\omega_\\pm $ band. The interaction may be responsible for the greater than predicted intensification, steepen and break of boundary trapped and equatorially trapped Kelvin waves, which can affect El Ni\\~{n}o. The problem on the parametric interaction of the nonlinear Kelvin wave at the frequency $\\omega $ and the low-frequency narrow-band nose with representative frequency $\\Omega\\ll\\omega $ is investigated with the theory of nonlinear week dispersion waves.
Quantification and prediction of rare events in nonlinear waves
Sapsis, Themistoklis; Cousins, Will; Mohamad, Mustafa
2014-11-01
The scope of this work is the quantification and prediction of rare events characterized by extreme intensity, in nonlinear dispersive models that simulate water waves. In particular we are interested for the understanding and the short-term prediction of rogue waves in the ocean and to this end, we consider 1-dimensional nonlinear models of the NLS type. To understand the energy transfers that occur during the development of an extreme event we perform a spatially localized analysis of the energy distribution along different wavenumbers by means of the Gabor transform. A stochastic analysis of the Gabor coefficients reveals i) the low-dimensionality of the intermittent structures, ii) the interplay between non-Gaussian statistical properties and nonlinear energy transfers between modes, as well as iii) the critical scales (or Gabor coefficients) where a critical energy can trigger the formation of an extreme event. The unstable character of these critical localized modes is analysed directly through the system equation and it is shown that it is defined as the result of the system nonlinearity and the wave dissipation (that mimics wave breaking). These unstable modes are randomly triggered through the dispersive ``heat bath'' of random waves that propagate in the nonlinear medium. Using these properties we formulate low-dimensional functionals of these Gabor coefficients that allow for the prediction of extreme event well before the strongly nonlinear interactions begin to occur. The prediction window is further enhanced by the combination of the developed scheme with traditional filtering schemes.
Adiabatic theory of solitons fed by dispersive waves
Pickartz, Sabrina; Bandelow, Uwe; Amiranashvili, Shalva
2016-09-01
We consider scattering of low-amplitude dispersive waves at an intense optical soliton which constitutes a nonlinear perturbation of the refractive index. Specifically, we consider a single-mode optical fiber and a group velocity matched pair: an optical soliton and a nearly perfectly reflected dispersive wave, a fiber-optical analog of the event horizon. By combining (i) an adiabatic approach that is used in soliton perturbation theory and (ii) scattering theory from quantum mechanics, we give a quantitative account of the evolution of all soliton parameters. In particular, we quantify the increase in the soliton peak power that may result in the spontaneous appearance of an extremely large, so-called champion soliton. The presented adiabatic theory agrees well with the numerical solutions of the pulse propagation equation. Moreover, we predict the full frequency band of the scattered dispersive waves and explain an emerging caustic structure in the space-time domain.
New Optical Solitons in High-Order Dispersive Cubic-Quintic Nonlinear Schrodinger Equation
Institute of Scientific and Technical Information of China (English)
LI Hua-Mei; XU You-Shen; LIN Ji
2004-01-01
By using the generalized tanh-function method, we find bright and dark solitary wave solutions to an extended nonlinear Schrodinger equation with the third-order and fourth-order dispersion and the cubic-quintic nonlinear terms, describing the propagation of extremely short pulses. At the same time, we also obtained other types of exact solutions.
Modeling highly-dispersive transparency in planar nonlinear metamaterials
Potravkin, N. N.; Makarov, V. A.; Perezhogin, I. A.
2017-02-01
We consider propagation of light in planar optical metamaterial, which basic element is composed of two silver stripes, and it possesses strong dispersion in optical range. Our method of numerical modeling allows us to take into consideration the nonlinearity of the material and the effects of light self-action without considerable increase of the calculation time. It is shown that plasmonic resonances originating in such a structure result in multiple enhancement of local field and high sensitivity of the transmission coefficient to the intensity of incident monochromatic wave.
Skeletonized wave equation of surface wave dispersion inversion
Li, Jing
2016-09-06
We present the theory for wave equation inversion of dispersion curves, where the misfit function is the sum of the squared differences between the wavenumbers along the predicted and observed dispersion curves. Similar to wave-equation travel-time inversion, the complicated surface-wave arrivals in traces are skeletonized as simpler data, namely the picked dispersion curves in the (kx,ω) domain. Solutions to the elastic wave equation and an iterative optimization method are then used to invert these curves for 2D or 3D velocity models. This procedure, denoted as wave equation dispersion inversion (WD), does not require the assumption of a layered model and is less prone to the cycle skipping problems of full waveform inversion (FWI). The synthetic and field data examples demonstrate that WD can accurately reconstruct the S-wave velocity distribution in laterally heterogeneous media.
Interface-wave dispersion curves inversion based on nonlinear Bayesian theory%根据非线性贝叶斯理论的界面波频散曲线反演
Institute of Scientific and Technical Information of China (English)
李翠琳; Stan E Dosso; Hefeng Dong
2012-01-01
通过时频分析法从海底环境噪声数据中提取界面波频散曲线,进而采用非线性贝叶斯反演方法估算海底沉积物厚度、剪切波速度、压缩波速度和密度等参数及其不确定性.参数的最大后验概率(MAP)估计值和边缘概率分布分别通过自适应单纯形模拟退火法和Metropolis-Hastings采样法在各参数先验区间内搜索获得,采用贝叶斯信息准则(BIC)从不同参数化模型中选择最优模型.界面波频散曲线反演结果表明:满足实测数据的最优海底模型结构为3层均匀分布剪切波速度剖面结构,海底深度的反演精度在800 m以内,比起压缩波速度和密度,剪切波速度的不确定性更小,对界面波频散曲线更敏感.%This paper applies a dataset of ocean ambient noise data to extract interface-wave dispersion curves using time-frequency analysis. The nonlinear Bayesian inversion is applied to estimate seabed sediment parameters such as thickness, shear-wave velocity, compression wave velocity and density, and their uncertainties from interface-wave dispersion curves. The maximum a posterior (MAP) model and marginal probability distributions of parameters are estimated using posterior probability densities computed by adaptive simplex simulated annealing and Metropolis-Hastings sampling methods. The Bayesian information criterion is applied to determine the optimal model that fully explains the observed data by the different parameterizations. The inversion results indicate that 3-uniform-layer model is chosen as the preferred parameterization. The resolution of inversion is up to 800 m-depth. The shear-wave velocity and layer thickness have fewer uncertainties and are more sensitive to the interface wave dispersion than the compression wave velocity and density.
The Whitham approach to dispersive shocks in systems with cubic–quintic nonlinearities
Crosta, M
2012-09-12
By employing a rigorous approach based on the Whitham modulation theory, we investigate dispersive shock waves arising in a high-order nonlinear Schrödinger equation with competing cubic and quintic nonlinear responses. This model finds important applications in both nonlinear optics and Bose–Einstein condensates. Our theory predicts the formation of dispersive shocks with totally controllable properties, encompassing both steering and compression effects. Numerical simulations confirm these results perfectly. Quite remarkably, shock tuning can be achieved in the regime of a very small high order, i.e. quintic, nonlinearity.
Hyperbolic Mild Slope Equations with Inclusion of Amplitude Dispersion Effect: Regular Waves
Institute of Scientific and Technical Information of China (English)
JIN Hong; ZOU Zhi-li
2008-01-01
A new form of hyperbolic mild slope equations is derived with the inclusion of the amplitude dispersion of nonlinear waves. The effects of including the amplitude dispersion effect on the wave propagation are discussed. Wave breaking mechanism is incorporated into the present model to apply the new equations to surf zone. The equations are solved numerically for regular wave propagation over a shoal and in surf zone, and a comparison is made against measurements. It is found that the inclusion of the amplitude dispersion can also improve model's performance on prediction of wave heights around breaking point for the wave motions in surf zone.
Nonlinear Fourier analysis with cnoidal waves
Energy Technology Data Exchange (ETDEWEB)
Osborne, A.R. [Dipt. di Fisica Generale dell`Universita, Torino (Italy)
1996-12-31
Fourier analysis is one of the most useful tools to the ocean engineer. The approach allows one to analyze wave data and thereby to describe a dynamical motion in terms of a linear superposition of ordinary sine waves. Furthermore, the Fourier technique allows one to compute the response function of a fixed or floating structure: each sine wave in the wave or force spectrum yields a sine wave in the response spectrum. The counting of fatigue cycles is another area where the predictable oscillations of sine waves yield procedures for the estimation of the fatigue life of structures. The ocean environment, however, is a source of a number of nonlinear effects which must also be included in structure design. Nonlinearities in ocean waves deform the sinusoidal shapes into other kinds of waves such as the Stokes wave, cnoidal wave or solitary wave. A key question is: Does there exist a generalization of linear Fourier analysis which uses nonlinear basis functions rather than the familiar sine waves? Herein addresses the dynamics of nonlinear wave motion in shallow water where the basis functions are cnoidal waves and discuss nonlinear Fourier analysis in terms of a linear superposition of cnoidal waves plus their mutual nonlinear interactions. He gives a number of simple examples of nonlinear Fourier wave motion and then analyzes an actual surface-wave time series obtained on an offshore platform in the Adriatic Sea. Finally, he briefly discusses application of the cnoidal wave spectral approach to the computation of the frequency response function of a floating vessel. The results given herein will prove useful in future engineering studies for the design of fixed, floating and complaint offshore structures.
GEOMETRICAL NONLINEAR WAVES IN FINITE DEFORMATION ELASTIC RODS
Institute of Scientific and Technical Information of China (English)
GUO Jian-gang; ZHOU Li-jun; ZHANG Shan-yuan
2005-01-01
By using Hamilton-type variation principle in non-conservation system, the nonlinear equation of wave motion of a elastic thin rod was derived according to Lagrange description of finite deformation theory. The dissipation caused due to viscous effect and the dispersion introduced by transverse inertia were taken into consideration so that steady traveling wave solution can be obtained. Using multi-scale method the nonlinear equation is reduced to a KdV-Burgers equation which corresponds with saddle-spiral heteroclinic orbit on phase plane. Its solution is called the oscillating-solitary wave or saddle-spiral shock wave.If viscous effect or transverse inertia is neglected, the equation is degraded to classical KdV or Burgers equation. The former implies a propagating solitary wave with homoclinic on phase plane, the latter means shock wave and heteroclinic orbit.
Signal velocity for anomalous dispersive waves
Energy Technology Data Exchange (ETDEWEB)
Mainardi, F. (Bologna Univ. (Italy))
1983-03-11
The concept of signal velocity for dispersive waves is usually identified with that of group velocity. When the dispersion is anomalous, this interpretation is not correct since the group velocity can assume nonphysical values. In this note, by using the steepest descent method first introduced by Brillouin, the phase velocity is shown to be the signal velocity when the dispersion is anomalous in the full range of frequencies.
Nonlinear evolution of oblique whistler waves in radiation belts
Sharma, R. P.; Nandal, P.; Yadav, N.; Sharma, Swati
2017-02-01
Magnetic power spectrum and formation of coherent structures have been investigated in the present work applicable to Van Allen radiation belt. The nonlinear interaction of high frequency oblique whistler wave and low frequency magnetosonic wave has been investigated. Simulation was performed of the coupled equation of these two waves. The nonlinear interaction of these waves leads to the formation of the localized structures. These resulting localized structures are of complex nature. The associated magnetic power spectrum has also been studied. Dispersive nonlinear processes account for the high frequency part of the spectrum. The resulting magnetic power spectrum shows a scaling of k^{ - 4.5}. The energy transfer process from injection scales to smaller scales is explained by the results.
Spatial-mode-interaction-induced dispersive-waves and their active tuning in microresonators
Yang, Qi-Fan; Yang, Ki Youl; Vahala, Kerry
2016-01-01
The nonlinear propagation of optical pulses in dielectric waveguides and resonators provides a laboratory to investigate a wide range of remarkable interactions. Many of the resulting phenomena find applications in optical systems. One example is dispersive wave generation, the optical analog of Cherenkov radiation. These waves have an essential role in fiber spectral broadeners that are routinely used in spectrocopy and metrology. Dispersive waves form when a soliton pulse begins to radiate power as a result of higher-order dispersion. Recently, dispersive wave generation in microcavities has been reported by phase matching the waves to dissipative Kerr cavity (DKC) solitons. Here, it is shown that spatial mode interactions within a microcavity can also be used to induce dispersive waves. These interactions are normally avoided altogether in DKC soliton generation. The soliton self frequency shift is also shown to induce fine tuning control of the dispersive wave frequency. Both this mechanism and spatial mo...
Traveling wave solutions for some factorized nonlinear PDEs
Cornejo-Pérez, Octavio
2009-01-01
In this work, some new special traveling wave solutions of the convective Fisher equation, the time-delayed Burgers-Fisher equation, the Burgers-Fisher equation and a nonlinear dispersive-dissipative equation (Kakutani and Kawahara 1970 J. Phys. Soc. Japan 29 1068) are obtained through the factorization technique. All of them share the same type of factorization scheme, which reduces the original equation to a Riccati equation of the same kind, whose general solution is given in terms of Bessel and Neumann functions. In addition, some novel particular solutions of the nonlinear dispersive-dissipative equation are provided.
Hyperbolic Mild Slope Equations with Inclusion of Amplitude Dispersion Effect: Random Waves
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
New hyperbolic mild slope equations for random waves are developed with the inclusion of amplitude dispersion. The frequency perturbation around the peak frequency of random waves is adopted to extend the equations for regular waves to random waves. The nonlinear effect of amplitude dispersion is incorporated approximately into the model by only considering the nonlinear effect on the carrier waves of random waves, which is done by introducing a representative wave amplitude for the carrier waves. The computation time is greatly saved by the introduction of the representative wave amplitude. The extension of the present model to breaking waves is also considered in order to apply the new equations to surf zone. The model is validated for random waves propagate over a shoal and in surf zone against measurements.
Weakly relativistic dispersion of Bernstein waves
Robinson, P. A.
1988-01-01
Weakly relativistic effects on the dispersion of Bernstein waves are investigated for waves propagating nearly perpendicular to a uniform magnetic field in a Maxwellian plasma. Attention is focused on those large-wave-vector branches that are either weakly damped or join continuously onto weakly damped branches since these are the modes of most interest in applications. The transition between dispersion at perpendicular and oblique propagation is examined and major weakly relativistic effects can dominate even in low-temperature plasmas. A number of simple analytic criteria are obtained which delimit the ranges of harmonic number and propagation angle within which various types of weakly damped Bernstein modes can exist.
Weakly relativistic dispersion of Bernstein waves
Robinson, P. A.
1988-01-01
Weakly relativistic effects on the dispersion of Bernstein waves are investigated for waves propagating nearly perpendicular to a uniform magnetic field in a Maxwellian plasma. Attention is focused on those large-wave-vector branches that are either weakly damped or join continuously onto weakly damped branches since these are the modes of most interest in applications. The transition between dispersion at perpendicular and oblique propagation is examined and major weakly relativistic effects can dominate even in low-temperature plasmas. A number of simple analytic criteria are obtained which delimit the ranges of harmonic number and propagation angle within which various types of weakly damped Bernstein modes can exist.
Nonlinear evolution of whistler wave modulational instability
DEFF Research Database (Denmark)
Karpman, V.I.; Lynov, Jens-Peter; Michelsen, Poul;
1995-01-01
The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves (FMS) and to slow magnetosonic waves (SMS) is investigated. Results from direct numerical solutions in two spatial dimensions agree with simplified results from a set of ordinary different......The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves (FMS) and to slow magnetosonic waves (SMS) is investigated. Results from direct numerical solutions in two spatial dimensions agree with simplified results from a set of ordinary...
Dark solitons, dispersive shock waves, and transverse instabilities
Hoefer, M A
2011-01-01
The nature of transverse instabilities to dark solitons and dispersive shock waves for the (2+1)-dimensional defocusing nonlinear Schrodinger equation / Gross-Pitaevskii (NLS / GP) equation is considered. Special attention is given to the small (shallow) amplitude regime, which limits to the Kadomtsev-Petviashvili (KP) equation. We study analytically and numerically the eigenvalues of the linearized NLS / GP equation. The dispersion relation for shallow solitons is obtained asymptotically beyond the KP limit. This yields 1) the maximum growth rate and associated wavenumber of unstable perturbations; and 2) the separatrix between convective and absolute instabilities. The latter result is used to study the transition between convective and absolute instabilities of oblique dispersive shock waves (DSWs). Stationary and nonstationary oblique DSWs are constructed analytically and investigated numerically by direct simulations of the NLS / GP equation. The instability properties of oblique DSWs are found to be dir...
Inflationary cosmology with nonlinear dispersion relations
Zhu, Tao; Cleaver, Gerald; Kirsten, Klaus; Sheng, Qin
2013-01-01
We present a technique, {\\em the uniform asymptotic approximation}, to construct accurate analytical solutions of the linear perturbations of inflation after quantum effects of the early universe are taken into account, for which the dispersion relations generically become nonlinear. We construct explicitly the error bounds associated with the approximations and then study them in detail. With the understanding of the errors and the proper choice of the Liouville transformations of the differential equations of the perturbations, we show that the analytical solutions describe the exact evolution of the linear perturbations extremely well even only to the first-order approximations. As a simple application of the approximate analytical solutions, we calculate the power spectra and indices of scalar and tensor perturbations in the de Sitter background, and find that the amplitudes of the power spectra get modified due to the quantum effects, while the power spectrum indices remain the same as in the linear case...
Nonlinear Alfv\\'en waves in extended magnetohydrodynamics
Abdelhamid, Hamdi M
2015-01-01
Large-amplitude Alfv\\'en waves are observed in various systems in space and laboratories, demonstrating an interesting property that the wave shapes are stable even in the nonlinear regime. The ideal magnetohydrodynamics (MHD) model predicts that an Alfv\\'en wave keeps an arbitrary shape constant when it propagates on a homogeneous ambient magnetic field. However, such arbitrariness is an artifact of the idealized model that omits the dispersive effects. Only special wave forms, consisting of two component sinusoidal functions, can maintain the shape; we derive fully nonlinear Alfv\\'en waves by an extended MHD model that includes both the Hall and electron inertia effects. Interestingly, these \\small-scale effects" change the picture completely; the large-scale component of the wave cannot be independent of the small scale component, and the coexistence of them forbids the large scale component to have a free wave form. This is a manifestation of the nonlinearity-dispersion interplay, which is somewhat differ...
A Stochastic Nonlinear Water Wave Model for Efficient Uncertainty Quantification
Bigoni, Daniele; Eskilsson, Claes
2014-01-01
A major challenge in next-generation industrial applications is to improve numerical analysis by quantifying uncertainties in predictions. In this work we present a stochastic formulation of a fully nonlinear and dispersive potential flow water wave model for the probabilistic description of the evolution waves. This model is discretized using the Stochastic Collocation Method (SCM), which provides an approximate surrogate of the model. This can be used to accurately and efficiently estimate the probability distribution of the unknown time dependent stochastic solution after the forward propagation of uncertainties. We revisit experimental benchmarks often used for validation of deterministic water wave models. We do this using a fully nonlinear and dispersive model and show how uncertainty in the model input can influence the model output. Based on numerical experiments and assumed uncertainties in boundary data, our analysis reveals that some of the known discrepancies from deterministic simulation in compa...
Standing waves for discrete nonlinear Schrodinger equations
Directory of Open Access Journals (Sweden)
Ming Jia
2016-07-01
Full Text Available The discrete nonlinear Schrodinger equation is a nonlinear lattice system that appears in many areas of physics such as nonlinear optics, biomolecular chains and Bose-Einstein condensates. By using critical point theory, we establish some new sufficient conditions on the existence results of standing waves for the discrete nonlinear Schrodinger equations. We give an appropriate example to illustrate the conclusion obtained.
On the propagation of truncated localized waves in dispersive silica
Salem, Mohamed
2010-01-01
Propagation characteristics of truncated Localized Waves propagating in dispersive silica and free space are numerically analyzed. It is shown that those characteristics are affected by the changes in the relation between the transverse spatial spectral components and the wave vector. Numerical experiments demonstrate that as the non-linearity of this relation gets stronger, the pulses propagating in silica become more immune to decay and distortion whereas the pulses propagating in free-space suffer from early decay and distortion. © 2010 Optical Society of America.
Numerical and experimental investigation of nonlinear ultrasonic Lamb waves at low frequency
Zuo, Peng; Zhou, Yu; Fan, Zheng
2016-07-01
Nonlinear ultrasonic Lamb waves are popular to characterize the nonlinearity of materials. However, the widely used nonlinear Lamb mode suffers from two associated complications: inherent dispersive and multimode natures. To overcome these, the symmetric Lamb mode (S0) at low frequency region is explored. At the low frequency region, the S0 mode is little dispersive and easy to generate. However, the secondary mode still exists, and increases linearly for significant distance. Numerical simulations and experiments are used to validate the nonlinear features and therefore demonstrate an easy alternative for nonlinear Lamb wave applications.
Dispersive waves induced by self-defocusing temporal solitons in a beta-barium-borate crystal
DEFF Research Database (Denmark)
Zhou, Binbin; Bache, Morten
2015-01-01
We experimentally observe dispersive waves in the anomalous dispersion regime of a beta-barium-borate (BBO) crystal, induced by a self-defocusing few-cycle temporal soliton. Together the soliton and dispersive waves form an energetic octave-spanning supercontinuum. The soliton was excited...... in the normal dispersion regime of BBO through a negative cascaded quadratic nonlinearity. Using pump wavelengths from 1.24 to 1.4 μm, dispersive waves are found from 1.9 to 2.2 μm, agreeing well with calculated resonant phasematching wavelengths due to degenerate four-wave mixing to the soliton. We also...... observe resonant radiation from nondegenerate four-wave mixing between the soliton and a probe wave, which was formed by leaking part of the pump spectrum into the anomalous dispersion regime. We confirm the experimental results through simulations....
Dispersive waves induced by self-defocusing temporal solitons in a beta-barium-borate crystal.
Zhou, Binbin; Bache, Morten
2015-09-15
We experimentally observe dispersive waves in the anomalous dispersion regime of a beta-barium-borate (BBO) crystal, induced by a self-defocusing few-cycle temporal soliton. Together the soliton and dispersive waves form an energetic octave-spanning supercontinuum. The soliton was excited in the normal dispersion regime of BBO through a negative cascaded quadratic nonlinearity. Using pump wavelengths from 1.24 to 1.4 μm, dispersive waves are found from 1.9 to 2.2 μm, agreeing well with calculated resonant phase-matching wavelengths due to degenerate four-wave mixing to the soliton. We also observe resonant radiation from nondegenerate four-wave mixing between the soliton and a probe wave, which was formed by leaking part of the pump spectrum into the anomalous dispersion regime. We confirm the experimental results through simulations.
Time-reversal of nonlinear waves: Applicability and limitations
Ducrozet, G.; Fink, M.; Chabchoub, A.
2016-09-01
Time-reversal (TR) refocusing of waves is one of the fundamental principles in wave physics. Using the TR approach, time-reversal mirrors can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backward. Laboratory experiments have proved that this approach can be applied not only in acoustics and electromagnetism, but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic time-reversal using a unidirectional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configurations, pointing out the importance of high-order dispersive and particularly nonlinear effects in the refocusing of hydrodynamic stationary envelope solitons and breathers. We expect that the results may motivate similar experiments in other nonlinear dispersive media and encourage several applications with particular emphasis on the field of ocean engineering.
Solving Nonlinear Wave Equations by Elliptic Equation
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Da; LIU Shi-Kuo
2003-01-01
The elliptic equation is taken as a transformation and applied to solve nonlinear wave equations. It is shown that this method is more powerful to give more kinds of solutions, such as rational solutions, solitary wave solutions,periodic wave solutions and so on, so it can be taken as a generalized method.
Statistical distribution of nonlinear random wave height
Institute of Scientific and Technical Information of China (English)
HOU; Yijun; GUO; Peifang; SONG; Guiting; SONG; Jinbao; YIN; Baoshu; ZHAO; Xixi
2006-01-01
A statistical model of random wave is developed using Stokes wave theory of water wave dynamics. A new nonlinear probability distribution function of wave height is presented. The results indicate that wave steepness not only could be a parameter of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution. The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated. The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution. Wave height data taken from East China Normal University are used to verify the new distribution. The results indicate that the new distribution fits the measurements much better than the Rayleigh distribution.
Generation and propagation of nonlinear internal waves in Massachusetts Bay
Scotti, A.; Beardsley, R.C.; Butman, B.
2007-01-01
During the summer, nonlinear internal waves (NLIWs) are commonly observed propagating in Massachusetts Bay. The topography of the area is unique in the sense that the generation area (over Stellwagen Bank) is only 25 km away from the shoaling area, and thus it represents an excellent natural laboratory to study the life cycle of NLIWs. To assist in the interpretation of the data collected during the 1998 Massachusetts Bay Internal Wave Experiment (MBIWE98), a fully nonlinear and nonhydrostatic model covering the generation/shoaling region was developed, to investigate the response of the system to the range of background and driving conditions observed. Simplified models were also used to elucidate the role of nonlinearity and dispersion in shaping the NLIW field. This paper concentrates on the generation process and the subsequent evolution in the basin. The model was found to reproduce well the range of propagation characteristics observed (arrival time, propagation speed, amplitude), and provided a coherent framework to interpret the observations. Comparison with a fully nonlinear hydrostatic model shows that during the generation and initial evolution of the waves as they move away from Stellwagen Bank, dispersive effects play a negligible role. Thus the problem can be well understood considering the geometry of the characteristics along which the Riemann invariants of the hydrostatic problem propagate. Dispersion plays a role only during the evolution of the undular bore in the middle of Stellwagen Basin. The consequences for modeling NLIWs within hydrostatic models are briefly discussed at the end.
Control methods for localization of nonlinear waves
Porubov, Alexey; Andrievsky, Boris
2017-03-01
A general form of a distributed feedback control algorithm based on the speed-gradient method is developed. The goal of the control is to achieve nonlinear wave localization. It is shown by example of the sine-Gordon equation that the generation and further stable propagation of a localized wave solution of a single nonlinear partial differential equation may be obtained independently of the initial conditions. The developed algorithm is extended to coupled nonlinear partial differential equations to obtain consistent localized wave solutions at rather arbitrary initial conditions. This article is part of the themed issue 'Horizons of cybernetical physics'.
Hui, Zhan-Qiang; Zhang, Bo; Zhang, Jian-Guo
2016-04-01
All-optical NRZ-to-RZ format conversion with a function of wavelength multicasting is proposed in this paper, which is realized by exploiting cross-phase modulation (XPM) and four-wave-mixing (FWM) in a dispersion-flattened highly nonlinear photonic crystal fiber (DF-HNL-PCF). The designed format converter is experimentally demonstrated, for which the 1-to-4 wavelength multicasting is achieved simultaneously by filtering out two FWM idler waves and both blue-chirped and red-chirped components of the broadened NRZ spectrum induced by XPM. Moreover, the wavelength tunability and dynamic characteristics of the proposed NRZ-to-RZ format converter are also exploited using the different central wavelengths of an optical clock signal and varying the input optical power at a DF-HNL-PCF in our experiment. It is shown that the designed format converter can possess a wide range of operational wavelength over 17 nm, an optimal extinction ratio of 11.6 dB, and a Q-factor of 7.1, respectively. Since the proposed scheme uses an optical fiber-based configuration and is easy for implementation, it can be very useful for future applications in advanced fiber-optic communication networks.
Nonlinear and Dispersive Optical Pulse Propagation
Dijaili, Sol Peter
In this dissertation, there are basically four novel contributions to the field of picosecond pulse propagation and measurement. The first contribution is the temporal ABCD matrix which is an analog of the traditional ABCD ray matrices used in Gaussian beam propagation. The temporal ABCD matrix allows for the easy calculation of the effects of linear chirp or group velocity dispersion in the time domain. As with Gaussian beams in space, there also exists a complete Hermite-Gaussian basis in time whose propagation can be tracked with the temporal ABCD matrices. The second contribution is the timing synchronization between a colliding pulse mode-locked dye laser and a gain-switched Fabry-Perot type AlGaAs laser diode that has achieved less than 40 femtoseconds of relative timing jitter by using a pulsed optical phase lock loop (POPLL). The relative timing jitter was measured using the error voltage of the feedback loop. This method of measurement is accurate since the frequencies of all the timing fluctuations fall within the loop bandwidth. The novel element is a broad band optical cross-correlator that can resolve femtosecond time delay errors between two pulse trains. The third contribution is a novel dispersive technique of determining the nonlinear frequency sweep of a picosecond pulse with relatively good accuracy. All the measurements are made in the time domain and hence there is no time-bandwidth limitation to the accuracy. The fourth contribution is the first demonstration of cross -phase modulation in a semiconductor laser amplifier where a variable chirp was observed. A simple expression for the chirp imparted on a weak signal pulse by the action of a strong pump pulse is derived. A maximum frequency excursion of 16 GHz due to the cross-phase modulation was measured. A value of 5 was found for alpha _{xpm} which is a factor for characterizing the cross-phase modulation in a similar manner to the conventional linewidth enhancement factor, alpha.
Strongly nonlinear steepening of long interfacial waves
Directory of Open Access Journals (Sweden)
N. Zahibo
2007-06-01
Full Text Available The transformation of nonlinear long internal waves in a two-layer fluid is studied in the Boussinesq and rigid-lid approximation. Explicit analytic formulation of the evolution equation in terms of the Riemann invariants allows us to obtain analytical results characterizing strongly nonlinear wave steepening, including the spectral evolution. Effects manifesting the action of high nonlinear corrections of the model are highlighted. It is shown, in particular, that the breaking points on the wave profile may shift from the zero-crossing level. The wave steepening happens in a different way if the density jump is placed near the middle of the water bulk: then the wave deformation is almost symmetrical and two phases appear where the wave breaks.
Nonlinear waves in strongly interacting relativistic fluids
Fogaça, D A; Filho, L G Ferreira
2013-01-01
During the past decades the study of strongly interacting fluids experienced a tremendous progress. In the relativistic heavy ion accelerators, specially the RHIC and LHC colliders, it became possible to study not only fluids made of hadronic matter but also fluids of quarks and gluons. Part of the physics program of these machines is the observation of waves in this strongly interacting medium. From the theoretical point of view, these waves are often treated with li-nearized hydrodynamics. In this text we review the attempts to go beyond linearization. We show how to use the Reductive Perturbation Method to expand the equations of (ideal and viscous) relativistic hydrodynamics to obtain nonlinear wave equations. These nonlinear wave equations govern the evolution of energy density perturbations (in hot quark gluon plasma) or baryon density perturbations (in cold quark gluon plasma and nuclear matter). Different nonlinear wave equations, such as the breaking wave, Korteweg-de Vries and Burgers equations, are...
Rossby wave energy dispersion from tropical cyclone in zonal basic flows
Shi, Wenli; Fei, Jianfang; Huang, Xiaogang; Liu, Yudi; Ma, Zhanhong; Yang, Lu
2016-04-01
This study investigates tropical cyclone energy dispersion under horizontally sheared flows using a nonlinear barotropic model. In addition to common patterns, unusual features of Rossby wave trains are also found in flows with constant vorticity and vorticity gradients. In terms of the direction of the energy dispersion, the wave train can rotate clockwise and elongate southwestward under anticyclonic circulation (ASH), which contributes to the reenhancement of the tropical cyclone (TC). The wave train even splits into two obvious wavelike trains in flows with a southward vorticity gradient (WSH). Energy dispersed from TCs varies over time, and variations in the intensity of the wave train components typically occur in two stages. Wave-activity flux diagnosis and ray tracing calculations are extended to the frame that moves along with the TC to reveal the concrete progress of wave propagation. The direction of the wave-activity flux is primarily determined by the combination of the basic flow and the TC velocity. Along the flux, the distribution of pseudomomentum effectively illustrates the development of wave trains, particularly the rotation and split of wave propagation. Ray tracing involves the quantitative tracing of wave features along rays, which effectively coincide with the wave train regimes. Flows of a constant shear (parabolic meridional variation) produce linear (nonlinear) wave number variations. For the split wave trains, the real and complex wave number waves move along divergent trajectories and are responsible for different energy dispersion ducts.
On the polarization of nonlinear gravitational waves
Poplawski, Nikodem J.
2011-01-01
We derive a relation between the two polarization modes of a plane, linear gravitational wave in the second-order approximation. Since these two polarizations are not independent, an initially monochromatic gravitational wave loses its periodic character due to the nonlinearity of the Einstein field equations. Accordingly, real gravitational waves may differ from solutions of the linearized field equations, which are being assumed in gravitational-wave detectors.
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.
Nonlinear surface waves over topography
Janssen, T.T.
2006-01-01
As ocean surface waves radiate into shallow coastal areas and onto beaches, their lengths shorten, wave heights increase, and the wave shape transforms from nearsinusoidal to the characteristic saw-tooth shapes at the onset of breaking; in the ensuing breaking process the wave energy is cascaded to
Dispersive radiation induced by shock waves in passive resonators.
Malaguti, Stefania; Conforti, Matteo; Trillo, Stefano
2014-10-01
We show that passive Kerr resonators pumped close to zero dispersion wavelengths on the normal dispersion side can develop the resonant generation of linear waves driven by cavity (mixed dispersive-dissipative) shock waves. The resonance mechanism can be successfully described in the framework of the generalized Lugiato-Lefever equation with higher-order dispersive terms. Substantial differences with radiation from cavity solitons and purely dispersive shock waves dispersion are highlighted.
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...
Modeling of Rayleigh wave dispersion in Iberia
Directory of Open Access Journals (Sweden)
José Badal
2011-01-01
Full Text Available Phase and group velocities of 15–70 s Rayleigh waves propagating across the Iberian Peninsula have been transformed into local dispersion curves by linear inversion of travel times. The procedure permits that the waveform dispersion to be obtained as a continuous period-dependent velocity function at grid points belonging to the area probed by the waves, thus providing phase- and group-velocity contour maps for several periods within the interval of interest. The regionalization process rests on a homogeneous initial data set in which the number of observations remains almost constant for all periods of reference. Damped least-squares inversion of the local dispersion curves for shear-wave velocity structure is performed to obtain depth-dependent S-wave velocity profiles at the grid points covering the model region. The reliability of the results should improve significantly owing to the use of phase and group velocities simultaneously. On this basis, we have built horizontal depth sections that give an updated view of the seismic velocity structure of the peninsula at lithospheric and upper mantle depths (20–200 km. After averaging all the pure-path S-wave velocities previously determined at each grid point, the velocity-depth models so obtained for major tectonic units allow the comparison between the Hercynian basement and other areas of Mesozoic folding and Tertiary basins.
Louis, Hélène; Odent, Vincent; Louvergneaux, Eric
2016-04-01
Shock waves are well-known nonlinear waves, displaying an abrupt discontinuity. Observation can be made in a lot of physical fields, as in water wave, plasma and nonlinear optics. Shock waves can either break or relax through either catastrophic or regularization phenomena. In this work, we restrain our study to dispersive shock waves. This regularization phenomenon implies the emission of dispersive waves. We demonstrate experimentally and numerically the generation of spatial dispersive shock waves in a nonlocal focusing media. The generation of dispersive shock wave in a focusing media is more problematic than in a defocusing one. Indeed, the modulational instability has to be frustrated to observe this phenomenon. In 2010, the dispersive shock wave was demonstrated experimentally in a focusing media with a partially coherent beam [1]. Another way is to use a nonlocal media [2]. The impact of nonlocality is more important than the modulational instability frustration. Here, we use nematic liquid crystals (NLC) as Kerr-like nonlocal medium. To achieve shock formation, we use the Riemann condition as initial spatial condition (edge at the beam entrance of the NLC cell). In these experimental conditions, we generate, experimentally and numerically, shock waves that relax through the emission of dispersive waves. Associated with this phenomenon, we evidence the emergence of a localized wave that travels through the transverse beam profile. The beam steepness, which is a good indicator of the shock formation, is maximal at the shock point position. This latter follows a power law versus the injected power as in [3]. Increasing the injected power, we found multiple shock points. We have good agreements between the numerical simulations and the experimental results. [1] W. Wan, D. V Dylov, C. Barsi, and J. W. Fleischer, Opt. Lett. 35, 2819 (2010). [2] G. Assanto, T. R. Marchant, and N. F. Smyth, Phys. Rev. A - At. Mol. Opt. Phys. 78, 1 (2008). [3] N. Ghofraniha, L. S
Dispersion engineering silicon nitride waveguides for broadband nonlinear frequency conversion
Epping, J.P.
2015-01-01
In this thesis, we investigated nonlinear frequency conversion of optical wavelengths using integrated silicon nitride (Si3N4) waveguides. Two nonlinear conversion schemes were considered: seeded four-wave mixing and supercontinuum generation. The first—seeded four-wave mixing—is investigated by a n
Nonlinear water waves with soluble surfactant
Lapham, Gary; Dowling, David; Schultz, William
1998-11-01
The hydrodynamic effects of surfactants have fascinated scientists for generations. This presentation describes an experimental investigation into the influence of a soluble surfactant on nonlinear capillary-gravity waves in the frequency range from 12 to 20 Hz. Waves were generated in a plexiglass wave tank (254 cm long, 30.5 cm wide, and 18 cm deep) with a triangular plunger wave maker. The tank was filled with carbon- and particulate-filtered water into which the soluble surfactant Triton-X-100® was added in known amounts. Wave slope was measured nonintrusively with a digital camera running at 225 fps by monitoring the position of light beams which passed up through the bottom of the tank, out through the wavy surface, and onto a white screen. Wave slope data were reduced to determine wave damping and the frequency content of the wave train. Both were influenced by the presence of the surfactant. Interestingly, a subharmonic wave occurring at one-sixth the paddle-driving frequency was found only when surfactant was present and the paddle was driven at amplitudes high enough to produce nonlinear waves in clean water. Although the origins of this subharmonic wave remain unclear, it appears to be a genuine manifestation of the combined effects of the surfactant and nonlinearity.
Dispersion of Sound in Dilute Suspensions with Nonlinear Particle Relaxation
Kandula, Max
2010-01-01
The theory accounting for nonlinear particle relaxation (viscous and thermal) has been applied to the prediction of dispersion of sound in dilute suspensions. The results suggest that significant deviations exist for sound dispersion between the linear and nonlinear theories at large values of Omega(Tau)(sub d), where Omega is the circular frequency, and Tau(sub d) is the Stokesian particle relaxation time. It is revealed that the nonlinear effect on the dispersion coefficient due to viscous contribution is larger relative to that of thermal conduction
TESTING FOR VARYING DISPERSION IN DISCRETE EXPONENTIAL FAMILY NONLINEAR MODELS
Institute of Scientific and Technical Information of China (English)
LinJinguan; WeiBocheng; ZhangNansong
2003-01-01
It is necessary to test for varying dispersion in generalized nonlinear models. Wei ,et al(1998) developed a likelihood ratio test,a score test and their adjustments to test for varying dispersion in continuous exponential family nonlinear models. This type of problem in the framework of general discrete exponential family nonlinear models is discussed. Two types of varying dispersion, which are random coefficients model and random effects model, are proposed,and corresponding score test statistics are constructed and expressed in simple ,easy to use ,matrix formulas.
The density stratification and amplitude dispersion of internal waves
Makarenko, N.; Ulanova, E.
2012-04-01
We consider the theoretical model of large amplitude internal solitary waves propagating in a weakly stratified fluid under gravity. It is well known that steady 2D Euler equations of non-homogeneous fluid reduce in this case to the second-order quasi-linear equation for a stream function (the Dubreil-Jacotin-Long equation). Subsequently, the shape of traveling solitary wave can be determined in the long-wave scaling limit by solving the dispersive KdV-type model equation. The non-linear terms of this equation depend considerably on the instantaneous fine-scale density profile formed over background linear- or exponential stratification (Benney&Ko, 1978; Borisov&Derzho 1990; Derzho&Grimshaw 1997; Makarenko, 1999; Makarenko, Maltseva and Kazakov, 2009). Now we derive and analyze Fredholm-type integral equations coupling immediately the fluid density coefficient with the dispersion function for internal solitary waves. The inverse problem which means to find the fine-scale density by known curve of the amplitude dispersion is discussed in more details.
Small amplitude nonlinear electron acoustic solitary waves in weakly magnetized plasma
Energy Technology Data Exchange (ETDEWEB)
Dutta, Manjistha; Khan, Manoranjan [Department of Instrumentation Science, Jadavpur University, Kolkata-700 032 (India); Ghosh, Samiran [Department of Applied Mathematics, University of Calcutta, 92, Acharya Prafulla Chandra Road, Kolkata-700 009 (India); Roychoudhury, Rajkumar [Indian Statistical Institute, Kolkata-700 108 (India); Chakrabarti, Nikhil [Saha Institute of Nuclear Physics, 1/AF Bidhannagar Kolkata-700 064 (India)
2013-01-15
Nonlinear propagation of electron acoustic waves in homogeneous, dispersive plasma medium with two temperature electron species is studied in presence of externally applied magnetic field. The linear dispersion relation is found to be modified by the externally applied magnetic field. Lagrangian transformation technique is applied to carry out nonlinear analysis. For small amplitude limit, a modified KdV equation is obtained, the modification arising due to presence of magnetic field. For weakly magnetized plasma, the modified KdV equation possesses stable solitary solutions with speed and amplitude increasing temporally. The solutions are valid upto some finite time period beyond which the nonlinear wave tends to wave breaking.
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.
Excitation of nonlinear ion acoustic waves in CH plasmas
Feng, Q S; Liu, Z J; Xiao, C Z; Wang, Q; He, X T
2016-01-01
Excitation of nonlinear ion acoustic wave (IAW) by an external electric field is demonstrated by Vlasov simulation. The frequency calculated by the dispersion relation with no damping is verified much closer to the resonance frequency of the small-amplitude nonlinear IAW than that calculated by the linear dispersion relation. When the wave number $ k\\lambda_{De} $ increases, the linear Landau damping of the fast mode (its phase velocity is greater than any ion's thermal velocity) increases obviously in the region of $ T_i/T_e < 0.2 $ in which the fast mode is weakly damped mode. As a result, the deviation between the frequency calculated by the linear dispersion relation and that by the dispersion relation with no damping becomes larger with $k\\lambda_{De}$ increasing. When $k\\lambda_{De}$ is not large, such as $k\\lambda_{De}=0.1, 0.3, 0.5$, the nonlinear IAW can be excited by the driver with the linear frequency of the modes. However, when $k\\lambda_{De}$ is large, such as $k\\lambda_{De}=0.7$, the linear ...
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.
EXACT SOLUTIONS TO NONLINEAR WAVE EQUATION
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
In this paper,we use an invariant set to construct exact solutions to a nonlinear wave equation with a variable wave speed. Moreover,we obtain conditions under which the equation admits a nonclassical symmetry. Several different nonclassical symmetries for equations with different diffusion terms are presented.
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 between...
Nonlinear ship waves and computational fluid dynamics
National Research Council Canada - National Science Library
MIYATA, Hideaki; ORIHARA, Hideo; SATO, Yohei
2014-01-01
.... Finding of the occurrence of nonlinear waves (named Free-Surface Shock Waves) in the vicinity of a ship advancing at constant speed provided the start-line for the progress of innovative technologies in the ship hull-form design...
The Influence of the Balance of Dispersion and Nonlinearity on the Transmission Quality in Fiber
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
This article analyzes the effect of the balance of dispersion and nonlinearity on the quality of a transmission system with super Gauss pulse input by altering the input power and adding a section of dispersion compensation fiber (DCF). The same mechanisms are applied to a 2-channel wave divide multiplex system(WDM) as well. DCF is proved to be a good solution in both situations.
Sundkvist, David; Krasnoselskikh, V; Bale, S D; Schwartz, S J; Soucek, J; Mozer, F
2012-01-13
Whistler wave trains are observed in the foot region of high Mach number quasiperpendicular shocks. The waves are oblique with respect to the ambient magnetic field as well as the shock normal. The Poynting flux of the waves is directed upstream in the shock normal frame starting from the ramp of the shock. This suggests that the waves are an integral part of the shock structure with the dispersive shock as the source of the waves. These observations lead to the conclusion that the shock ramp structure of supercritical high Mach number shocks is formed as a balance of dispersion and nonlinearity.
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...... is perturbed by a small amplitude incoherent wave-field. The initial evolution is exponential, following the growth of perturbations predicted by linear stability theory. The fluctuations saturate at relatively high amplitudes, by forming a pair of magnetic field aligned vortex-like structures of opposite...
The Nonlinear Talbot Effect of Rogue Waves
Zhang, Yiqi; Zheng, Huaibin; Chen, Haixia; Li, Changbiao; Song, Jianping; Zhang, Yanpeng
2014-01-01
Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schr\\"odinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a \\pi-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.
Institute of Scientific and Technical Information of China (English)
Liu Bing-Can; Yu Li; Lu Zhi-Xin
2011-01-01
The analytic surface plasmon polaritons (SPPs) dispersion relation is studied in a system consisting of a thin metallic film bounded by two sides media of nonlinear dielectric of arbitrary nonlinearity is studied by applying a generalised first integral approach. We consider both asymmetric and symmetric structures. Especially, in the symmetric system, two possible modes can exist: the odd mode and the even mode. The dispersion relations of the two modes are obtained. Due to the nonlinear dielectric, the magnitude of the electric field at the interface appears and alters the dispersion relations. The changes in SPPs dispersion relations depending on film thicknesses and nonlinearity are studied.
Nonlinear Landau damping and Alfven wave dissipation
Vinas, Adolfo F.; Miller, James A.
1995-01-01
Nonlinear Landau damping has been often suggested to be the cause of the dissipation of Alfven waves in the solar wind as well as the mechanism for ion heating and selective preacceleration in solar flares. We discuss the viability of these processes in light of our theoretical and numerical results. We present one-dimensional hybrid plasma simulations of the nonlinear Landau damping of parallel Alfven waves. In this scenario, two Alfven waves nonresonantly combine to create second-order magnetic field pressure gradients, which then drive density fluctuations, which in turn drive a second-order longitudinal electric field. Under certain conditions, this electric field strongly interacts with the ambient ions via the Landau resonance which leads to a rapid dissipation of the Alfven wave energy. While there is a net flux of energy from the waves to the ions, one of the Alfven waves will grow if both have the same polarization. We compare damping and growth rates from plasma simulations with those predicted by Lee and Volk (1973), and also discuss the evolution of the ambient ion distribution. We then consider this nonlinear interaction in the presence of a spectrum of Alfven waves, and discuss the spectrum's influence on the growth or damping of a single wave. We also discuss the implications for wave dissipation and ion heating in the solar wind.
Analytical description of nonlinear acoustic waves in the solar chromosphere
Litvinenko, Yuri E.; Chae, Jongchul
2017-02-01
Aims: Vertical propagation of acoustic waves of finite amplitude in an isothermal, gravitationally stratified atmosphere is considered. Methods: Methods of nonlinear acoustics are used to derive a dispersive solution, which is valid in a long-wavelength limit, and a non-dispersive solution, which is valid in a short-wavelength limit. The influence of the gravitational field on wave-front breaking and shock formation is described. The generation of a second harmonic at twice the driving wave frequency, previously detected in numerical simulations, is demonstrated analytically. Results: Application of the results to three-minute chromospheric oscillations, driven by velocity perturbations at the base of the solar atmosphere, is discussed. Numerical estimates suggest that the second harmonic signal should be detectable in an upper chromosphere by an instrument such as the Fast Imaging Solar Spectrograph installed at the 1.6-m New Solar Telescope of the Big Bear Observatory.
Nonlinear unified equations for water waves propagating over uneven bottoms in the nearshore region
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
Considering the continuous characteristics for water waves propagating over complex topography in the nearshore region, the unified nonlinear equations, based on the hypothesis for a typical uneven bottom, are presented by employing the Hamiltonian variational principle for water waves. It is verified that the equations include the following special cases: the extension of Airy's nonlinear shallow-water equations, the generalized mild-slope equation, the dispersion relation for the second-order Stokes waves and the higher order Boussinesq-type equations.
Local Influence Analysis for Semiparametric Reproductive Dispersion Nonlinear Models
Institute of Scientific and Technical Information of China (English)
Xue-dong CHEN; Nian-sheng TANG; Xue-ren WANG
2012-01-01
The present paper proposes a semiparametric reproductive dispersion nonlinear model (SRDNM)which is an extension of the nonlinear reproductive dispersion models and the semiparameter regression models.Maximum penalized likelihood estimates (MPLEs) of unknown parameters and nonparametric functions in SRDNM are presented.Assessment of local influence for various perturbation schemes are investigated.Some local influence diagnostics are given.A simulation study and a real example are used to illustrate the proposed methodologies.
Absorption and dispersion of ultrasonic waves
Herzfeld, Karl F; Massey, H S W; Brueckner, Keith A
1959-01-01
Absorption and Dispersion of Ultrasonic Waves focuses on the influence of ultrasonics on molecular processes in liquids and gases, including hydrodynamics, energy exchange, and chemical reactions. The book first offers information on the Stokes-Navier equations of hydrodynamics, as well as equations of motion, viscosity, formal introduction of volume viscosity, and linearized wave equation for a nonviscous fluid. The manuscript then ponders on energy exchange between internal and external degrees of freedom as relaxation phenomenon; effect of slow energy exchange on sound propagation; differe
Analytical and numerical investigation of nonlinear internal gravity waves
Directory of Open Access Journals (Sweden)
S. P. Kshevetskii
2001-01-01
coincidence of simulation outcomes with analytical ones is revealed and some examples of numerical simulations illustrating wave disintegration into solitons are given. The phenomenon of internal wave mixing is considered and is explained from the point of view of the results obtained. The numerical methods for internal wave simulation are examined. In particular, the influence of difference interval finiteness on a numerical solution is investigated. It is revealed that a numerical viscosity and numerical dispersion can play the role of regularizators to a nonlinear quasistatic problem. To avoid this effect, the grid steps should be taken less than some threshold values found theoretically.
The inverse problem based on a full dispersive wave equation
Institute of Scientific and Technical Information of China (English)
Gegentana Bao; Naranmandula Bao
2012-01-01
The inverse problem for harmonic waves and wave packets was studied based on a full dispersive wave equation. First, a full dispersive wave equation which describes wave propagation in nondissipative microstructured linear solids is established based on the Mindlin theory, and the dispersion characteristics are discussed. Second, based on the full dispersive wave equation, an inverse problem for determining the four unknown coefficients of wave equa- tion is posed in terms of the frequencies and corresponding wave numbers of four different harmonic waves, and the inverse problem is demonstrated with rigorous mathematical theory. Research proves that the coefficients of wave equation related to material properties can be uniquely determined in cases of normal and anomalous dispersions by measuring the frequen- cies and corresponding wave numbers of four different harmonic waves which propagate in a nondissipative microstructured linear solids.
Shear wave speed and dispersion measurements using crawling wave chirps.
Hah, Zaegyoo; Partin, Alexander; Parker, Kevin J
2014-10-01
This article demonstrates the measurement of shear wave speed and shear speed dispersion of biomaterials using a chirp signal that launches waves over a range of frequencies. A biomaterial is vibrated by two vibration sources that generate shear waves inside the medium, which is scanned by an ultrasound imaging system. Doppler processing of the acquired signal produces an image of the square of vibration amplitude that shows repetitive constructive and destructive interference patterns called "crawling waves." With a chirp vibration signal, successive Doppler frames are generated from different source frequencies. Collected frames generate a distinctive pattern which is used to calculate the shear speed and shear speed dispersion. A special reciprocal chirp is designed such that the equi-phase lines of a motion slice image are straight lines. Detailed analysis is provided to generate a closed-form solution for calculating the shear wave speed and the dispersion. Also several phantoms and an ex vivo human liver sample are scanned and the estimation results are presented.
Observation of Self-Cavitating Envelope Dispersive Shock Waves in Yttrium Iron Garnet Thin Films.
Janantha, P A Praveen; Sprenger, Patrick; Hoefer, Mark A; Wu, Mingzhong
2017-07-14
The formation and properties of envelope dispersive shock wave (DSW) excitations from repulsive nonlinear waves in a magnetic film are studied. Experiments involve the excitation of a spin wave step pulse in a low-loss magnetic Y_{3}Fe_{5}O_{12} thin film strip, in which the spin wave amplitude increases rapidly, realizing the canonical Riemann problem of shock theory. Under certain conditions, the envelope of the spin wave pulse evolves into a DSW that consists of an expanding train of nonlinear oscillations with amplitudes increasing from front to back, terminated by a black soliton. The onset of DSW self-cavitation, indicated by a point of zero power and a concomitant 180° phase jump, is observed for sufficiently large steps, indicative of the bidirectional dispersive hydrodynamic nature of the DSW. The experimental observations are interpreted with theory and simulations of the nonlinear Schrödinger equation.
Detailed Characterization of Continuous-Wave and Pulsed-Pump Four-Wave Mixing in Nonlinear Fibers
DEFF Research Database (Denmark)
Lillieholm, Mads; Galili, Michael; Grüner-Nielsen, Lars;
2016-01-01
We explore the parametric gain differences for continuous-wave and pulse-pumped four-wave mixing, using various highly nonlinear fibers. Detailed simulations support our findings that the dispersion slope determines the experimentally observed differences, limiting the pulsed-pump performance....
Dispersion-induced nonlinearities in semiconductors
DEFF Research Database (Denmark)
Mørk, Jesper; Mecozzi, A.
2002-01-01
A dispersive and saturable medium is shown, under very general conditions, to possess ultrafast dynamic behaviour due to non-adiabatic polarisation dynamics. Simple analytical expressions relating the effect to the refractive index dispersion of a semiconductor ire derived and the magnitude...... of the equivalent Kerr coefficient is shown to be in qualitative agreement with measurements on active semiconductor waveguides....
Adaptive dispersion compensation for guided wave imaging
Hall, James S.; Michaels, Jennifer E.
2012-05-01
Ultrasonic guided waves offer the promise of fast and reliable methods for interrogating large, plate-like structures. Distributed arrays of permanently attached, inexpensive piezoelectric transducers have thus been proposed as a cost-effective means to excite and measure ultrasonic guided waves for structural health monitoring (SHM) applications. Guided wave data recorded from a distributed array of transducers are often analyzed and interpreted through the use of guided wave imaging algorithms, such as conventional delay-and-sum imaging or the more recently applied minimum variance imaging. Both imaging algorithms perform reasonably well using signal envelopes, but can exhibit significant performance improvements when phase information is used. However, the use of phase information inherently requires knowledge of the dispersion relations, which are often not known to a sufficient degree of accuracy for high quality imaging since they are very sensitive to environmental conditions such as temperature, pressure, and loading. This work seeks to perform improved imaging with phase information by leveraging adaptive dispersion estimates obtained from in situ measurements. Experimentally obtained data from a distributed array is used to validate the proposed approach.
Evolution of Nonlinear Internal Waves in China Seas
Liu, Antony K.; Hsu, Ming-K.; Liang, Nai K.
1997-01-01
Synthetic Aperture Radar (SAR) images from ERS-I have been used to study the characteristics of internal waves of Taiwan in the East China Sea, and east of Hainan Island in the South China Sea. Rank-ordered packets of internal solitons propagating shoreward from the edge of the continental shelf were observed in the SAR images. Based on the assumption of a semidiurnal tidal origin, the wave speed can be estimated and is consistent with the internal wave theory. By using the SAR images and hydrographic data, internal waves of elevation have been identified in shallow water due to a thicker mixed layer as compared with the bottom layer on the continental shelf. The generation mechanism includes the influences of the tide and the Kuroshio intrusion across the continental shelf for the formations of elevation internal waves. The effects of water depth on the evolution of solitons and wave packets are modeled by nonlinear Kortweg-deVries (KdV) type equation and linked to satellite image observations. The numerical calculations of internal wave evolution on the continental shelf have been performed and compared with the SAR observations. For a case of depression waves in deep water, the solitons first disintegrate into dispersive wave trains and then evolve to a packet of elevation waves in the shallow water area after they pass through a turning point of approximately equal layer depths has been observed in the SAR image and simulated by numerical model.
Energy Technology Data Exchange (ETDEWEB)
Artemyev, A. V., E-mail: ante0226@gmail.com; Vasiliev, A. A. [Space Research Institute, RAS, Moscow (Russian Federation); Mourenas, D.; Krasnoselskikh, V. V. [LPC2E/CNRS—University of Orleans, Orleans (France); Agapitov, O. V. [Space Sciences Laboratory, University of California, Berkeley, California 94720 (United States)
2014-10-15
In this paper, we consider high-energy electron scattering and nonlinear trapping by oblique whistler waves via the Landau resonance. We use recent spacecraft observations in the radiation belts to construct the whistler wave model. The main purpose of the paper is to provide an estimate of the critical wave amplitude for which the nonlinear wave-particle resonant interaction becomes more important than particle scattering. To this aim, we derive an analytical expression describing the particle scattering by large amplitude whistler waves and compare the corresponding effect with the nonlinear particle acceleration due to trapping. The latter is much more rare but the corresponding change of energy is substantially larger than energy jumps due to scattering. We show that for reasonable wave amplitudes ∼10–100 mV/m of strong whistlers, the nonlinear effects are more important than the linear and nonlinear scattering for electrons with energies ∼10–50 keV. We test the dependencies of the critical wave amplitude on system parameters (background plasma density, wave frequency, etc.). We discuss the role of obtained results for the theoretical description of the nonlinear wave amplification in radiation belts.
Quasi self-adjoint nonlinear wave equations
Energy Technology Data Exchange (ETDEWEB)
Ibragimov, N H [Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona (Sweden); Torrisi, M; Tracina, R, E-mail: nib@bth.s, E-mail: torrisi@dmi.unict.i, E-mail: tracina@dmi.unict.i [Dipartimento di Matematica e Informatica, University of Catania (Italy)
2010-11-05
In this paper we generalize the classification of self-adjoint second-order linear partial differential equation to a family of nonlinear wave equations with two independent variables. We find a class of quasi self-adjoint nonlinear equations which includes the self-adjoint linear equations as a particular case. The property of a differential equation to be quasi self-adjoint is important, e.g. for constructing conservation laws associated with symmetries of the differential equation. (fast track communication)
Nonlinear Interaction of Waves in Geomaterials
Ostrovsky, L. A.
2009-05-01
Progress of 1990s - 2000s in studying vibroacoustic nonlinearities in geomaterials is largely related to experiments in resonance samples of rock and soils. It is now a common knowledge that many such materials are very strongly nonlinear, and they are characterized by hysteresis in the dependence between the stress and strain tensors, as well as by nonlinear relaxation ("slow time"). Elastic wave propagation in such media has many peculiarities; for example, third harmonic amplitude is a quadratic (not cubic as in classical solids) function of the main harmonic amplitude, and average wave velocity is linearly (not quadratically as usual) dependent on amplitude. The mechanisms of these peculiarities are related to complex structure of a material typically consisting of two phases: a hard matrix and relatively soft inclusions such as microcracks and grain contacts. Although most informative experimental results have been obtained in rock in the form of resonant bars, few theoretical models are yet available to describe and calculate waves interacting in such samples. In this presentation, a brief overview of structural vibroacoustic nonlinearities in rock is given first. Then, a simple but rather general approach to the description of wave interaction in solid resonators is developed based on accounting for resonance nonlinear perturbations which are cumulating from period to period. In particular, the similarity and the differences between traveling waves and counter-propagating waves are analyzed for materials with different stress-strain dependences. These data can be used for solving an inverse problem, i.e. characterizing nonlinear properties of a geomaterial by its measured vibroacoustic parameters. References: 1. L. Ostrovsky and P. Johnson, Riv. Nuovo Chimento, v. 24, 1-46, 2007 (a review); 2. L. Ostrovsky, J. Acoust. Soc. Amer., v. 116, 3348-3353, 2004.
Explicit solutions of nonlinear wave equation systems
Institute of Scientific and Technical Information of China (English)
Ahmet Bekir; Burcu Ayhan; M.Naci (O)zer
2013-01-01
We apply the (G'/G)-expansion method to solve two systems of nonlinear differential equations and construct traveling wave solutions expressed in terms of hyperbolic functions,trigonometric functions,and rational functions with arbitrary parameters.We highlight the power of the (G'/G)-expansion method in providing generalized solitary wave solutions of different physical structures.It is shown that the (G'/G)-expansion method is very effective and provides a powerful mathematical tool to solve nonlinear differential equation systems in mathematical physics.
Reduced order prediction of rare events in unidirectional nonlinear water waves
Cousins, Will
2015-01-01
We consider the problem of short-term prediction of rare, extreme water waves in unidirectional fields, a critical topic for ocean structures and naval operations. One possible mechanism for the occurrence of such rare, unusually-intense waves is nonlinear wave focusing. Recent results have demonstrated that random localizations of energy, induced by the dispersive mixing of different harmonics, can grow significantly due to localized nonlinear focusing. Here we show how the interplay between i) statistical properties captured through linear information such as the waves power spectrum and ii) nonlinear dynamical properties of focusing localized wave groups defines a critical length scale associated with the formation of extreme events. The energy that is locally concentrated over this length scale acts as the "trigger" of nonlinear focusing for wave groups and the formation of subsequent rare events. We use this property to develop inexpensive, short-term predictors of large water waves. Specifically, we sho...
Nonlinear dynamics of hydrostatic internal gravity waves
Energy Technology Data Exchange (ETDEWEB)
Stechmann, Samuel N.; Majda, Andrew J. [New York University, Courant Institute of Mathematical Sciences, NY (United States); Khouider, Boualem [University of Victoria, Department of Mathematics and Statistics, Victoria, BC (Canada)
2008-11-15
Stratified hydrostatic fluids have linear internal gravity waves with different phase speeds and vertical profiles. Here a simplified set of partial differential equations (PDE) is derived to represent the nonlinear dynamics of waves with different vertical profiles. The equations are derived by projecting the full nonlinear equations onto the vertical modes of two gravity waves, and the resulting equations are thus referred to here as the two-mode shallow water equations (2MSWE). A key aspect of the nonlinearities of the 2MSWE is that they allow for interactions between a background wind shear and propagating waves. This is important in the tropical atmosphere where horizontally propagating gravity waves interact together with wind shear and have source terms due to convection. It is shown here that the 2MSWE have nonlinear internal bore solutions, and the behavior of the nonlinear waves is investigated for different background wind shears. When a background shear is included, there is an asymmetry between the east- and westward propagating waves. This could be an important effect for the large-scale organization of tropical convection, since the convection is often not isotropic but organized on large scales by waves. An idealized illustration of this asymmetry is given for a background shear from the westerly wind burst phase of the Madden-Julian oscillation; the potential for organized convection is increased to the west of the existing convection by the propagating nonlinear gravity waves, which agrees qualitatively with actual observations. The ideas here should be useful for other physical applications as well. Moreover, the 2MSWE have several interesting mathematical properties: they are a system of nonconservative PDE with a conserved energy, they are conditionally hyperbolic, and they are neither genuinely nonlinear nor linearly degenerate over all of state space. Theory and numerics are developed to illustrate these features, and these features are
Parametric dispersion and amplification of acoustohelicon waves in piezoelectric semiconductors
Neogi, A.; Ghosh, S.
1991-01-01
Assuming that the origin of the nonlinear interaction lies in the second-order optical susceptibility arising from the nonlinear induced current density and using the coupled-mode theory, the parametric dispersion and amplification of acoustohelicon waves is analytically investigated in a longitudinally magnetized piezoelectric semiconductor of noncentrosymmetric nature. The relevant experiments have not been reported. The threshold value of the pump electric field E0th and its corresponding excitation intensity is obtained. The longitudinal magnetic field decreases the required magnitude of E0th for the excitation of parametric amplification. The phenomenon of self-defocusing of the signal in the prevailing case is found to be a consequence of the negative dispersive characteristics exhibited by the acoustohelicon waves. Numerical analyses are performed for an InSb crystal at 77 K, duly irradiated by frequency-doubled pulsed 10.6-μm CO2 lasers. The parametric gain constant is observed to be maximum when the cyclotron frequency ωc attains the magnitude equal to that of ω0, the incident laser frequency (=1.78×1014 s-1 ).
Optics in a nonlinear gravitational wave
Harte, Abraham I
2015-01-01
Gravitational waves can act like gravitational lenses, affecting the observed positions, brightnesses, and redshifts of distant objects. Exact expressions for such effects are derived here, allowing for arbitrarily-moving sources and observers in the presence of plane-symmetric gravitational waves. The commonly-used predictions of linear perturbation theory are shown to be generically overshadowed---even for very weak gravitational waves---by nonlinear effects when considering observations of sufficiently distant sources; higher-order perturbative corrections involve secularly-growing terms which cannot necessarily be neglected. Even on more moderate scales where linear effects remain at least marginally dominant, nonlinear corrections are qualitatively different from their linear counterparts. There is a sense in which they can, for example, mimic the existence of a third type of gravitational wave polarization.
Optics in a nonlinear gravitational plane wave
Harte, Abraham I.
2015-09-01
Gravitational waves can act like gravitational lenses, affecting the observed positions, brightnesses, and redshifts of distant objects. Exact expressions for such effects are derived here in general relativity, allowing for arbitrarily-moving sources and observers in the presence of plane-symmetric gravitational waves. At least for freely falling sources and observers, it is shown that the commonly-used predictions of linear perturbation theory can be generically overshadowed by nonlinear effects; even for very weak gravitational waves, higher-order perturbative corrections involve secularly-growing terms which cannot necessarily be neglected when considering observations of sufficiently distant sources. Even on more moderate scales where linear effects remain at least marginally dominant, nonlinear corrections are qualitatively different from their linear counterparts. There is a sense in which they can, for example, mimic the existence of a third type of gravitational wave polarization.
Nonlinear Acoustic Wave Interactions in Layered Media.
1980-03-06
Generated Components in Dispersive Media. . . . . . . . . . . . . 62 4.4 Dispersion in Medium II . . . . . . . . .. 68 V. CONCLUSIONS...give rise to leaky wave modes which are more thoroughly discussed 17 18 by Kapany and Burke, and by Marcuse . Leaky modes are C.C. Ghizoni, J.M...1977), 843-848. 1 7N.S. Kapany and J.J. Burke, Optical Waveeeuides, (New York: Academic Press, 1972), pp. 24-34. D. Marcuse , Theory of Dielectric Optical
Linear and Nonlinear Surface Waves in Electrohydrodynamics
Hunt, Matthew; Vanden-broeck, Jean-Marc; Papageorgiou, Demetrios
2015-01-01
The problem of interest in this article are waves on a layer of finite depth governed by the Euler equations in the presence of gravity, surface tension, and vertical electric fields. Perturbation theory is used to identify canonical scalings and to derive a Kadomtsev-Petviashvili equation withan additional non-local term arising in interfacial electrohydrodynamics.When the Bond number is equal to 1/3, dispersion disappears and shock waves could potentially form. In the additional limit of vanishing electric fields, a new evolution equation is obtained which contains third and fifth-order dispersion as well as a non-local electric field term.
Nonlinear Gamow vectors, shock waves and irreversibility in optically nonlocal media
Gentilini, Silvia; Marcucci, Giulia; DelRe, Eugenio; Conti, Claudio
2015-01-01
Dispersive shock waves dominate wave-breaking phenomena in Hamiltonian systems. In the absence of loss, these highly irregular and disordered waves are potentially reversible. However, no experimental evidence has been given about the possibility of inverting the dynamics of a dispersive shock wave and turn it into a regular wave-front. Nevertheless, the opposite scenario, i.e., a smooth wave generating turbulent dynamics is well studied and observed in experiments. Here we introduce a new theoretical formulation for the dynamics in a highly nonlocal and defocusing medium described by the nonlinear Schroedinger equation. Our theory unveils a mechanism that enhances the degree of irreversibility. This mechanism explains why a dispersive shock cannot be reversed in evolution even for an arbitrarirly small amount of loss. Our theory is based on the concept of nonlinear Gamow vectors, i.e., power dependent generalizations of the counter-intuitive and hereto elusive exponentially decaying states in Hamiltonian sys...
Modulational development of nonlinear gravity-wave groups
Chereskin, T. K.; Mollo-Christensen, E.
1985-01-01
Observations of the development of nonlinear surface gravity-wave groups are presented, and the amplitude and phase modulations are calculated using Hilbert-transform techniques. With increasing propagation distance and wave steepness, the phase modulation develops local phase reversals whose locations correspond to amplitude minima or nodes. The concomitant frequency modulation develops jumps or discontinuities. The observations are compared with recent similar results for wavetrains. The observations are modelled numerically using the cubic nonlinear Schroedinger equation. The motivation is twofold: to examine quantitatively the evolution of phase as well as amplitude modulation, and to test the inviscid predictions for the asymptotic behavior of groups versus long-time observations. Although dissipation rules out the recurrence, there is a long-time coherence of the groups. The phase modulation is found to distinguish between dispersive and soliton behavior.
Effect of electron inertia on dispersive properties of Alfvén waves in cold plasmas
Jana, Sayanee; Ghosh, Samiran; Chakrabarti, Nikhil
2017-10-01
The effect of electron inertia on Alfvén wave propagation is investigated in the framework of the two-fluid theory in a compressible magnetized plasma. The linear analysis of the governing equations manifests the dispersion relation of the circularly polarized Alfvén waves where the electron inertia is found to act as a source of dispersion. In the finite amplitude limit, the nonlinear Alfvén wave may be described by the Derivative Nonlinear Schrödinger equation (DNLSE) modified by third order dispersion arising due to finite electron inertia. The derived equation seems to be novel with respect to what exists in the literature of Alfvén wave dynamics. We have shown that this electron inertia modified DNLSE is completely integrable and an analytical solution is demonstrated with vanishing boundary conditions. The results are expected to be of special importance in the context of space and laboratory plasmas.
Adaptive modeling of shallow fully nonlinear gravity waves
Dutykh, Denys; Mitsotakis, Dimitrios
2014-01-01
This paper presents an extended version of the celebrated Serre-Green-Naghdi (SGN) system. This extension is based on the well-known Bona-Smith-Nwogu trick which aims to improve the linear dispersion properties. We show that in the fully nonlinear setting it results in modifying the vertical acceleration. Even if this technique is well-known, the effect of this modification on the nonlinear properties of the model is not clear. The first goal of this study is to shed some light on the properties of solitary waves, as the most important class of nonlinear permanent solutions. Then, we propose a simple adaptive strategy to choose the optimal value of the free parameter at every instance of time. This strategy is validated by comparing the model prediction with the reference solutions of the full Euler equations and its classical counterpart. Numerical simulations show that the new adaptive model provides a much better accuracy for the same computational complexity.
Spatial versus temporal deterministic wave breakup of nonlinearly coupled light waves.
Salerno, D; Minardi, S; Trull, J; Varanavicius, A; Tamosauskas, G; Valiulis, G; Dubietis, A; Caironi, D; Trillo, S; Piskarskas, A; Di Trapani, P
2003-10-01
We investigate experimentally the competition between spatial and temporal breakup due to modulational instability in chi((2)) nonlinear mixing. The modulation of the wave packets caused by the energy exchange between fundamental and second-harmonic components is found to be the prevailing trigger mechanism which, according to the relative weight of diffraction and dispersion, leads to the appearance of a multisoliton pattern in the low-dimensional spatial or temporal domain.
Amplitude-dependent contraction/elongation of nonlinear Lamb waves
Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2016-04-01
Nonlinear elastic guided waves find application in various disciplines of science and engineering, such as non- destructive testing and structural health monitoring. Recent recognition and quantification of their amplitude- dependent changes in spectral properties has contributed to the development of new monitoring concepts for mechanical structures. The focus of this work is to investigate and predict amplitude-dependent shifts in Lamb wave dispersion curves. The theory for frequency/wavenumber shifts for plate waves, based on a Lindstedt-Poincaré perturbation approach, was presented by the authors in previous years. Equivalently, spectral properties changes can be seen as wavelength contraction/elongation. Within the proposed framework, the wavelength of a Lamb wave depends on several factors; e.g., wave amplitude and second-, third- and fourth-order elastic constants, and others. Various types of nonlinear effects are considered in presented studies. Sensitivity studies for model parameters, i.e. higher-order elastic constants, are performed to quantify their influence on Lamb wave frequency/wavenumber shifting, and to identify the key parameters governing wavelength tuning.
A flexible genuinely nonlinear approach for nonlinear wave propagation, breaking and run-up
Filippini, A. G.; Kazolea, M.; Ricchiuto, M.
2016-04-01
In this paper we evaluate hybrid strategies for the solution of the Green-Naghdi system of equations for the simulation of fully nonlinear and weakly dispersive free surface waves. We consider a two step solution procedure composed of: a first step where the non-hydrostatic source term is recovered by inverting the elliptic coercive operator associated to the dispersive effects; a second step which involves the solution of the hyperbolic shallow water system with the source term, computed in the previous phase, which accounts for the non-hydrostatic effects. Appropriate numerical methods, that can be also generalized on arbitrary unstructured meshes, are used to discretize the two stages: the standard C0 Galerkin finite element method for the elliptic phase; either third order Finite Volume or third order stabilized Finite Element method for the hyperbolic phase. The discrete dispersion properties of the fully coupled schemes obtained are studied, showing accuracy close to or better than that of a fourth order finite difference method. The hybrid approach of locally reverting to the nonlinear shallow water equations is used to recover energy dissipation in breaking regions. To this scope we evaluate two strategies: simply neglecting the non-hydrostatic contribution in the hyperbolic phase; imposing a tighter coupling of the two phases, with a wave breaking indicator embedded in the elliptic phase to smoothly turn off the dispersive effects. The discrete models obtained are thoroughly tested on benchmarks involving wave dispersion, breaking and run-up, showing a very promising potential for the simulation of complex near shore wave physics in terms of accuracy and robustness.
Nonlinear random optical waves: Integrable turbulence, rogue waves and intermittency
Randoux, Stéphane; Walczak, Pierre; Onorato, Miguel; Suret, Pierre
2016-10-01
We examine the general question of statistical changes experienced by ensembles of nonlinear random waves propagating in systems ruled by integrable equations. In our study that enters within the framework of integrable turbulence, we specifically focus on optical fiber systems accurately described by the integrable one-dimensional nonlinear Schrödinger equation. We consider random complex fields having a Gaussian statistics and an infinite extension at initial stage. We use numerical simulations with periodic boundary conditions and optical fiber experiments to investigate spectral and statistical changes experienced by nonlinear waves in focusing and in defocusing propagation regimes. As a result of nonlinear propagation, the power spectrum of the random wave broadens and takes exponential wings both in focusing and in defocusing regimes. Heavy-tailed deviations from Gaussian statistics are observed in focusing regime while low-tailed deviations from Gaussian statistics are observed in defocusing regime. After some transient evolution, the wave system is found to exhibit a statistically stationary state in which neither the probability density function of the wave field nor the spectrum changes with the evolution variable. Separating fluctuations of small scale from fluctuations of large scale both in focusing and defocusing regimes, we reveal the phenomenon of intermittency; i.e., small scales are characterized by large heavy-tailed deviations from Gaussian statistics, while the large ones are almost Gaussian.
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...
Nonlinear Landau damping of Alfven waves.
Hollweg, J. V.
1971-01-01
Demonstration that large-amplitude linearly or elliptically polarized Alfven waves propagating parallel to the average magnetic field can be dissipated by nonlinear Landau damping. The damping is due to the longitudinal electric field associated with the ion sound wave which is driven (in second order) by the Alfven wave. The damping rate can be large even in a cold plasma (beta much less than 1, but not zero), and the mechanism proposed may be the dominant one in many plasmas of astrophysical interest.
Dispersive waves generated by an underwater landslide
Dutykh, Denys; Beysel, Sonya; Shokina, Nina; Khakimzyanov, Gayaz
2011-01-01
In this work we study the generation of water waves by an underwater sliding mass. The wave dynamics are assumed to fell into the shallow water regime. However, the characteristic wavelength of the free surface motion is generally smaller than in geophysically generated tsunamis. Thus, dispersive effects need to be taken into account. In the present study the fluid layer is modeled by the Peregrine system modified appropriately and written in conservative variables. The landslide is assumed to be a quasi-deformable body of mass whose trajectory is completely determined by its barycenter motion. A differential equation modeling the landslide motion along a curvilinear bottom is obtained by projecting all the forces acting on the submerged body onto a local moving coordinate system. One of the main novelties of our approach consists in taking into account curvature effects of the sea bed.
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.
Multiple four-wave mixing and Kerr combs in a bichromatically pumped nonlinear fiber ring cavity.
Ceoldo, D; Bendahmane, A; Fatome, J; Millot, G; Hansson, T; Modotto, D; Wabnitz, S; Kibler, B
2016-12-01
We report numerical and experimental studies of multiple four-wave mixing processes emerging from dual-frequency pumping of a passive nonlinear fiber ring cavity. We observe the formation of a periodic train of nearly background-free soliton pulses associated with Kerr frequency combs. The generation of resonant dispersive waves is also reported.
Wave envelopes method for description of nonlinear acoustic wave propagation.
Wójcik, J; Nowicki, A; Lewin, P A; Bloomfield, P E; Kujawska, T; Filipczyński, L
2006-07-01
A novel, free from paraxial approximation and computationally efficient numerical algorithm capable of predicting 4D acoustic fields in lossy and nonlinear media from arbitrary shaped sources (relevant to probes used in medical ultrasonic imaging and therapeutic systems) is described. The new WE (wave envelopes) approach to nonlinear propagation modeling is based on the solution of the second order nonlinear differential wave equation reported in [J. Wójcik, J. Acoust. Soc. Am. 104 (1998) 2654-2663; V.P. Kuznetsov, Akust. Zh. 16 (1970) 548-553]. An incremental stepping scheme allows for forward wave propagation. The operator-splitting method accounts independently for the effects of full diffraction, absorption and nonlinear interactions of harmonics. The WE method represents the propagating pulsed acoustic wave as a superposition of wavelet-like sinusoidal pulses with carrier frequencies being the harmonics of the boundary tone burst disturbance. The model is valid for lossy media, arbitrarily shaped plane and focused sources, accounts for the effects of diffraction and can be applied to continuous as well as to pulsed waves. Depending on the source geometry, level of nonlinearity and frequency bandwidth, in comparison with the conventional approach the Time-Averaged Wave Envelopes (TAWE) method shortens computational time of the full 4D nonlinear field calculation by at least an order of magnitude; thus, predictions of nonlinear beam propagation from complex sources (such as phased arrays) can be available within 30-60 min using only a standard PC. The approximate ratio between the computational time costs obtained by using the TAWE method and the conventional approach in calculations of the nonlinear interactions is proportional to 1/N2, and in memory consumption to 1/N where N is the average bandwidth of the individual wavelets. Numerical computations comparing the spatial field distributions obtained by using both the TAWE method and the conventional approach
Resonant dispersive waves generated with multi-input femtosecond pulses
Wang, Kai; Peng, Jiahui; Sokolov, Alex
2010-10-01
We investigated the resonant dispersive waves generated by high-order dispersion theoretically. We considered different femtosecond pulses propagating in the kagome-lattice hollow-core photonics crystal fibers. The two third order and fourth order resonant dispersive waves would be produced in the visible range to produce the ultrashort pulse.
Nonlinear interactions between gravity waves and tides
Institute of Scientific and Technical Information of China (English)
LIU Xiao; XU JiYao; MA RuiPing
2007-01-01
In this study, we present the nonlinear interactions between gravity waves (GWs) and tides by using the 2D numerical model for the nonlinear propagation of GWs in the compressible atmosphere. During the propagation in the tidal background, GWs become instable in three regions, that is z = 75-85 km, z =90-110 km and z= 115-130 km. The vertical wavelength firstly varies gradually from the initial 12 km to 27 km. Then the newly generated longer waves are gradually compressed. The longer and shorter waves occur in the regions where GWs propagate in the reverse and the same direction of the horizontal mean wind respectively. In addition, GWs can propagate above the main breaking region (90-110 km). During GWs propagation, not only the mean wind is accelerated, but also the amplitude of tide is amplified. Especially, after GWs become instable, this amplified effect to the tidal amplitude is much obvious.
Nonlinear interactions between gravity waves and tides
Institute of Scientific and Technical Information of China (English)
2007-01-01
In this study, we present the nonlinear interactions between gravity waves (GWs) and tides by using the 2D numerical model for the nonlinear propagation of GWs in the compressible atmosphere. During the propagation in the tidal background, GWs become instable in three regions, that is z = 75―85 km, z = 90―110 km and z = 115―130 km. The vertical wavelength firstly varies gradually from the initial 12 km to 27 km. Then the newly generated longer waves are gradually compressed. The longer and shorter waves occur in the regions where GWs propagate in the reverse and the same direction of the hori-zontal mean wind respectively. In addition, GWs can propagate above the main breaking region (90—110 km). During GWs propagation, not only the mean wind is accelerated, but also the amplitude of tide is amplified. Especially, after GWs become instable, this amplified effect to the tidal amplitude is much obvious.
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.
Jiang, Shixiao W.; Lu, Haihao; Zhou, Douglas; Cai, David
2016-08-01
Characterizing dispersive wave turbulence in the long time dynamics is central to understanding of many natural phenomena, e.g., in atmosphere ocean dynamics, nonlinear optics, and plasma physics. Using the β-Fermi-Pasta-Ulam nonlinear system as a prototypical example, we show that in thermal equilibrium and non-equilibrium steady state the turbulent state even in the strongly nonlinear regime possesses an effective linear stochastic structure in renormalized normal variables. In this framework, we can well characterize the spatiotemporal dynamics, which are dominated by long-wavelength renormalized waves. We further demonstrate that the energy flux is nearly saturated by the long-wavelength renormalized waves in non-equilibrium steady state. The scenario of such effective linear stochastic dynamics can be extended to study turbulent states in other nonlinear wave systems.
Enhanced continuous-wave four-wave mixing efficiency in nonlinear AlGaAs waveguides.
Apiratikul, Paveen; Wathen, Jeremiah J; Porkolab, Gyorgy A; Wang, Bohan; He, Lei; Murphy, Thomas E; Richardson, Christopher J K
2014-11-03
Enhancements of the continuous-wave four-wave mixing conversion efficiency and bandwidth are accomplished through the application of plasma-assisted photoresist reflow to reduce the sidewall roughness of sub-square-micron-modal area waveguides. Nonlinear AlGaAs optical waveguides with a propagation loss of 0.56 dB/cm demonstrate continuous-wave four-wave mixing conversion efficiency of -7.8 dB. Narrow waveguides that are fabricated with engineered processing produce waveguides with uncoated sidewalls and anti-reflection coatings that show group velocity dispersion of +0.22 ps²/m. Waveguides that are 5-mm long demonstrate broadband four-wave mixing conversion efficiencies with a half-width 3-dB bandwidth of 63.8-nm.
A splitting approach for the fully nonlinear and weakly dispersive Green-Naghdi model
Bonneton, Philippe; Lannes, David; Marche, Fabien; Tissier, Marion
2010-01-01
The fully nonlinear and weakly dispersive Green-Naghdi model for shallow water waves of large amplitude is studied. The original model is first recast under a new formulation more suitable for numerical resolution. An hybrid finite volume and finite difference splitting approach is then proposed. The hyperbolic part of the equations is handled with a high-order finite volume scheme allowing for breaking waves and dry areas. The dispersive part is treated with a classical finite difference approach. Extensive numerical validations are then performed in one horizontal dimension, relying both on analytical solutions and experimental data. The results show that our approach gives a good account of all the processes of wave transformation in coastal areas: shoaling, wave breaking and run-up.
On Global attraction to solitary waves for Klein-Gordon equation with concentrated nonlinearity
Kopylova, Elena
2016-01-01
The global attraction is proved for the nonlinear 3D Klein-Gordon equation with a nonlinearity concentrated at one point. Our main result is the convergence of each "finite energy solution" to the manifold of all solitary waves as $t\\to\\pm\\infty$. This global attraction is caused by the nonlinear energy transfer from lower harmonics to the continuous spectrum and subsequent dispersion radiation. We justify this mechanism by the following strategy based on inflation of spectrum by the nonlinea...
Three octave spanning supercontinuum by red-shifted dispersive wave in photonic crystal fibers
Sharma, Mohit
2015-01-01
This paper presents a three layer index guided lead silicate (SF57) photonic crystal fiber which simultaneously promises to yield large effective optical nonlinear coefficient and low anomalous dispersion that makes it suitable for supercontinuum generation. At an operating wavelength 1550 nm, the typical optimized value of anomalous dispersion and effective nonlinear coefficient turns out to be ~4 ps/km/nm and ~1078 W^(-1) km^(-1), respectively. Through numerical simulation it is realized that the designed fiber promises to exhibit three octave spanning supercontinuum from 900 to 7200 nm by using 50 fs sech optical pulses of 5 kW peak power. Due to the cross-phase modulation and four-wave mixing processes, a long range of red-shifted dispersive wave generated, which assist to achieve such large broadening. In addition, we have investigated the compatibility of supercontinuum generation with input pulse peak power increment and briefly discussed the impact of nonlinear processes on supercontinuum generation.
Three octave spanning supercontinuum by red-shifted dispersive wave in photonic crystal fibers
Sharma, Mohit; Konar, S.
2016-03-01
This article presents a three-layer index guided lead silicate (SF57) photonic crystal fiber which simultaneously promises to yield large effective optical nonlinear coefficient and low anomalous dispersion that makes it suitable for supercontinuum (SC) generation. At an operating wavelength 1550 nm, the typical optimized value of anomalous dispersion and effective nonlinear coefficient turns out to be ~4 ps/km/nm and ~1078 W-1km-1, respectively. Through numerical simulation, it is realized that the designed fiber promises to exhibit three octave spanning SC from 900 to 7200 nm using 50 fs 'sech' optical pulses of 5 kW peak power. Due to the cross-phase modulation and four-wave mixing processes, a long range of red-shifted dispersive wave generated, which assists to achieve such large broadening. In addition, we have investigated the compatibility of SC generation with input pulse peak power increment and briefly discussed the impact of nonlinear processes on SC generation.
Nonlinear plasma wave in magnetized plasmas
Energy Technology Data Exchange (ETDEWEB)
Bulanov, Sergei V. [Kansai Photon Science Institute, JAEA, Kizugawa, Kyoto 619-0215 (Japan); Prokhorov Institute of General Physics, Russian Academy of Sciences, Moscow 119991 (Russian Federation); Moscow Institute of Physics and Technology, Dolgoprudny, Moscow region 141700 (Russian Federation); Esirkepov, Timur Zh.; Kando, Masaki; Koga, James K. [Kansai Photon Science Institute, JAEA, Kizugawa, Kyoto 619-0215 (Japan); Hosokai, Tomonao; Zhidkov, Alexei G. [Photon Pioneers Center, Osaka University, 2-8 Yamadaoka, Suita, Osaka 565-0871 (Japan); Japan Science and Technology Agency, CREST, 2-1, Yamadaoka, Suita, Osaka 565-0871 (Japan); Kodama, Ryosuke [Photon Pioneers Center, Osaka University, 2-8 Yamadaoka, Suita, Osaka 565-0871 (Japan); Graduate School of Engineering, Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871 (Japan)
2013-08-15
Nonlinear axisymmetric cylindrical plasma oscillations in magnetized collisionless plasmas are a model for the electron fluid collapse on the axis behind an ultrashort relativisically intense laser pulse exciting a plasma wake wave. We present an analytical description of the strongly nonlinear oscillations showing that the magnetic field prevents closing of the cavity formed behind the laser pulse. This effect is demonstrated with 3D PIC simulations of the laser-plasma interaction. An analysis of the betatron oscillations of fast electrons in the presence of the magnetic field reveals a characteristic “Four-Ray Star” pattern.
Dispersive MHD waves and alfvenons in charge non-neutral plasmas
Directory of Open Access Journals (Sweden)
K. Stasiewicz
2008-08-01
Full Text Available Dispersive properties of linear and nonlinear MHD waves, including shear, kinetic, electron inertial Alfvén, and slow and fast magnetosonic waves are analyzed using both analytical expansions and a novel technique of dispersion diagrams. The analysis is extended to explicitly include space charge effects in non-neutral plasmas. Nonlinear soliton solutions, here called alfvenons, are found to represent either convergent or divergent electric field structures with electric potentials and spatial dimensions similar to those observed by satellites in auroral regions. Similar solitary structures are postulated to be created in the solar corona, where fast alfvenons can provide acceleration of electrons to hundreds of keV during flares. Slow alfvenons driven by chromospheric convection produce positive potentials that can account for the acceleration of solar wind ions to 300–800 km/s. New results are discussed in the context of observations and other theoretical models for nonlinear Alfvén waves in space plasmas.
Study of Linear and Nonlinear Wave Excitation
Chu, Feng; Berumen, Jorge; Hood, Ryan; Mattingly, Sean; Skiff, Frederick
2013-10-01
We report an experimental study of externally excited low-frequency waves in a cylindrical, magnetized, singly-ionized Argon inductively-coupled gas discharge plasma that is weakly collisional. Wave excitation in the drift wave frequency range is accomplished by low-percentage amplitude modulation of the RF plasma source. Laser-induced fluorescence is adopted to study ion-density fluctuations in phase space. The laser is chopped to separate LIF from collisional fluorescence. A single negatively-biased Langmuir probe is used to detect ion-density fluctuations in the plasma. A ring array of Langmuir probes is also used to analyze the spatial and spectral structure of the excited waves. We apply coherent detection with respect to the wave frequency to obtain the ion distribution function associated with externally generated waves. Higher-order spectra are computed to evaluate the nonlinear coupling between fluctuations at various frequencies produced by the externally generated waves. Parametric decay of the waves is observed. This work is supported by U.S. DOE Grant No. DE-FG02-99ER54543.
Nonhydrostatic effects of nonlinear internal wave propagation in the South China Sea
Zhang, Z.; Fringer, O. B.
2007-05-01
It is well known that internal tides are generated over steep topography at the Luzon Strait on the eastern boundary of the South China Sea. These internal tides propagate westward and steepen into trains of weakly nonlinear internal waves that propagate relatively free of dissipation until they interact with the continental shelf on the western side of the South China Sea, some 350 km from their generation point. The rate at which the internal tide transforms into trains of nonlinear waves depends on the Froude number at the generation site, which is defined as the ratio of the barotropic current speed to the local internal wave speed. Large Froude numbers lead to rapid evolution of wave trains while low Froude numbers generate internal tides that may not evolve into wave trains before reaching the continental shelf. Although the evolution into trains of weakly nonlinear waves results from the delicate interplay between nonlinear steepening and nonhydrostatic dispersion, the steepening process is represented quite well, at least from a qualitative standpoint, by hydrostatic models, which contain no explicit nonhydrostatic dispersion. Furthermore, hydrostatic models predict the propagation speed of the leading wave in wave trains extremely well, indicating that its propagation speed depends very weakly on nonlinear or dispersive effects. In order to examine how hydrostatic models introduce dispersion that leads to the formation of wave trains, we simulate the generation and evolution of nonlinear waves in the South China Sea with and without the hydrostatic approximation using the nonhydrostatic model SUNTANS, which can be run in either hydrostatic or nonhydrostatic mode. We show that the dispersion leading to the formation of wave trains in the hydrostatic model results from numerically-induced dispersion that is implicit in the numerical formulation of the advection terms. While the speed of the leading wave in the wave trains is correct, the amplitude and number
Acoustic Wave Dispersion and Scattering in Complex Marine Sediment Structures
2015-09-30
Acoustic wave dispersion and scattering in complex marine sediment structures Charles W. Holland The Pennsylvania State University Applied...volume scattering and 2) the effects of shear waves in general layered media. These advances will provide the basis for measuring dispersion in in-situ...shear waves on dispersion in marine sediments. The first step will be development of the theory. WORK COMPLETED A brief summary of the work
Theory of director precession and nonlinear waves in nematic liquid crystals under elliptical shear.
Krekhov, A P; Kramer, L
2005-09-01
We study theoretically the slow director precession and nonlinear waves observed in homeotropically oriented nematic liquid crystals subjected to circular or elliptical Couette and Poiseuille flow and an electric field. From a linear analysis of the nematodynamic equations it is found that in the presence of the flow the electric bend Fréedericksz transition is transformed into a Hopf-type bifurcation. In the framework of an approximate weakly nonlinear analysis we have calculated the coefficients of the modified complex Ginzburg-Landau equation, which slightly above onset describes nonlinear waves with strong nonlinear dispersion. We also derive the equation describing the precession and waves well above the Fréedericksz transition and for small flow amplitudes. Then the nonlinear waves are of diffusive nature. The results are compared with full numerical simulations and with experimental data.
Wave-kinetic description of nonlinear photons
Marklund, M; Brodin, G; Stenflo, L
2004-01-01
The nonlinear interaction, due to quantum electrodynamical (QED) effects, between photons is investigated using a wave-kinetic description. Starting from a coherent wave description, we use the Wigner transform technique to obtain a set of wave-kinetic equations, the so called Wigner-Moyal equations. These equations are coupled to a background radiation fluid, whose dynamics is determined by an acoustic wave equation. In the slowly varying acoustic limit, we analyse the resulting system of kinetic equations, and show that they describe instabilities, as well as Landau-like damping. The instabilities may lead to break-up and focusing of ultra-high intensity multi-beam systems, which in conjunction with the damping may result in stationary strong field structures. The results could be of relevance for the next generation of laser-plasma systems.
Directory of Open Access Journals (Sweden)
Mostafa H. Ali, Ahmed E. Elsamahy, Maher A. Farhoud and Taymour A. Hamdalla
2012-10-01
Full Text Available Near field distribution, propagation constant and dispersion characteristics of nonlinear single-mode optical fibers have been investigated. Shooting-method technique is used and implemented into a computer code for both profiles of step-index and graded-index fibers. An error function is defined to estimate the discrepancy between the expected electric-field radial derivative at the core-cladding interface and that obtained by numerically integrating the wave equation through the use of Runge-Kutta method. All of the above calculations done under the ocean depth in which the depth will affect the refractive index that have a direct effect on all the optical fiber parameters.KeyWords: Nonlinear refractive index, Normalized propagation constant, Mode delay factor, Material dispersion, Waveguide dispersion.
Wave train generation of solitons in systems with higher-order nonlinearities.
Mohamadou, Alidou; LatchioTiofack, C G; Kofané, Timoléon C
2010-07-01
Considering the higher-order nonlinearities in a material can significantly change its behavior. We suggest the extended nonlinear Schrödinger equation to describe the propagation of ultrashort optical pulses through a dispersive medium with higher-order nonlinearities. Soliton trains are generated through the modulational instability and we point out the influence of the septic nonlinearity in the modulational instability gain. Experimental values are used for the numerical simulations and the input plane wave leads to the development of pulse trains, depending upon the sign of the septic nonlinearity.
A nonlinear Schroedinger wave equation with linear quantum behavior
Energy Technology Data Exchange (ETDEWEB)
Richardson, Chris D.; Schlagheck, Peter; Martin, John; Vandewalle, Nicolas; Bastin, Thierry [Departement de Physique, University of Liege, 4000 Liege (Belgium)
2014-07-01
We show that a nonlinear Schroedinger wave equation can reproduce all the features of linear quantum mechanics. This nonlinear wave equation is obtained by exploring, in a uniform language, the transition from fully classical theory governed by a nonlinear classical wave equation to quantum theory. The classical wave equation includes a nonlinear classicality enforcing potential which when eliminated transforms the wave equation into the linear Schroedinger equation. We show that it is not necessary to completely cancel this nonlinearity to recover the linear behavior of quantum mechanics. Scaling the classicality enforcing potential is sufficient to have quantum-like features appear and is equivalent to scaling Planck's constant.
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.
Formation of Vector Solitary waves with Mixed Dispersion in Bose-Einstein Condensates
Plaja, L.; Roman, J. San
2005-01-01
We demonstrate the existence of a new class of two-component vector solitary waves in which dispersion coefficients have of opposite signs. Stability is achieved by inclusion of an additional linear coupling between the vector components that counterbalances the instability produced by the mixed dispersion and the non-linearity. In addition, we demonstrate that these solutions are experimentally observable as gap vector solitons in Bose-Einstein condensates located in oscillating optical latt...
Pakarzadeh, H.; Rezaei, S. M.
2016-01-01
In this article, we investigate for the first time the dispersion and the nonlinear characteristics of the tapered photonic crystal fibers (PCFs) as a function of length z, via solving the eigenvalue equation of the guided mode using the finite-difference frequency-domain method. Since the structural parameters such as the air-hole diameter and the pitch of the microstructured cladding change along the tapered PCFs, dispersion and nonlinear properties change with the length as well. Therefore, it is important to know the exact behavior of such fiber parameters along z which is necessary for nonlinear optics applications. We simulate the z dependency of the zero-dispersion wavelength, dispersion slope, effective mode area, nonlinear parameter, and the confinement loss along the tapered PCFs and propose useful relations for describing dispersion and nonlinear parameters. The results of this article, which are in a very good agreement with the available experimental data, are important for simulating pulse propagation as well as investigating nonlinear effects such as supercontinuum generation and parametric amplification in tapered PCFs.
Institute of Scientific and Technical Information of China (English)
WANG Qi; CHEN Yong; LI Biao; ZHANG Hong-Qing
2004-01-01
Based on the computerized symbolic Maple, we study two important nonlinear evolution equations, i.e.,the Hirota equation and the (1+1)-dimensional dispersive long wave equation by use of a direct and unified algebraic method named the general projective Riccati equation method to find more exact solutions to nonlinear differential equations. The method is more powerful than most of the existing tanh method. New and more general form solutions are obtained. The properties of the new formal solitary wave solutions are shown by some figures.
Deliktaş, Ekin; Teymür, Mevlüt
2017-07-01
In this study, the propagation of shear horizontal (SH) waves in a nonlinear elastic half space covered by a nonlinear elastic layer with a slowly varying interface is examined. The constituent materials are assumed to be homogenous, isotropic, elastic and having different mechanical properties. By employing the method of multiple scales, a nonlinear Schrödinger equation (NLS) with variable coefficients is derived for the nonlinear self-modulation of SH waves. We examine the effects of dispersion, irregularity of the interface and nonlinearity on the propagation characteristics of SH waves.
Variational modelling of nonlinear water waves
Kalogirou, Anna; Bokhove, Onno
2015-11-01
Mathematical modelling of water waves is demonstrated by investigating variational methods. A potential flow water wave model is derived using variational techniques and extented to include explicit time-dependence, leading to non-autonomous dynamics. As a first example, we consider the problem of a soliton splash in a long wave channel with a contraction at its end, resulting after a sluice gate is removed at a finite time. The removal of the sluice gate is included in the variational principle through a time-dependent gravitational potential. A second example involving non-autonomous dynamics concerns the motion of a free surface in a vertical Hele-Shaw cell. Explicit time-dependence now enters the model through a linear damping term due to the effect of wall friction and a term representing the motion of an artificially driven wave pump. In both cases, the model is solved numerically using a Galerkin FEM and the numerical results are compared to wave structures observed in experiments. The water wave model is also adapted to accommodate nonlinear ship dynamics. The novelty is this case is the coupling between the water wave dynamics, the ship dynamics and water line dynamics on the ship. For simplicity, we consider a simple ship structure consisting of V-shaped cross-sections.
Observation of dispersive shock waves developing from initial depressions in shallow water
Trillo, S.; Klein, M.; Clauss, G. F.; Onorato, M.
2016-10-01
We investigate surface gravity waves in a shallow water tank, in the limit of long wavelengths. We report the observation of non-stationary dispersive shock waves rapidly expanding over a 90 m flume. They are excited by means of a wave maker that allows us to launch a controlled smooth (single well) depression with respect to the unperturbed surface of the still water, a case that contains no solitons. The dynamics of the shock waves are observed at different levels of nonlinearity equivalent to a different relative smallness of the dispersive effect. The observed undulatory behavior is found to be in good agreement with the dynamics described in terms of a Korteweg-de Vries equation with evolution in space, though in the most nonlinear cases the description turns out to be improved over the quasi linear trailing edge of the shock by modeling the evolution in terms of the integro-differential (nonlocal) Whitham equation.
Weak and strong interactions between dark solitons and dispersive waves
Oreshnikov, Ivan; Yulin, Alexey
2015-01-01
The effect of mutual interaction between dark solitons and dispersive waves is investigated numerically and analytically. The condition of the resonant scattering of dispersive waves on dark solitons is derived and compared against the results of numerical simulations. It is shown that the interaction with intense dispersive waves affects the dynamics of the soltons strongly changing their frequencies and accelerating or decelerating the solitons. It is also demonstrated that two dark solitons can form a cavity for dispersive weaves bouncing between the two dark solitons. The differences of the resonant scattering of the dispersive waves on the dark and bright solitons are discussed. In particular we demonstrate that two dark solitons and dispersive wave bouncing in between them create solitonic cavity with convex "mirrors" unlike the concave "mirror" in case of the bright solitons.
Dispersion of the nonlinear refractive index of optical crystals
Adair, Robert; Chase, L. L.; Payne, Stephen A.
1992-09-01
The nonlinear refractive indices of several important optical materials have been measured at the second and third harmonic wavelengths of the Nd laser using nearly degenerate four-wave mixing. Measurements made relative to the nonlinear index of fused silica have the highest accuracy. Absolute measurements were also made using the Raman cross-section of benzene as a nonlinear reference standard. The relative measurements are compared with a despersion model base on parameters fitted to the linear refractive indicies and also to a recently proposed model based on Kramers-Kronig transformation of the calculated, two-band, two-photon loss spectrum.
Matda, Y.; Crawford, F. W.
1974-01-01
An economical low noise plasma simulation model is applied to a series of problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwellian plasma, in the absence of magnetic field. The model is described and tested, first in the absence of an applied signal, and then with a small amplitude perturbation, to establish the low noise features and to verify the theoretical linear dispersion relation at wave energy levels as low as 0.000,001 of the plasma thermal energy. The method is then used to study propagation of an essentially monochromatic plane wave. Results on amplitude oscillation and nonlinear frequency shift are compared with available theories. The additional phenomena of sideband instability and satellite growth, stimulated by large amplitude wave propagation and the resulting particle trapping, are described.
Spectrograms of ship wakes: identifying linear and nonlinear wave signals
Pethiyagoda, Ravindra; Moroney, Timothy J
2016-01-01
A spectrogram is a useful way of using short-time discrete Fourier transforms to visualise surface height measurements taken of ship wakes in real world conditions. For a steadily moving ship that leaves behind small-amplitude waves, the spectrogram is known to have two clear linear components, a sliding-frequency mode caused by the divergent waves and a constant-frequency mode for the transverse waves. However, recent observations of high speed ferry data have identified three additional components of the spectrograms that are not yet explained. We use computer simulations of linear and nonlinear ship wave patterns and apply time-frequency analysis to generate spectrograms for an idealised ship. We clarify the role of the linear dispersion relation and ship speed on the two linear components. Further, we show that additional features in the experimental data are caused by nonlinearity. Finally, we explain a discrepancy between the high speed ferry spectrograms and linear theory by accounting for ship acceler...
Cosmic neutrinos: A dispersive and nonlinear fluid
Inman, Derek; Pen, Ue-Li
2017-03-01
We present a description of cosmic neutrinos as a dispersive fluid. In this approach, the neutrino phase space is reduced to density and velocity fields alongside a scale-dependent sound speed. This sound speed depends on redshift, the initial neutrino phase space density and the cold dark matter gravitational potential. The latter is a new coupling between neutrinos and large scale structure not described by previous fluid approaches. We compute the sound speed in linear theory and find that it asymptotes to constants at small and large scales regardless of the gravitational potential. By comparing with neutrino N-body simulations, we measure the small scale sound speed and find it to be lower than linear theory predictions. This allows for an explanation of the discrepancy between N-body and linear response predictions for the neutrino power spectrum: neutrinos are still driven predominantly by the cold dark matter, but the sound speed on small scales is not stable to perturbations and decreases. Finally, we present a calibrated model for the neutrino power spectrum that requires no additional integrations outside of standard Boltzmann codes.
Cosmic neutrinos: dispersive and non-linear
Inman, Derek
2016-01-01
We present a description of cosmic neutrinos as a dispersive fluid. In this approach, the neutrino phase space is reduced to density and velocity fields alongside a scale-dependent sound speed. This sound speed depends on redshift, the initial neutrino phase space density and the cold dark matter gravitational potential. The latter is a new coupling between neutrinos and large scale structure not described by previous fluid approaches. We compute the sound speed in linear theory and find that it asymptotes to constants at small and large scales regardless of the gravitational potential. By comparing with neutrino N-body simulations, we measure the small scale sound speed and find it to be lower than linear theory predictions. This allows for an explanation of the discrepency between N-body and linear response predictions for the neutrino power spectrum: neutrinos are still driven predominantly by the cold dark matter, but the sound speed on small scales is not stable to perturbations and decreases. Finally, w...
Observation of dispersive shock waves, solitons, and their interactions in viscous fluid conduits
Anderson, Dalton; Maiden, Michelle; Lowman, Nicholas; Schubert, Marika; Hoefer, Mark
2016-11-01
Dispersive shock waves (DSWs) and solitons are fundamental structures in dispersive hydrodynamics, but studies have been severely constrained. Here we report on a novel testbed called the conduit system where one fluid is moved through another via a fluid pipe with virtually no mass diffusion. The interfacial dynamics of this pipe are conservative and are modeled by a scalar, nonlinear, dispersive wave equation, similar to those describing a superfluid. Resultantly, the interfacial waves are effectively dissipationless, which enables high fidelity observations of coherent phenomena such as large amplitude DSWs. Experiments involving solitons, wavebreaking leading to DSWs, and their interactions will be presented. The results include the refraction and absorption of a soliton by a DSW and the refraction of a DSW by a second DSW, resulting in two-phase behavior. Excellent agreement between nonlinear wave averaging, numerics, and laboratory experiments will be presented. The nonlinear wave dynamics observed in this model system have implications for a broad range of other conservative dispersive hydrodynamic systems. NSF.
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....
Nonlinear Pulse-reshaping of Sub-picosecond Pulses by Non-degenerate Four-wave Mixing
DEFF Research Database (Denmark)
Christensen, Jesper; Andersen, Lasse Mejling; Rottwitt, Karsten
Four-wave mixing does according to various models allow for arbitrary pulse-reshaping of the generated idler. Using subpicosecond pulses, we investigate numerically whether nonlinear effects and dispersion broadening begin to prevent this ability.......Four-wave mixing does according to various models allow for arbitrary pulse-reshaping of the generated idler. Using subpicosecond pulses, we investigate numerically whether nonlinear effects and dispersion broadening begin to prevent this ability....
Yu, Changyuan
Chromatic dispersion, polarization mode dispersion (PMD) and nonlinear effects are important issues on the physical layer of high-speed reconfigurable WDM optical fiber communication systems. For beyond 10 Gbit/s optical fiber transmission system, it is essential that chromatic dispersion and PMD be well managed by dispersion monitoring and compensation. One the other hand, dispersive and nonlinear effects in optical fiber systems can also be beneficial and has applications on pulse management, all-optical signal processing and network function, which will be essential for high bite-rate optical networks and replacing the expensive optical-electrical-optical (O/E/O) conversion. In this Ph.D. dissertation, we present a detailed research on dispersive and nonlinear effects in high-speed optical communication systems. We have demonstrated: (i) A novel technique for optically compensating the PMD-induced RF power fading that occurs in single-sideband (SSB) subcarrier-multiplexed systems. By aligning the polarization states of the optical carrier and the SSB, RF power fading due to all orders of PMD can be completely compensated. (ii) Chromatic-dispersion-insensitive PMD monitoring by using a narrowband FBG notch filter to recover the RF clock power for 10Gb/s NRZ data, and apply it as a control signal for PMD compensation. (iii) Chirp-free high-speed optical pulse generation with a repetition rate of 160 GHz (which is four times of the frequency of the electrical clock) using a phase modulator and polarization maintaining (PM) fiber. (iv) Polarization-insensitive all-optical wavelength conversion based on four-wave mixing in dispersion-shifted fiber (DSF) with a fiber Bragg grating and a Faraday rotator mirror. (v) Width-tunable optical RZ pulse train generation based on four-wave mixing in highly-nonlinear fiber. By electrically tuning the delay between two pump pulse trains, the pulse-width of a generated pulse train is continuously tuned. (vi) A high-speed all
Soliton solutions to a few fractional nonlinear evolution equations in shallow water wave dynamics
Mirzazadeh, Mohammad; Ekici, Mehmet; Sonmezoglu, Abdullah; Ortakaya, Sami; Eslami, Mostafa; Biswas, Anjan
2016-05-01
This paper studies a few nonlinear evolution equations that appear with fractional temporal evolution and fractional spatial derivatives. These are Benjamin-Bona-Mahoney equation, dispersive long wave equation and Nizhnik-Novikov-Veselov equation. The extended Jacobi's elliptic function expansion method is implemented to obtain soliton and other periodic singular solutions to these equations. In the limiting case, when the modulus of ellipticity approaches zero or unity, these doubly periodic functions approach solitary waves or shock waves or periodic singular solutions emerge.
High-order Boussinesq-type modelling of nonlinear wave phenomena in deep and shallow water
DEFF Research Database (Denmark)
Madsen, Per A.; Fuhrman, David R.
2010-01-01
In this work, we start with a review of the development of Boussinesq theory for water waves covering the period from 1872 to date. Previous reviews have been given by Dingemans,1 Kirby,2,3 and Madsen & Schäffer.4 Next, we present our most recent high-order Boussinesq-type formulation valid...... for fully nonlinear and highly dispersive waves traveling over a rapidly varying bathymetry. Finally, we cover applications of this Boussinesq model, and we study a number of nonlinear wave phenomena in deep and shallow water. These include (1) Kinematics in highly nonlinear progressive deep-water waves; (2......) Kinematics in progressive solitary waves; (3) Reflection of solitary waves from a vertical wall; (4) Reflection and diffraction around a vertical plate; (5) Quartet and quintet interactions and class I and II instabilities; (6) Extreme events from focused directionally spread waveelds; (7) Bragg scattering...
High-order Boussinesq-type modelling of nonlinear wave phenomena in deep and shallow water
DEFF Research Database (Denmark)
Madsen, Per A.; Fuhrman, David R.
2010-01-01
In this work, we start with a review of the development of Boussinesq theory for water waves covering the period from 1872 to date. Previous reviews have been given by Dingemans,1 Kirby,2,3 and Madsen & Schäffer.4 Next, we present our most recent high-order Boussinesq-type formulation valid...... for fully nonlinear and highly dispersive waves traveling over a rapidly varying bathymetry. Finally, we cover applications of this Boussinesq model, and we study a number of nonlinear wave phenomena in deep and shallow water. These include (1) Kinematics in highly nonlinear progressive deep-water waves; (2......) Kinematics in progressive solitary waves; (3) Reflection of solitary waves from a vertical wall; (4) Reflection and diffraction around a vertical plate; (5) Quartet and quintet interactions and class I and II instabilities; (6) Extreme events from focused directionally spread waveelds; (7) Bragg scattering...
Nonlinear behavior of electron acoustic waves in an un-magnetized plasma
Energy Technology Data Exchange (ETDEWEB)
Dutta, Manjistha; Khan, Manoranjan [Department of Instrumentation Science, Jadavpur University, Kolkata 700 032 (India); Chakrabarti, Nikhil [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064 (India); Roychoudhury, Rajkumar [Indian Statistical Institute, Kolkata 700 108 (India)
2011-10-15
The nonlinear electron acoustic wave, which is found in the earth's magnetosphere by satellite observations, is studied analytically by Lagrangian fluid description. The basic linear mode is observed in a two temperature electron species plasma where ions form stationary charge neutral background. We have obtained nonlinear description of this mode, which depends on both time and space. A possible solution shows a soliton like structure, which is localized in space, and the amplitude increases with time in the absence of dispersion. Small dispersive correction, however, shows spread of the solution in space. This method can be generalized to study the nonlinear behavior of a general class of multispecies plasma.
Nonlinear Alfvén wave dynamics at a 2D magnetic null point: ponderomotive force
Thurgood, J. O.; McLaughlin, J. A.
2013-07-01
Context. In the linear, β = 0 MHD regime, the transient properties of magnetohydrodynamic (MHD) waves in the vicinity of 2D null points are well known. The waves are decoupled and accumulate at predictable parts of the magnetic topology: fast waves accumulate at the null point; whereas Alfvén waves cannot cross the separatricies. However, in nonlinear MHD mode conversion can occur at regions of inhomogeneous Alfvén speed, suggesting that the decoupled nature of waves may not extend to the nonlinear regime. Aims: We investigate the behaviour of low-amplitude Alfvén waves about a 2D magnetic null point in nonlinear, β = 0 MHD. Methods: We numerically simulate the introduction of low-amplitude Alfvén waves into the vicinity of a magnetic null point using the nonlinear LARE2D code. Results: Unlike in the linear regime, we find that the Alfvén wave sustains cospatial daughter disturbances, manifest in the transverse and longitudinal fluid velocity, owing to the action of nonlinear magnetic pressure gradients (viz. the ponderomotive force). These disturbances are dependent on the Alfvén wave and do not interact with the medium to excite magnetoacoustic waves, although the transverse daughter becomes focused at the null point. Additionally, an independently propagating fast magnetoacoustic wave is generated during the early stages, which transports some of the initial Alfvén wave energy towards the null point. Subsequently, despite undergoing dispersion and phase-mixing due to gradients in the Alfvén-speed profile (∇cA ≠ 0) there is no further nonlinear generation of fast waves. Conclusions: We find that Alfvén waves at 2D cold null points behave largely as in the linear regime, however they sustain transverse and longitudinal disturbances - effects absent in the linear regime - due to nonlinear magnetic pressure gradients.
Nonlinear electron acoustic cyclotron waves in presence of uniform magnetic field
Energy Technology Data Exchange (ETDEWEB)
Dutta, Manjistha; Khan, Manoranjan [Department of Instrumentation Science, Jadavpur University, Kolkata 700 032 (India); Ghosh, Samiran [Department of Applied Mathematics, University of Calcutta, 92, Acharya Prafulla Chandra Road, Kolkata 700 009 (India); Roychoudhury, Rajkumar [Indian Statistical Institute, Kolkata 700 108 (India); Chakrabarti, Nikhil [Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700 064 (India)
2013-04-15
Nonlinear electron acoustic cyclotron waves (EACW) are studied in a quasineutral plasma in presence of uniform magnetic field. The fluid model is used to describe the dynamics of two temperature electron species in a stationary charge neutral inhomogeneous background. In long wavelength limit, it is shown that the linear electron acoustic wave is modified by the uniform magnetic field similar to that of electrostatic ion cyclotron wave. Nonlinear equations for these waves are solved by using Lagrangian variables. Results show that the spatial solitary wave-like structures are formed due to nonlinearities and dispersions. These structures transiently grow to larger amplitude unless dispersive effect is actively operative and able to arrest this growth. We have found that the wave dispersion originated from the equilibrium inhomogeneity through collective effect and is responsible for spatiotemporal structures. Weak dispersion is not able to stop the wave collapse and singular structures of EACW are formed. Relevance of the results in the context of laboratory and space plasmas is discussed.
Dispersive waves in fs cascaded second-harmonic generation
DEFF Research Database (Denmark)
Bache, Morten; Bang, Ole; Krolikowski, Wieslaw
2009-01-01
Dispersive waves are observed in simulations of cascaded (phase-mismatched) second-harmonic generation. When generating ultra-short fs compressed near-IR solitons the dispersive waves are strongly red-shifted, depending on the soliton wavelength. Semi-analytical calculations predict the wavelengths....
Characterization of thin films using generalized lamb wave dispersion relations
Richard, P; Behrend, O.; Gremaud, G.; Kulik, A.
1993-01-01
We used the Continuous Wave Scanning Acoustic Microscope to characterize thin film materials. The measurement of the dispersion curve of surface waves and the inversion of this dispersion equation relation, allow to determine the elastic constants, the density or the thickness of a thin layer on a substrate. Besides, it is possible to have qualitative information on the adhesion properties of the layer.
Long wave-short wave resonance in nonlinear negative refractive index media.
Chowdhury, Aref; Tataronis, John A
2008-04-18
We show that long wave-short wave resonance can be achieved in a second-order nonlinear negative refractive index medium when the short wave lies on the negative index branch. With the medium exhibiting a second-order nonlinear susceptibility, a number of nonlinear phenomena such as solitary waves, paired solitons, and periodic wave trains are possible or enhanced through the cascaded second-order effect. Potential applications include the generation of terahertz waves from optical pulses.
Analytic descriptions of cylindrical electromagnetic waves in a nonlinear medium.
Xiong, Hao; Si, Liu-Gang; Yang, Xiaoxue; Wu, Ying
2015-06-15
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.
NONLINEAR WAVES AND PERIODIC SOLUTION IN FINITE DEFORMATION ELASTIC ROD
Institute of Scientific and Technical Information of China (English)
Liu Zhifang; Zhang Shanyuan
2006-01-01
A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expansion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition of exact periodic solutions, shock solution and solitary solution existence is discussed.
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
Characterizing Electron Trapping Nonlinearity in Langmuir Waves
Strozzi, D J; Rose, H A; Hinkel, D E; Langdon, A B; Banks, J W
2012-01-01
We assess when electron trapping nonlinearities are expected to be important in Langmuir waves. The basic criterion is that the effective lifetime, t_d, of resonant electrons in the trapping region of velocity space must exceed the period of trapped motion for deeply-trapped electrons, tau_B = (n_e/delta n)^{1/2} 2pi/omega_pe. A unitless figure of merit, the "bounce number" N_B = t_d/tau_B, encapsulates this condition and allows an effective threshold amplitude for which N_B=1 to be defined. The lifetime is found for convective loss (transverse and longitudinal) out of a spatially finite Langmuir wave. Simulations of driven waves with a finite transverse profile, using the 2D-2V Vlasov code Loki, show trapping nonlinearity increases continuously with N_B for side loss, and is significant for N_B ~ 1. The lifetime due to Coulomb collisions (both electron-electron and electron-ion) is also found, with pitch-angle scattering and parallel drag and diffusion treated in a unified way. A simple way to combine convec...
Nonlinear MHD waves in a Prominence Foot
Ofman, Leon; Kucera, Therese; Schmieder, Brigitte
2015-01-01
We study nonlinear waves in a prominence foot using 2.5D MHD model motivated by recent high-resolution observations with Hinode/SOT in Ca~II emission of a prominence on October 10, 2012 showing highly dynamic small-scale motions in the prominence material. Observations of H$\\alpha$ intensities and of Doppler shifts show similar propagating fluctuations. However the optically thick nature of the emission lines inhibits 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 ($\\delta I/I\\sim \\delta n/n$). 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 typical period in the range of 5-11 minutes, and wavelengths $\\sim <$2000 km. Recent Doppler shift observations show the transverse displacement of the propagating wav...
Nonlinear ion acoustic waves scattered by vortexes
Ohno, Yuji; Yoshida, Zensho
2016-09-01
The Kadomtsev-Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here, we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes 'scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are 'ambient' because they do not receive reciprocal reactions from the waves (i.e., the vortex equation is independent of the wave fields). This model describes a minimal departure from the integrable KP system. By the Painlevé test, we delineate how the vorticity term violates integrability, bringing about an essential three-dimensionality to the solutions. By numerical simulation, we show how the solitons are scattered by vortexes and become chaotic.
Lamb wave Shearwave dispersion ultrasound Vibrometry (SDUV) validation study.
Nenadic, Ivan; Urban, Matthew W; Mitchell, Scott A; Greenleaf, James F
2010-01-01
Our group has been investigating the use of Shearwave Dispersion Ultrasound Vibrometry (SDUV) for quantifying viscoelasticity of the myocardium. The primary aim of this study is the design and testing of viscoelastic materials suitable for validation of the Lamb wave model in the heart. The Lamb wave SDUV method was used to measure shear wave velocity dispersion of gelatin and urethane rubber plates in the range 40-500 Hz and estimate the material properties. A finite element model (FEM) of a viscoelastic plate submerged in water was used to study the appropriateness of the Lamb wave dispersion equations. An embedded sphere method was used as an independent measurement of viscoelasticity. The FEM wave velocity dispersion data were in excellent agreement with the theoretical predictions. Elasticity and viscosity of urethane and gelatin obtained using the Lamb wave SDUV and embedded sphere methods agree within one standard deviation.
Nonlinear shallow ocean-wave soliton interactions on flat beaches.
Ablowitz, Mark J; Baldwin, Douglas E
2012-09-01
Ocean waves are complex and often turbulent. While most ocean-wave interactions are essentially linear, sometimes two or more waves interact in a nonlinear way. For example, two or more waves can interact and yield waves that are much taller than the sum of the original wave heights. Most of these shallow-water nonlinear interactions look like an X or a Y or two connected Ys; at other times, several lines appear on each side of the interaction region. It was thought that such nonlinear interactions are rare events: they are not. Here we report that such nonlinear interactions occur every day, close to low tide, on two flat beaches that are about 2000 km apart. These interactions are closely related to the analytic, soliton solutions of a widely studied multidimensional nonlinear wave equation. On a much larger scale, tsunami waves can merge in similar ways.
Nonlinear Plasma Wave in Magnetized Plasmas
Bulanov, Sergei V; Kando, Masaki; Koga, James K; Hosokai, Tomonao; Zhidkov, Alexei G; Kodama, Ryosuke
2013-01-01
Nonlinear axisymmetric cylindrical plasma oscillations in magnetized collisionless plasmas are a model for the electron fluid collapse on the axis behind an ultrashort relativisically intense laser pulse exciting a plasma wake wave. We present an analytical description of the strongly nonlinear oscillations showing that the magnetic field prevents closing of the cavity formed behind the laser pulse. This effect is demonstrated with 3D PIC simulations of the laser-plasma interaction. An analysis of the betatron oscillations of fast electrons in the presence of the magnetic field reveals a characteristic "Four-Ray Star" pattern which has been observed in the image of the electron bunch in experiments [T. Hosokai, et al., Phys. Rev. Lett. 97, 075004 (2006)].
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation[
Institute of Scientific and Technical Information of China (English)
HUANGDing-Jiang; ZHANGHong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation
Institute of Scientific and Technical Information of China (English)
HUANG Ding-Jiang; ZHANG Hong-Qing
2004-01-01
By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.
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...
Dispersive Blow-Up Ⅱ.Schr(o)dinger-Type Equations,Optical and Oceanic Rogue Waves
Institute of Scientific and Technical Information of China (English)
Jerry L.BONA; Jean-Claude SAUT
2010-01-01
Addressed here is the occurrence of point singularities which owe to the fo-cusing of short or long waves,a phenomenon labeled dispersive blow-up.The context of this investigation is linear and nonlinear,strongly dispersive equations or systems of equa-tions.The present essay deals with linear and nonlinear Schr(o)dinger equations,a class of fractional order SchrSdinger equations and the linearized water wave equations,with and without surface tension. Commentary about how the results may bear upon the formation of rogue waves in fluid and optical environments is also included.
On the dissipation and dispersion of entropy waves in heat transferring channel flows
Fattahi, A.; Hosseinalipour, S. M.; Karimi, N.
2017-08-01
This paper investigates the hydrodynamic and heat transfer effects on the dissipation and dispersion of entropy waves in non-reactive flows. These waves, as advected density inhomogeneities downstream of unsteady flames, may decay partially or totally before reaching the exit nozzle, where they are converted into sound. Attenuation of entropy waves dominates the significance of the subsequent acoustic noise generation. Yet, the extent of this decay process is currently a matter of contention and the pertinent mechanisms are still largely unexplored. To resolve this issue, a numerical study is carried out by compressible large eddy simulation of the wave advection in a channel subject to convective and adiabatic thermal boundary conditions. The dispersion, dissipation, and spatial correlation of the wave are evaluated by post-processing of the numerical results. This includes application of the classical coherence function as well as development of nonlinear quantitative measures of wave dissipation and dispersion. The analyses reveal that the high frequency components of the entropy wave are always strongly damped. The survival of the low frequency components heavily depends on the turbulence intensity and thermal boundary conditions of the channel. In general, high turbulence intensities and particularly heat transfer intensify the decay and destruction of the spatial coherence of entropy waves. In some cases, they can even result in the complete annihilation of the wave. The current work can therefore resolve the controversies arising over the previous studies of entropy waves with different thermal boundary conditions.
Time shift of pulses due to dispersion slope and nonlinearity
Energy Technology Data Exchange (ETDEWEB)
Marcuse, D.; Menyuk, C.R.; Holzloehner, R.
1999-12-01
The authors show that the time delay of optical pulses traveling in long fibers is influenced by the dispersion slope and the fiber nonlinearity. Consequently, one or more new pulses that are inserted by add-drop operations into a pulse train that has already traveled a long distance may shift relative to the old pulses. This time shift delays the initial pulses more than the newly inserted ones, so that the newly inserted pulses can leave their time frames, leading to errors.
Zhang, Zhendong
2016-07-26
We present a surface-wave inversion method that inverts for the S-wave velocity from the Rayleigh wave dispersion curve using a difference approximation to the gradient of the misfit function. We call this wave equation inversion of skeletonized surface waves because the skeletonized dispersion curve for the fundamental-mode Rayleigh wave is inverted using finite-difference solutions to the multi-dimensional elastic wave equation. The best match between the predicted and observed dispersion curves provides the optimal S-wave velocity model. Our method can invert for lateral velocity variations and also can mitigate the local minimum problem in full waveform inversion with a reasonable computation cost for simple models. Results with synthetic and field data illustrate the benefits and limitations of this method. © 2016 Elsevier B.V.
The interaction of chemical dispersants and suspended sediments with crude oil influences the fate and transport of oil spills in coastal waters. A wave tank study was conducted to investigate the effects of chemical dispersants and mineral fines on the dispersion of oil and the ...
The interaction of chemical dispersants and suspended sediments with crude oil influences the fate and transport of oil spills in coastal waters. A wave tank study was conducted to investigate the effects of chemical dispersants and mineral fines on the dispersion of oil and the ...
P-wave dispersion in children with acute rheumatic fever.
Kocaoglu, Celebi; Sert, Ahmet; Aypar, Ebru; Oran, Bulent; Odabas, Dursun; Arslan, Derya; Akin, Fatih
2012-01-01
As a new and simple electrocardiographic marker, P-wave dispersion is reported to be associated with inhomogeneous and discontinuous propagation of sinus impulses. The current study aimed to investigate P-wave dispersion in children with acute rheumatic fever. The study population consisted of 47 children with acute rheumatic fever (29 patients with carditis and 18 patients without carditis) and 31 healthy control subjects. Maximum and minimum P-wave durations were measured from the 12-lead surface electrocardiogram. The P-wave dispersion was calculated as the difference between maximum and minimum P-wave durations. The maximum P-wave duration and the P-wave dispersion of the patients with and without carditis were significantly greater than those of the control subjects. The P-wave dispersion of the patients with carditis was significantly greater than that of the patients without carditis. In conclusion, the P-wave dispersion was higher in the children with acute rheumatic fever than in the healthy control subjects.
A THIRD-ORDER BOUSSINESQ MODEL APPLIED TO NONLINEAR EVOLUTION OF SHALLOW-WATER WAVES
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The conventional Boussinesq model is extended to the third order in dispersion and nonlinearity. The new equations are shown to possess better linear dispersion characteristics. For the evolution of periodic waves over a constant depth, the computed wave envelops are spatially aperiodic and skew. The model is then applied to the study of wave focusing by a topographical lens and the results are compared with Whalin's (1971) experimental data as well as some previous results from the conventional Boussinesq model. Encouragingly, improved agreement with Whalin's experimental data is found.
Particle Scattering off of Right-Handed Dispersive Waves
Schreiner, Cedric; Spanier, Felix
2016-01-01
Resonant scattering of fast particles off low frequency plasma waves is a major process determining transport characteristics of energetic particles in the heliosphere and contributing to their acceleration. Usually, only Alfv\\'en waves are considered for this process, although dispersive waves are also present throughout the heliosphere. We investigate resonant interaction of energetic electrons with dispersive, right-handed waves. For the interaction of particles and a single wave a variable transformation into the rest frame of the wave can be performed. Here, wellestablished analytic models derived in the framework of magnetostatic quasi-linear theory (QLT) can be used as a reference to validate simulation results. However, this approach fails as soon as several dispersive waves are involved. Based on analytic solutions modeling the scattering amplitude in the magnetostatic limit, we present an approach to modify these equations for the use in the plasma frame. Thereby we aim at a description of particle ...
Saturation process of nonlinear standing waves
Institute of Scientific and Technical Information of China (English)
马大猷; 刘克
1996-01-01
The sound pressure of the nonlinear standing waves is distorted as expected, but also tends to saturate as being found in standing-wave tube experiments with increasing sinusoidal excitation. Saturation conditions were not actually reached, owing to limited excitation power, but the evidence of tendency to saturation is without question. It is the purpose of this investigation to find the law of saturation from the existing experimental data. The results of curve fitting indicate that negative feedback limits the growth of sound pressure with increasing excitation, the growth of the fundamental and the second harmonic by the negative feedback of their sound pressures, and the growth of the third and higher harmonics, however, by their energies (sound pressures squared). The growth functions of all the harmonics are derived, which are confirmed by the experiments. The saturation pressures and their properties are found.
Dispersive optical nonlinearities in an EIT-Rydberg medium
Stanojevic, Jovica; Bimbard, Erwan; Ourjoumtsev, Alexei; Grangier, Philippe
2013-01-01
We investigate dispersive optical nonlinearities that arise from Rydberg excitation blockade in cold Rydberg gases. We consider a two-photon transition scheme and study the non-linear response to a weak optical probe in presence of a strong control beam. For very low probe fields, the dominant nonlinearities are of the third order and they can be exactly evaluated in a steady state regime. In a more general case, the change in average atomic populations and coherences due to Rydberg interactions can be characterized by properly defined scaling parameters, which are generally complex numbers but in certain situations take the usual meaning of the number of atoms in a blockade sphere. They can be used in a simple "universal scaling" formula to determine the dispersive optical nonlinearity of the medium. We also develop a novel technique to account for the Rydberg interaction effects, by simplifying the treatment of nonlocal interaction terms, the so-called collisional integrals. We find algebraic relations that...
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...
All-optical observation and reconstruction of spin wave dispersion
Hashimoto, Yusuke; Daimon, Shunsuke; Iguchi, Ryo; Oikawa, Yasuyuki; Shen, Ka; Sato, Koji; Bossini, Davide; Tabuchi, Yutaka; Satoh, Takuya; Hillebrands, Burkard; Bauer, Gerrit E. W.; Johansen, Tom H.; Kirilyuk, Andrei; Rasing, Theo; Saitoh, Eiji
2017-06-01
To know the properties of a particle or a wave, one should measure how its energy changes with its momentum. The relation between them is called the dispersion relation, which encodes essential information of the kinetics. In a magnet, the wave motion of atomic spins serves as an elementary excitation, called a spin wave, and behaves like a fictitious particle. Although the dispersion relation of spin waves governs many of the magnetic properties, observation of their entire dispersion is one of the challenges today. Spin waves whose dispersion is dominated by magnetostatic interaction are called pure-magnetostatic waves, which are still missing despite of their practical importance. Here, we report observation of the band dispersion relation of pure-magnetostatic waves by developing a table-top all-optical spectroscopy named spin-wave tomography. The result unmasks characteristics of pure-magnetostatic waves. We also demonstrate time-resolved measurements, which reveal coherent energy transfer between spin waves and lattice vibrations.
Directory of Open Access Journals (Sweden)
Jian Cai
2016-12-01
Full Text Available The results of Lamb wave identification for the aerospace structures could be easily affected by the nonlinear-dispersion characteristics. In this paper, dispersion compensation of Lamb waves is of particular concern. Compared with the similar research works on the traditional signal domain transform methods, this study is based on signal construction from the viewpoint of nonlinear wavenumber linearization. Two compensation methods of linearly-dispersive signal construction (LDSC and non-dispersive signal construction (NDSC are proposed. Furthermore, to improve the compensation effect, the influence of the signal construction process on the other crucial signal properties, including the signal waveform and amplitude spectrum, is considered during the investigation. The linear-dispersion and non-dispersion effects are firstly analyzed. Then, after the basic signal construction principle is explored, the numerical realization of LDSC and NDSC is discussed, in which the signal waveform and amplitude spectrum preservation is especially regarded. Subsequently, associated with the delay-and-sum algorithm, LDSC or NDSC is employed for high spatial resolution damage imaging, so that the adjacent multi-damage or quantitative imaging capacity of Lamb waves can be strengthened. To verify the proposed signal construction and damage imaging methods, the experimental and numerical validation is finally arranged on the aluminum plates.
Cai, Jian; Yuan, Shenfang; Wang, Tongguang
2016-12-23
The results of Lamb wave identification for the aerospace structures could be easily affected by the nonlinear-dispersion characteristics. In this paper, dispersion compensation of Lamb waves is of particular concern. Compared with the similar research works on the traditional signal domain transform methods, this study is based on signal construction from the viewpoint of nonlinear wavenumber linearization. Two compensation methods of linearly-dispersive signal construction (LDSC) and non-dispersive signal construction (NDSC) are proposed. Furthermore, to improve the compensation effect, the influence of the signal construction process on the other crucial signal properties, including the signal waveform and amplitude spectrum, is considered during the investigation. The linear-dispersion and non-dispersion effects are firstly analyzed. Then, after the basic signal construction principle is explored, the numerical realization of LDSC and NDSC is discussed, in which the signal waveform and amplitude spectrum preservation is especially regarded. Subsequently, associated with the delay-and-sum algorithm, LDSC or NDSC is employed for high spatial resolution damage imaging, so that the adjacent multi-damage or quantitative imaging capacity of Lamb waves can be strengthened. To verify the proposed signal construction and damage imaging methods, the experimental and numerical validation is finally arranged on the aluminum plates.
Nonlinear ion acoustic waves scattered by vortexes
Ohno, Yuji
2015-01-01
The Kadomtsev--Petviashvili (KP) hierarchy is the archetype of infinite-dimensional integrable systems, which describes nonlinear ion acoustic waves in two-dimensional space. This remarkably ordered system resides on a singular submanifold (leaf) embedded in a larger phase space of more general ion acoustic waves (low-frequency electrostatic perturbations). The KP hierarchy is characterized not only by small amplitudes but also by irrotational (zero-vorticity) velocity fields. In fact, the KP equation is derived by eliminating vorticity at every order of the reductive perturbation. Here we modify the scaling of the velocity field so as to introduce a vortex term. The newly derived system of equations consists of a generalized three-dimensional KP equation and a two-dimensional vortex equation. The former describes `scattering' of vortex-free waves by ambient vortexes that are determined by the latter. We say that the vortexes are `ambient' because they do not receive reciprocal reactions from the waves (i.e.,...
Exact solutions of optical wave propagation in nonlinear negative refractive medium
Nanda, Lipsa
2016-04-01
An analytical and simulation based method has been used to exactly solve the nonlinear Schrödinger's equation (NLSE) and study the solitonic forms in a medium which exhibits frequency dependent dielectric permittivity (ɛ) and magnetic permeability (μ). The model has been extended to describe the propagation of a wave in a nonlinear negative refractive medium (NRM) which is dispersive and negative in nature.
Nonlinear wave propagation in constrained solids subjected to thermal loads
Nucera, Claudio; Lanza di Scalea, Francesco
2014-01-01
The classical mathematical treatment governing nonlinear wave propagation in solids relies on finite strain theory. In this scenario, a system of nonlinear partial differential equations can be derived to mathematically describe nonlinear phenomena such as acoustoelasticity (wave speed dependency on quasi-static stress), wave interaction, wave distortion, and higher-harmonic generation. The present work expands the topic of nonlinear wave propagation to the case of a constrained solid subjected to thermal loads. The origin of nonlinear effects in this case is explained on the basis of the anharmonicity of interatomic potentials, and the absorption of the potential energy corresponding to the (prevented) thermal expansion. Such "residual" energy is, at least, cubic as a function of strain, hence leading to a nonlinear wave equation and higher-harmonic generation. Closed-form solutions are given for the longitudinal wave speed and the second-harmonic nonlinear parameter as a function of interatomic potential parameters and temperature increase. The model predicts a decrease in longitudinal wave speed and a corresponding increase in nonlinear parameter with increasing temperature, as a result of the thermal stresses caused by the prevented thermal expansion of the solid. Experimental measurements of the ultrasonic nonlinear parameter on a steel block under constrained thermal expansion confirm this trend. These results suggest the potential of a nonlinear ultrasonic measurement to quantify thermal stresses from prevented thermal expansion. This knowledge can be extremely useful to prevent thermal buckling of various structures, such as continuous-welded rails in hot weather.
Tomita, Yasuo; Matsushima, Shun-suke; Yamagami, Ryu-ichi; Jinzenji, Taka-aki; Sakuma, Shohei; Liu, Xiangming; Izuishi, Takuya; Shen, Qing
2017-06-01
We describe the nonlinear optical properties of inorganic-organic nanocomposite films in which semiconductor CdSe quantum dots as high as 6.8 vol.% are dispersed. Open/closed Z-scan measurements, degenerate multi-wave mixing and femtosecond pump-probe/transient grating measurements are conducted. It is shown that the observed fifth-order optical nonlinearity has the cascaded third-order contribution that becomes prominent at high concentrations of CdSe QDs. It is also shown that there are picosecond-scale intensity-dependent and nanosecond-scale intensity-independent decay components in absorptive and refractive nonlinearities. The former is caused by the Auger process, while the latter comes from the electron-hole recombination process.
Detailed characterization of CW- and pulsed-pump four-wave mixing in highly nonlinear fibers
DEFF Research Database (Denmark)
Lillieholm, Mads; Galili, Michael; Grüner-Nielsen, L.
2016-01-01
We present a quantitative comparison of continuouswave- (CW) and pulsed-pump four-wave mixing (FWM) in commercially available highly nonlinear fibers (HNLFs), and suggest properties for which the CW and pulsed FWM bandwidths are limited in practice. The CWand pulsed-pump parametric gain...... bandwidth. However, an inverse scaling of the TOD with the dispersion fluctuations, leads to different CW-optimized fibers, which depend only on the even dispersion-orders....
Bifurcation methods of dynamical systems for handling nonlinear wave equations
Indian Academy of Sciences (India)
Dahe Feng; Jibin Li
2007-05-01
By using the bifurcation theory and methods of dynamical systems to construct the exact travelling wave solutions for nonlinear wave equations, some new soliton solutions, kink (anti-kink) solutions and periodic solutions with double period are obtained.
Dispersive and diffusive-dispersive shock waves for nonconvex conservation laws
El, G A; Shearer, M
2015-01-01
We compare the structure of solutions of Riemann problems for a conservation law with nonconvex (specifically, cubic) flux, regularized by two different mechanisms: 1) dispersion (in the modified Korteweg--de Vries (mKdV) equation); and 2) a combination of diffusion and dispersion (in the mKdV-Burgers equation). In the first case, the possible dynamics involve two qualitatively different types of expanding dispersive shock waves (DSWs), rarefaction waves (RWs) and kinks (smooth fronts). In the second case, in addition to RWs, there are travelling wave solutions approximating both classical (Lax) and nonclassical (undercompressive) shock waves. Despite the singular nature of the zero-diffusion limit and rather differing analytical approaches employed in the descriptions of dispersive and diffusive-dispersive regularization, the resulting comparison of the two cases reveals a number of striking parallels. In particular the mKdV kink solution is identified as an undercompressive DSW. Other prominent features, su...
Nonlinear Taylor dispersion in gravity currents in porous media
Szulczewski, Michael; Juanes, Ruben
2012-11-01
Taylor dispersion describes how a non-uniform flow can accelerate diffusive mixing between fluids by elongating the fluid-fluid interface over which diffusion acts. While Taylor dispersion has been extensively studied in simple systems such as Poiseuille and Couette flows, it is poorly understood in more complex systems such as porous-media flows. Here, we study Taylor dispersion in porous media during a gravity-driven flow using theory and simulations. We consider a simple geometry for physical insight: a horizontal, confined layer of permeable rock in which two fluids of different densities are initially separated by a vertical interface. We show that the flow exhibits a non-uniform velocity field that leads to Taylor dispersion at the aquifer scale. Unlike the classical model of Taylor dispersion, however, the diffusive mixing is coupled to the flow velocity because it reduces the lateral density gradient that drives the flow. This coupling causes the flow to continually decelerate and eventually stop completely. To model the flow, we develop a non-linear diffusion equation for the concentration of the more dense fluid, which admits an analytical similarity solution. We discuss applications of the model to CO2 sequestration.
The nonlinear standing wave inside the space of liquid
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Based on the basic equations of hydrodynamics, the nonlinear acoustic wave equation is obtained. By taking into account the boundary condition and properties of nonlinear standing wave, the equation is solved through perturbation method, and the stable expressions of fundamental wave and second harmonic are presented. The sound pressures in an ultrasonic cleaner are measured by hydrophones, and the relationship between the received voltages of hydrophones and the output voltages of the ultrasonic generator is researched. The study shows the existence of the nonlinear effect of liquid and analyzes the frequency spectrum of the received signals by hydrophones, by which the fundamental wave, second and high order harmonics are found coexisting in the bounded space filled with liquids. The theory and experimental results testify the existence of the nonlinear standing wave in liquid. Owing to the restricted applicability of perturbation method, the theoretical results of the fundamental wave and second harmonic are good only for the weak nonlinear phenomenon.
Two-dimensional dispersive shock waves in dissipative optical media
Kartashov, Yaroslav V
2013-01-01
We study generation of two-dimensional dispersive shock waves and oblique dark solitons upon interaction of tilted plane waves with negative refractive index defects embedded into defocusing material with linear gain and two-photon absorption. Different evolution regimes are encountered including the formation of well-localized disturbances for input tilts below critical one, and generation of extended shock waves containing multiple intensity oscillations in the "upstream" region and gradually vanishing oblique dark solitons in "downstream" region for input tilts exceeding critical one. The generation of stable dispersive shock waves is possible only below certain critical defect strength.
Institute of Scientific and Technical Information of China (English)
Feng Yu-Lin; Liu Xiao-Zhou; Liu Jie-Hui; Ma Li
2009-01-01
Based on an equivalent medium approach,this paper presents a model describing the nonlinear propagation of acoustic waves in a viscoelastic medium containing cylindrical micropores. The influences of pores' nonlinear oscillations on sound attenuation,sound dispersion and an equivalent acoustic nonlinearity parameter are discussed. The calculated results show that the attenuation increases with an increasing volume fraction of mieropores. The peak of sound velocity and attenuation occurs at the resonant frequency of the micropores while the peak of the equivalent acoustic nonlinearity parameter occurs at the half of the resonant frequency of the micropores. Furthermore,multiple scattering has been taken into account,which leads to a modification to the effective wave number in the equivalent medium approach. We find that these linear and nonlinear acoustic parameters need to be corrected when the volume fraction of micropores is larger than 0.1%.
Exact periodic wave solutions for some nonlinear partial differential equations
Energy Technology Data Exchange (ETDEWEB)
El-Wakil, S.A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt); Elgarayhi, A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)]. E-mail: elgarayhi@yahoo.com; Elhanbaly, A. [Theoretical Physics Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)
2006-08-15
The periodic wave solutions for some nonlinear partial differential equations, including generalized Klein-Gordon equation, Kadomtsev-Petviashvili (KP) equation and Boussinesq equations, are obtained by using the solutions of Jacobi elliptic equation. Under limit conditions, exact solitary wave solutions, shock wave solutions and triangular periodic wave solutions have been recovered.
Energy Technology Data Exchange (ETDEWEB)
Picozzi, A., E-mail: Antonio.Picozzi@u-bourgogne.fr [Laboratoire Interdisciplinaire Carnot de Bourgogne, Université de Bourgogne, CNRS-UMR 5027, Dijon (France); Garnier, J. [Laboratoire de Probabilités et Modèles Aléatoires and Laboratoire Jacques-Louis Lions, Université Paris VII, 75205 Paris Cedex 13 (France); Hansson, T. [Department of Information Engineering, Università di Brescia, Brescia 25123 (Italy); Suret, P.; Randoux, S. [Laboratoire de Physique des Lasers, Atomes et Molécules, CNRS, Université de Lille (France); Millot, G. [Laboratoire Interdisciplinaire Carnot de Bourgogne, Université de Bourgogne, CNRS-UMR 5027, Dijon (France); Christodoulides, D.N. [College of Optics/CREOL, University of Central Florida, Orlando, FL 32816 (United States)
2014-09-01
The nonlinear propagation of coherent optical fields has been extensively explored in the framework of nonlinear optics, while the linear propagation of incoherent fields has been widely studied in the framework of statistical optics. However, these two fundamental fields of optics have been mostly developed independently of each other, so that a satisfactory understanding of statistical nonlinear optics is still lacking. This article is aimed at reviewing a unified theoretical formulation of statistical nonlinear optics on the basis of the wave turbulence theory, which provides a nonequilibrium thermodynamic description of the system of incoherent nonlinear waves. We consider the nonlinear Schrödinger equation as a representative model accounting either for a nonlocal or a noninstantaneous nonlinearity, as well as higher-order dispersion effects. Depending on the amount of nonlocal (noninstantaneous) nonlinear interaction and the amount of inhomogeneous (nonstationary) statistics of the incoherent wave, different types of kinetic equations are derived and discussed. In the spatial domain, when the incoherent wave exhibits inhomogeneous statistical fluctuations, different forms of the (Hamiltonian) Vlasov equation are obtained depending on the amount of nonlocality. This Vlasov approach describes the processes of incoherent modulational instability and localized incoherent soliton structures. In the temporal domain, the causality property inherent to the response function leads to a kinetic formulation analogous to the weak Langmuir turbulence equation, which describes nonlocalized spectral incoherent solitons. In the presence of a highly noninstantaneous response, this formulation reduces to a family of singular integro-differential kinetic equations (e.g., Benjamin–Ono equation), which describe incoherent dispersive shock waves. Conversely, a non-stationary statistics leads to a (non-Hamiltonian) long-range Vlasov formulation, whose self-consistent potential
Li, Wan-Tong; Wang, Jia-Bing; Zhang, Li
2016-08-01
This paper is concerned with the new types of entire solutions other than traveling wave solutions of nonlocal dispersal equations with monostable nonlinearity in space periodic habitats. We first establish the existence and properties of spatially periodic solutions connecting two steady states. Then new types of entire solutions are constructed by combining the rightward and leftward pulsating traveling fronts with different speeds and a spatially periodic solution. Finally, for a class of special heterogeneous reaction, we further establish the uniqueness of entire solutions and the continuous dependence of such an entire solution on parameters, such as wave speeds and the shifted variables. In other words, we build a five-dimensional manifold of solutions and the traveling wave solutions are on the boundary of the manifold.
Detailed characterization of CW- and pulsed-pump four-wave mixing in highly nonlinear fibers.
Lillieholm, M; Galili, M; Grüner-Nielsen, L; Oxenløwe, L K
2016-11-01
We present a quantitative comparison of continuous-wave- (CW) and pulsed-pump four-wave mixing (FWM) in commercially available highly nonlinear fibers (HNLFs), and suggest properties for which the CW- and pulsed-pump FWM bandwidths are limited in practice. The CW- and pulsed-pump parametric gain is characterized experimentally for several HNLFs with various dispersion properties, including zero-dispersion wavelength fluctuations, and the results are interpreted in conjunction with detailed numerical simulations. It is found that a low third-order dispersion (TOD) is essential for the pulsed-pump FWM bandwidth. However, an inverse scaling of the TOD with the dispersion fluctuations leads to different CW-optimized fibers, which depend only on the even dispersion orders.
Chromatic and Dispersive Effects in Nonlinear Integrable Optics
Webb, Stephen D; Valishev, Alexander; Nagaitsev, Sergei N; Danilov, Viatcheslav V
2015-01-01
Proton accumulator rings and other circular hadron accelerators are susceptible to intensity-driven parametric instabilities because the zero-current charged particle dynamics are characterized by a single tune. Landau damping can suppress these instabilities, which requires energy spread in the beam or introducing nonlinear magnets such as octupoles. However, this approach reduces dynamic aperture. Nonlinear integrable optics can suppress parametric instabilities independent of energy spread in the distribution, while preserving the dynamic aperture. This novel approach promises to reduce particle losses and enable order-of-magnitude increases in beam intensity. In this paper we present results, obtained using the Lie operator formalism, on how chromaticity and dispersion affect particle orbits in integrable optics. We conclude that chromaticity in general breaks the integrability, unless the vertical and horizontal chromaticities are equal. Because of this, the chromaticity correcting magnets can be weaker ...
Compactification of nonlinear patterns and waves.
Rosenau, Philip; Kashdan, Eugene
2008-12-31
We present a nonlinear mechanism(s) which may be an alternative to a missing wave speed: it induces patterns with a compact support and sharp fronts which propagate with a finite speed. Though such mechanism may emerge in a variety of physical contexts, its mathematical characterization is universal, very simple, and given via a sublinear substrate (site) force. Its utility is shown studying a Klein-Gordon -u(tt) + [phi/(u(x)]x = P'(u) equation, where phi'(sigma) = sigma + beta sigma3 and endowed with a subquadratic site potential P(u) approximately /1-u2/(alpha+1), 0 < or = alpha < 1, and the Schrödinger iZt + inverted delta2 Z = G(/Z/)Z equation in a plane with G(A) = gammaA(-delta) - sigmaA2, 0 < delta < or = 1.
Sabeen, A.; Masood, W.; Qureshi, M. N. S.; Shah, H. A.
2017-07-01
In this paper, linear and nonlinear coupling of kinetic Alfven and acoustic waves has been studied in a dusty plasma in the presence of trapping and self-gravitation effects. In this regard, we have derived the linear dispersion relations for positively and negatively coupled dust kinetic Alfven-acoustic waves. Stability analysis of the coupled dust kinetic Alfven-acoustic wave has also been presented. The formation of solitary structures has been investigated following the Sagdeev potential approach by using the two-potential theory. Numerical results show that the solitary structures can be obtained only for sub-Alfvenic regimes in the scenario of space plasmas.
Time-domain Wave Propagation in Dispersive Media①
Institute of Scientific and Technical Information of China (English)
无
1997-01-01
The equation of time-domain wave propagation in dispersive media and the explicit beam propagation method are presented in this paper.This method is demonstrated by the short optical pulses in a directional coupler with second order dispersive effect and shows to be in full agreement with former references.This method is simple,easy and practical.
Lotekar, Ajay; Kakad, Amar; Kakad, Bharati
2016-10-01
One-dimensional fluid simulation is performed for the unmagnetized plasma consisting of cold fluid ions and superthermal electrons. Such a plasma system supports the generation of ion acoustic (IA) waves. A standard Gaussian type perturbation is used in both electron and ion equilibrium densities to excite the IA waves. The evolutionary profiles of the IA waves are obtained by varying the superthermal index and the amplitude of the initial perturbation. This simulation demonstrates that the amplitude of the initial perturbation and the superthermal index play an important role in determining the time evolution and the characteristics of the generated IA waves. The initial density perturbation in the system creates charge separation that drives the finite electrostatic potential in the system. This electrostatic potential later evolves into the dispersive and nondispersive IA waves in the simulation system. The density perturbation with the amplitude smaller than 10% of the equilibrium plasma density evolves into the dispersive IA waves, whereas larger density perturbations evolve into both dispersive and nondispersive IA waves for lower and higher superthermal index. The dispersive IA waves are the IA oscillations that propagate with constant ion plasma frequency, whereas the nondispersive IA waves are the IA solitary pulses (termed as IA solitons in the stability region) that propagate with the constant wave speed. The characteristics of the stable nondispersive IA solitons are found to be consistent with the nonlinear fluid theory. To the best of our knowledge, this is the first fluid simulation study that has considered the superthermal distributions for the plasma species to model the electrostatic solitary waves.
Travelling waves in nonlinear diffusion-convection-reaction
Gilding, B.H.; Kersner, R.
2001-01-01
The study of travelling waves or fronts has become an essential part of the mathematical analysis of nonlinear diffusion-convection-reaction processes. Whether or not a nonlinear second-order scalar reaction-convection-diffusion equation admits a travelling-wave solution can be determined by the stu
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...
On a class of nonlinear dispersive-dissipative interactions
Energy Technology Data Exchange (ETDEWEB)
Rosenau, P. [Tel Aviv Univ. (Israel). School of Mathematical Sciences
1997-07-29
The authors study the prototypical, genuinely nonlinear, equation; u{sub t} + a(u{sup m}){sub x} + (u{sup n}){sub xxx} = {mu}(u{sup k}){sub xx}, a, {mu} = consts., which encompasses a wide variety of dissipative-dispersive interactions. The parametric surface k = (m + n)/2 separates diffusion dominated from dissipation dominated phenomena. On this surface dissipative and dispersive effects are in detailed balance for all amplitudes. In particular, the m = n + 2 = k + 1 subclass can be transformed into a form free of convection and dissipation making it accessible to theoretical studies. Both bounded and unbounded oscillations are found and certain exact solutions are presented. When a = (2{mu}3/){sup 2} the map yields a linear equation; rational, periodic and aperiodic solutions are constructed.
On a class of nonlinear dispersive-dissipative interactions
Energy Technology Data Exchange (ETDEWEB)
Rosenau, P. [Tel Aviv Univ. (Israel). School of Mathematical Sciences
1997-07-29
The authors study the prototypical, genuinely nonlinear, equation; u{sub t} + a(u{sup m}){sub x} + (u{sup n}){sub xxx} = {mu}(u{sup k}){sub xx}, a, {mu} = consts., which encompasses a wide variety of dissipative-dispersive interactions. The parametric surface k = (m + n)/2 separates diffusion dominated from dissipation dominated phenomena. On this surface dissipative and dispersive effects are in detailed balance for all amplitudes. In particular, the m = n + 2 = k + 1 subclass can be transformed into a form free of convection and dissipation making it accessible to theoretical studies. Both bounded and unbounded oscillations are found and certain exact solutions are presented. When a = (2{mu}3/){sup 2} the map yields a linear equation; rational, periodic and aperiodic solutions are constructed.
Study and verification on dispersion coefficient in wave field
Institute of Scientific and Technical Information of China (English)
SHEN LiangDuo; ZOU ZhiLi
2012-01-01
Transport and diffusion caused by coastal waves have different characteristics from those induced by flows.Through solving the vertical diffusion equation by an analytic method,this paper infers a theoretical formula of dispersion coefficient under the combined action of current and waves.It divides the general dispersion coefficient into six parts,including coefficients due to tidal current,Stokes drift,wave oscillation and interaction among them.It draws a conclusion that the contribution of dispersive effect induced by coastal waves is mainly produced by Stokes drift,while the contributions to time-averaged dispersion coefficient due to wave orbital motion and interaction between current and waves are very small.The results without tidal current are in agreement with the numerical and experimental results,which proves the correctness of the theoretical derivation.This paper introduces the variation characteristics of both the time-averaged and oscillating dispersion coefficients versus relative water depth,and demonstrates the physical implications of the oscillating mixing coefficient due to waves.We also apply the results to the costal vertical circulation and give its characteristics compared to Stokes drift.
Institute of Scientific and Technical Information of China (English)
SUN Xue-ming; ZHANG Hui-jian; ZUO Meng; GU Wan-yi; XU Da-xiong
2006-01-01
Dense wavelength division multiplexing (DWDM) system is the ultimate selection as an optical communication system because of its high speeds and capacities.However,the fiber nonlinear effects and polarization mode dispersion severely limit the performance of the system when signal propagates at 40 Gbit/s in a single channel.The coupled nonlinear Schr(o)dinger equations of a single channel in DWDM,which are all considered factors of group velocity dispersion (GVD),self phase modulation (SPM),cross phase modulation (XPM),four wave mixing (FWM) and polarization mode dispersion (PMD),are derived,while their number results are obtained with extended split-step Fourier method.Finally,to analyze the impacts of the fiber nonlinear effects and PMD on the optical communication system,the simulated results of an 8x40 Gbit/s DWDM system are discussed under different conditions respectively.
Development of a Nonlinear Internal Wave Tactical Decision Aid
2016-06-07
of a Nonlinear Internal Wave Tactical Decision Aid 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER...Development of a Nonlinear Internal Wave Tactical Decision Aid Christopher R. Jackson Global Ocean Associates 6220 Jean Louise Way Alexandria...www.internalwaveatlas.com LONG-TERM GOALS The long term goal of the project is to develop a prediction methodology for the occurrence of nonlinear
Study of nonlinear waves in astrophysical quantum plasmas
Energy Technology Data Exchange (ETDEWEB)
Hossen, M.R.; Mamun, A.A., E-mail: rasel.plasma@gmail.com [Department of Physics, Jahangirnagar University, Savar, Dhaka (Bangladesh)
2015-10-01
The nonlinear propagation of the electron acoustic solitary waves (EASWs) in an unmagnetized, collisionless degenerate quantum plasma system has been investigated theoretically. Our considered model consisting of two distinct groups of electrons (one of inertial non-relativistic cold electrons and other of inertialess ultrarelativistic hot electrons) and positively charged static ions. The Korteweg-de Vries (K-dV) equation has been derived by employing the reductive perturbation method and numerically examined to identify the basic features (speed, amplitude, width, etc.) of EASWs. It is shown that only rarefactive solitary waves can propagate in such a quantum plasma system. It is found that the effect of degenerate pressure and number density of hot and cold electron fluids, and positively charged static ions, significantly modify the basic features of EASWs. It is also noted that the inertial cold electron fluid is the source of dispersion for EA waves and is responsible for the formation of solitary structures. The applications of this investigation in astrophysical compact objects (viz. non-rotating white dwarfs, neutron stars, etc.) are briefly discussed. (author)
Mathematical modelling of generation and forward propagation of dispersive waves
Lie She Liam, L.S.L.
2013-01-01
This dissertation concerns the mathematical theory of forward propagation and generation of dispersive waves. We derive the AB2-equation which describes forward traveling waves in two horizontal dimension. It is the generalization of the Kadomtsev-Petviashvilli (KP) equation. The derivation is based
Experimental investigation of two oil dispersion pathways by breaking waves
Li, Cheng; Katz, Joseph
2014-11-01
This experimental study focuses on generation and size distribution of airborne and subsurface oil droplets as breaking surface waves interact with a crude oil slick (MC252 surrogate). Experiments in a specialized wave tank investigate the effects of wave height and wave properties (e.g. spilling vs. plunging), as well as drastically reducing the oil-water interfacial tension by orders of magnitude by introducing dispersant (Coexist 9500-A). This dispersant is applied at varying dispersant-to-oil ratios either by premixing or surface spraying, the latter consistent with typical application. The data include high-speed visualizations of processes affecting the entrainment of subsurface oil and bubbles as well as airborne aerosols. High-speed digital holographic cinematography is employed to track the droplet trajectories, and quantify the droplet size distributions above and below the surface. Introduction of dispersants drastically reduces the size of subsurface droplets to micron and even submicron levels. Ahead of the wave, the 25 μm (our present resolution limit) to 2 mm airborne droplet trajectories are aligned with the wave direction. Behind the wave, these droplets reverse their direction, presumably due to the airflow above the wave. Supported by Gulf of Mexico Research Initiative (GoMRI).
Distribution of the nonlinear random ocean wave period
Institute of Scientific and Technical Information of China (English)
HOU Yijun; LI Mingjie; SONG Guiting; SI Guangcheng; QI Peng; HU Po
2009-01-01
Because of the intrinsic difficulty in determining distributions for wave periods, previous studies on wave period distribution models have not taken nonlinearity into account and have not performed well in terms of describing and statistically analyzing the probability density distribution of ocean waves. In this study, a statistical model of random waves is developed using Stokes wave theory of water wave dynamics. In addition, a new nonlinear probability distribution function for the wave period is presented with the parameters of spectral density width and nonlinear wave steepness, which is more reasonable as a physical mechanism. The magnitude of wave steepness determines the intensity of the nonlinear effect, while the spectral width only changes the energy distribution. The wave steepness is found to be an important parameter in terms of not only dynamics but also statistics. The value of wave steepness reflects the degree that the wave period distribution skews from the Cauchy distribution, and it also describes the variation in the distribution function, which resembles that of the wave surface elevation distribution and wave height distribution. We found that the distribution curves skew leftward and upward as the wave steepness increases. The wave period observations for the SZFII-1 buoy, made off the coast of Weihai (37°27.6′ N, 122°15.1′ E), China, are used to verify the new distribution. The coefficient of the correlation between the new distribution and the buoy data at different spectral widths (υ=0.3-0.5) is within the range of 0.968 6 to 0.991 7. In addition, the Longuet-Higgins (1975) and Sun (1988) distributions and the new distribution presented in this work are compared. The validations and comparisons indicate that the new nonlinear probability density distribution fits the buoy measurements better than the Longuet-Higgins and Sun distributions do. We believe that adoption of the new wave period distribution would improve traditional
Analysis of efficient preconditioned defect correction methods for nonlinear water waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter
2014-01-01
prediction of free-surface wave transformation and accurate wave kinematics in both deep and shallow waters in large marine areas or for predicting the outcome of experiments in large numerical wave tanks. We revisit the classical governing equations are fully nonlinear and dispersive potential flow......Robust computational procedures for the solution of non-hydrostatic, free surface, irrotational and inviscid free-surface water waves in three space dimensions can be based on iterative preconditioned defect correction (PDC) methods. Such methods can be made efficient and scalable to enable...... models. Our study is particularly relevant for fast and efficient simulation of non-breaking fully nonlinear water waves over varying bottom topography that may be limited by computational resources or requirements. To gain insight into algorithmic properties and proper choices of discretization...
Energy Technology Data Exchange (ETDEWEB)
Chabchoub, A., E-mail: achabchoub@swin.edu.au [Centre for Ocean Engineering Science and Technology, Swinburne University of Technology, Hawthorn, Victoria 3122 (Australia); Kibler, B.; Finot, C.; Millot, G. [Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 6303 CNRS, Université de Bourgogne, 21078 Dijon (France); Onorato, M. [Dipartimento di Fisica, Università degli Studi di Torino, Torino 10125 (Italy); Istituto Nazionale di Fisica Nucleare, INFN, Sezione di Torino, Torino 10125 (Italy); Dudley, J.M. [Institut FEMTO-ST, UMR 6174 CNRS- Université de Franche-Comté, 25030 Besançon (France); Babanin, A.V. [Centre for Ocean Engineering Science and Technology, Swinburne University of Technology, Hawthorn, Victoria 3122 (Australia)
2015-10-15
The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose–Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin–Feir index, i.e. a nondimensional parameter related to the probability of formation of rogue waves in incoherent wave trains.
Nonlinear evolution of the modulational instability of whistler waves
DEFF Research Database (Denmark)
Karpman, V.I.; Hansen, F.R.; Huld, T.
1990-01-01
The nonlinear evolution of the modulational instability of whistler waves coupled to fast magnetosonic waves is investigated in two spatial dimensions by numerical simulations. The long time evolution of the modulational instability shows a quasirecurrent behavior with a slow spreading...... of the energy, originally confined to the lowest wave numbers, to larger and larger wave numbers resulting in an apparently chaotic or random wave field. © 1990 The American Physical Society...
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.
Nonlinear physics of shear Alfvén waves
Energy Technology Data Exchange (ETDEWEB)
Zonca, Fulvio [Associazione EURATOM-ENEA sulla Fusione, C.P. 65-00044 Frascati, Italy and Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 31007 (China); Chen, Liu [Institute for Fusion Theory and Simulation, Zhejiang University, Hangzhou 31007, P.R.C. and Department of Physics and Astronomy, University of California, Irvine, CA 92697 (United States)
2014-02-12
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.
Numerical calculation of dispersion relation for linear internal waves
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
With the horizontal Coriolis terms included in motion equations and the influence of compressibility of seawater on Brunt-V(a)is(a)l(a) frequency considered, a numerical method of calculating the dispersion relation for linear internal waves, which is an improvement of Cai and Gan (1995), and hence Fliegel and Hunkins (1975), had been set up. For different models (Pacific model, Atlantic model and Arctic model), simulations using the three different methods were compared and the following conclusions were reached: (1) the influence of horizontal Coriolis terms on dispersion relation cannot be neglected and is connected with the direction of the wave celerity, the latitude, and the modes of the wave;(2) the effect of compressibility of seawater in stratification is not an important factor for the dispersion relation of linear internal wave, at least for those three models. With the improved method, the wavefunction curves for the Pacific model had also been built.
SPHERICAL NONLINEAR PULSES FOR THE SOLUTIONS OF NONLINEAR WAVE EQUATIONS Ⅱ, NONLINEAR CAUSTIC
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
This article discusses spherical pulse like solutions of the system of semilinear wave equations with the pulses focusing at a point and emerging outgoing in three space variables. In small initial data case, it shows that the nonlinearities have a strong effect at the focal point. Scattering operator is introduced to describe the caustic crossing. With the aid of the L∞ norms, it analyzes the relative errors in approximate solutions.
Weight loss and P wave dispersion: a preliminary study.
Falchi, Anna Giulia; Grecchi, Ilaria; Muggia, Chiara; Tinelli, Carmine
2014-01-01
The aim of this study is to investigate if therapeutic weight loss reduces P wave dispersion. 20 obese patients (10 males and 10 females), part of a randomized clinical trial, were examined over a 6 month period. They were treated with a diet, aiming at 5% weight loss at the 6th month. After physical examination, they underwent laboratory tests, bioelectrical impedance analysis and a electrocardiogram (ECG). ECGs were transferred to a personal computer via a scanner and then magnified 400 times. We examined at baseline and at the 6th month, maximum and minimum P-wave duration, P-wave dispersion and heart rate. Comparing responders (patients who lost 5% of weight at t6) and not responders (who lost less than 5%), responders showed a significant reduction of P wave dispersion value (-0.38 [SD: 0.35] mm equal to -32.3 [SD: 11.3] % p=0.00001). All responders present a reduction of P wave dispersion, while for not-responders this is no longer evident. Finally, a good degree of correlation (r=0.54) between P wave dispersion difference and the decrease of weight was noticed. Females have a better response in P dispersion reduction strictly connected with their weight loss with a good correlation, (r=0.7, p=0.002), versus a moderate correlation evidenced in males (r=0.5, p=0.011). P wave duration and dispersion are significantly reduced in patients who lost more than 5% of weight and this decrease is highly related to the extent of weight loss. Copyright © 2014 Asian Oceanian Association for the Study of Obesity. Published by Elsevier Ltd. All rights reserved.
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
Four-wave mixing stability in hybrid photonic crystal fibers with two zero-dispersion wavelengths.
Sévigny, Benoit; Vanvincq, Olivier; Valentin, Constance; Chen, Na; Quiquempois, Yves; Bouwmans, Géraud
2013-12-16
The four-wave mixing process in optical fibers is generally sensitive to dispersion uniformity along the fiber length. However, some specific phase matching conditions show increased robustness to longitudinal fluctuations in fiber dimensions, which affect the dispersion, even for signal and idler wavelengths far from the pump. In this paper, we present the method by which this point is found, how the fiber design characteristics impact on the stable point and demonstrate the stability through propagation simulations using the non-linear Schrödinger equation.
Nonlinear ultrasound wave propagation in thermoviscous fluids
DEFF Research Database (Denmark)
Sørensen, Mads Peter
coupled nonlinear partial differential equations, which resembles those of optical chi-2 materials. We think this result makes a remarkable link between nonlinear acoustics and nonlinear optics. Finally our analysis reveal an exact kink solution to the nonlinear acoustic problem. This kink solution...
Nonlinear numerical simulation on extreme-wave kinematics
Institute of Scientific and Technical Information of China (English)
NING Dezhi; TENG Bin; LIU Shuxue
2009-01-01
A fully nonlinear numerical model based on a time-domain higher-order boundary element method (HOBEM) is founded to simulate the kinematics of extreme waves. In the model, the fully nonlinear free surface boundary conditions are satisfied and a semi-mixed Euler-Lagrange method is used to track free surface; a fourth-order Runga-Kutta technique is "adopted to refresh the wave elevation and velocity potential on the free surface at each time step; an image Green function is used in the numerical wave tank so that the integrations on the lateral surfaces and bottom are excluded. The extreme waves are generated by the method of wave focusing. The physical experiments are carried out in a wave flume. On the horizontal velocity of the measured point, numerical solutions agree well with experimental results. The characteristics of the nonlinear extreme-wave kinematics and the velocity distribution are studied here.
Othman, N.; Shah, N. S. M.; Tay, K. G.; Pakarzadeh, H.; Cholan, N. A.; Talib, R.
2017-09-01
The highly-nonlinear fiber is the ideal gain medium for many applications particularly because its dispersion can be easily engineered. However, the modification of the fiber dispersion will affect the higher-order dispersion coefficients. Hence, this paper investigates the effect of highly-nonlinear dispersion-shifted fiber dispersion profile on the higher-order dispersion coefficients which are the fourth-order and sixth-order dispersion coefficients. The dispersion profile was modified by varying the slope at zero-dispersion wavelength. The fourth-order dispersion coefficient exhibits changes from positive to negative value as the slope at zero-dispersion wavelength is getting higher. Meanwhile, sixth-order dispersion coefficient remains with the positive value even though it shows the reduction as the slope is increased, however it will eventually become negative when the dispersion is high enough. In short, the values of both fourth-order and sixth-order dispersion coefficients at zero-dispersion wavelength decrease when the slope increases.
Hasan, Md. Rabiul; Anower, Md. Shamim; Hasan, Md. Imran
2016-05-01
A simple hexagonal photonic crystal fiber is proposed to simultaneously achieve ultrahigh birefringence, large nonlinear coefficient, and two zero dispersion wavelengths (ZDWs). The finite element method with circular perfectly matched layer boundary condition is used to simulate the designed structure. Simulation results show that it is possible to achieve two closely lying ZDWs of 1.08 and 1.29 μm for x-polarization with 0.88 and 1.20 μm for y-polarization modes, respectively. In addition, an ultrahigh birefringence of 3.15×10-2 and a high nonlinear coefficient of 58 W-1 km-1 are also obtained at the excitation wavelength of 1.55 μm. The proposed fiber can have important applications in supercontinuum generation, parametric amplification, four-wave mixing, and optical sensors design.
The Peridic Wave Solutions for Two Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
ZHANG Jin-Liang; WANG Ming-Liang; CHENG Dong-Ming; FANG Zong-De
2003-01-01
By using the F-expansion method proposed recently, the periodic wave solutions expressed by Jacobielliptic functions for two nonlinear evolution equations are derived. In the limit cases, the solitary wave solutions andthe other type of traveling wave solutions for the system are obtained.
Propagation of Nonlinear Waves in Waveguides and Application to Nondestructive Stress Measurement
Nucera, Claudio
Propagation of nonlinear waves in waveguides is a field that has received an ever increasing interest in the last few decades. Nonlinear guided waves are excellent candidates for interrogating long waveguide like structures because they combine high sensitivity to structural conditions, typical of nonlinear parameters, with large inspection ranges, characteristic of wave propagation in bounded media. The primary topic of this dissertation is the analysis of ultrasonic waves, including ultrasonic guided waves, propagating in their nonlinear regime and their application to structural health monitoring problems, particularly the measurement of thermal stress in Continuous Welded Rail (CWR). Following an overview of basic physical principles generating nonlinearities in ultrasonic wave propagation, the case of higher-harmonic generation in multi-mode and dispersive guided waves is examined in more detail. A numerical framework is developed in order to predict favorable higher-order generation conditions (i.e. specific guided modes and frequencies) for waveguides of arbitrary cross-sections. This model is applied to various benchmark cases of complex structures. The nonlinear wave propagation model is then applied to the case of a constrained railroad track (CWR) subjected to thermal variations. This study is a direct response to the key need within the railroad transportation community to develop a technique able to measure thermal stresses in CWR, or determine the rail temperature corresponding to a null thermal stress (Neutral Temperature -- NT). The numerical simulation phase concludes with a numerical study performed using ABAQUS commercial finite element package. These analyses were crucial in predicting the evolution of the nonlinear parameter beta with thermal stress level acting in the rail. A novel physical model, based on interatomic potential, was developed to explain the origin of nonlinear wave propagation under constrained thermal expansion. In fact
Experimental characterization of nonlinear processes of whistler branch waves
Tejero, E. M.; Crabtree, C.; Blackwell, D. D.; Amatucci, W. E.; Ganguli, G.; Rudakov, L.
2016-05-01
Experiments in the Space Physics Simulation Chamber at the Naval Research Laboratory isolated and characterized important nonlinear wave-wave and wave-particle interactions that can occur in the Earth's Van Allen radiation belts by launching predominantly electrostatic waves in the intermediate frequency range with wave normal angle greater than 85 ° and measuring the nonlinearly generated electromagnetic scattered waves. The scattered waves have a perpendicular wavelength that is nearly an order of magnitude larger than that of the pump wave. Calculations of scattering efficiency from experimental measurements demonstrate that the scattering efficiency is inversely proportional to the damping rate and trends towards unity as the damping rate approaches zero. Signatures of both wave-wave and wave-particle scatterings are also observed in the triggered emission process in which a launched wave resonant with a counter-propagating electron beam generates a large amplitude chirped whistler wave. The possibility of nonlinear scattering or three wave decay as a saturation mechanism for the triggered emission is suggested. The laboratory experiment has inspired the search for scattering signatures in the in situ data of chorus emission in the radiation belts.
Dispersion Relation of Linear Waves in Quantum Magnetoplasmas
Zhu, Jun
2016-07-01
The quantum magnetohydrodynamic (QMHD) model is applied in investigating the propagation of linear waves in quantum magnetoplasmas. Using the QMHD model, the dispersion equation for quantum magnetoplasmas and the dispersion relations of linear waves are deduced. Results show that quantum effects affect the propagation of electron plasma waves and extraordinary waves (X waves). When we select the plasma parameters of the laser-based plasma compression (LBPC) schemes for calculation, the quantum correction cannot be neglected. Meanwhile, the corrections produced by the Fermi degeneracy pressure and Bohm potential are compared under different plasma parameter conditions. supported by National Natural Science Foundation of China (No. 11447125) and the Research Training Program for Undergraduates of Shanxi University of China (Nos. 2014012167, 2015013182)
Nonlinear time reversal of classical waves: experiment and model.
Frazier, Matthew; Taddese, Biniyam; Xiao, Bo; Antonsen, Thomas; Ott, Edward; Anlage, Steven M
2013-12-01
We consider time reversal of electromagnetic waves in a closed, wave-chaotic system containing a discrete, passive, harmonic-generating nonlinearity. An experimental system is constructed as a time-reversal mirror, in which excitations generated by the nonlinearity are gathered, time-reversed, transmitted, and directed exclusively to the location of the nonlinearity. Here we show that such nonlinear objects can be purely passive (as opposed to the active nonlinearities used in previous work), and we develop a higher data rate exclusive communication system based on nonlinear time reversal. A model of the experimental system is developed, using a star-graph network of transmission lines, with one of the lines terminated by a model diode. The model simulates time reversal of linear and nonlinear signals, demonstrates features seen in the experimental system, and supports our interpretation of the experimental results.
Nonlinear evolution of oblique waves on compressible shear layers
Goldstein, M. E.; Leib, S. J.
1989-01-01
The effects of critical-layer nonlinearity on spatially growing oblique instability waves on compressible shear layers between two parallel streams are considered. The analysis shows that mean temperature nonuniformities cause nonlinearity to occur at much smaller amplitudes than it does when the flow is isothermal. The nonlinear instability wave growth rate effects are described by an integrodifferential equation which bears some resemblance to the Landau equation, in that it involves a cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. Inviscid solutions always end in a singularity at a finite downstream distance, but viscosity can eliminate this singularity for certain parameter ranges.
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
THE CAUCHY PROBLEM FOR SOME DISPERSIVE WAVE EQUATIONS
Institute of Scientific and Technical Information of China (English)
Zhang Wenling
2004-01-01
In this paper, we consider the Cauchy problem for some dispersive equations. By means of nonlinear estimate in Besov spaces and fixed point theory, we prove the global well-posedness of the above problem. What's more, we improve the scattering result obtained in [1].
Rapid energization of radiation belt electrons by nonlinear wave trapping
Directory of Open Access Journals (Sweden)
Y. Katoh
2008-11-01
Full Text Available We show that nonlinear wave trapping plays a significant role in both the generation of whistler-mode chorus emissions and the acceleration of radiation belt electrons to relativistic energies. We have performed particle simulations that successfully reproduce the generation of chorus emissions with rising tones. During this generation process we find that a fraction of resonant electrons are energized very efficiently by special forms of nonlinear wave trapping called relativistic turning acceleration (RTA and ultra-relativistic acceleration (URA. Particle energization by nonlinear wave trapping is a universal acceleration mechanism that can be effective in space and cosmic plasmas that contain a magnetic mirror geometry.
Nonlinear time reversal in a wave chaotic system.
Frazier, Matthew; Taddese, Biniyam; Antonsen, Thomas; Anlage, Steven M
2013-02-01
Exploiting the time-reversal invariance and reciprocal properties of the lossless wave equation enables elegantly simple solutions to complex wave-scattering problems and is embodied in the time-reversal mirror. Here we demonstrate the implementation of an electromagnetic time-reversal mirror in a wave chaotic system containing a discrete nonlinearity. We demonstrate that the time-reversed nonlinear excitations reconstruct exclusively upon the source of the nonlinearity. As an example of its utility, we demonstrate a new form of secure communication and point out other applications.
Wave instabilities in the presence of non vanishing background in nonlinear Schrödinger systems.
Trillo, S; Gongora, J S Totero; Fratalocchi, A
2014-12-03
We investigate wave collapse ruled by the generalized nonlinear Schrödinger (NLS) equation in 1+1 dimensions, for localized excitations with non-zero background, establishing through virial identities a new criterion for blow-up. When collapse is arrested, a semiclassical approach allows us to show that the system can favor the formation of dispersive shock waves. The general findings are illustrated with a model of interest to both classical and quantum physics (cubic-quintic NLS equation), demonstrating a radically novel scenario of instability, where solitons identify a marginal condition between blow-up and occurrence of shock waves, triggered by arbitrarily small mass perturbations of different sign.
Wave instabilities in the presence of non vanishing background in nonlinear Schrödinger systems
Trillo, S.
2014-12-03
We investigate wave collapse ruled by the generalized nonlinear Schrödinger (NLS) equation in 1+1 dimensions, for localized excitations with non-zero background, establishing through virial identities a new criterion for blow-up. When collapse is arrested, a semiclassical approach allows us to show that the system can favor the formation of dispersive shock waves. The general findings are illustrated with a model of interest to both classical and quantum physics (cubic-quintic NLS equation), demonstrating a radically novel scenario of instability, where solitons identify a marginal condition between blow-up and occurrence of shock waves, triggered by arbitrarily small mass perturbations of different sign.
Wave Dispersion and Attenuation in Viscoelastic Split Hopkinson Pressure Bar
Directory of Open Access Journals (Sweden)
Z.Q. Cheng
1998-01-01
Full Text Available A viscoelastic split Hopkinson pressure bar intended for testing soft materials with low acoustic impedance is studied. Using one-dimensional linear viscoelastic wave propagation theory, the basic equations have been established for the determination of the stress—strain—strain rate relationship for the tested material. A method, based on the spectral analysis of wave motion and using measured wave signals along the split Hopkinson pressure bar, is developed for the correction of the dispersion and attenuation of viscoelastic waves. Computational simulations are performed to show the feasibility of the method.
Dispersion Characteristics of a New Slow-Wave Structure
Institute of Scientific and Technical Information of China (English)
WU Jian-Qiang
2004-01-01
@@ The microwave excitation in a new slow-wave structure, i.e. the plasma-filled coaxial cylindrical dielectric-loaded cylindrical waveguide, is investigated by using the self-consistent linear field theory in considering the collision effect between electrons and ions in the plasma via the collision frequency term. The determinant dispersion equation of the beam-wave interaction with a complex value of angular frequency is derived. The effects of plasma collision frequency on the output frequency and the wave growth rate of the beam-wave interaction are calculated and discussed.
Effects of Schwarzschild Geometry on Isothermal Plasma Wave Dispersion
Sharif, M
2007-01-01
The behavior of isothermal plasma waves has been analyzed near the Schwarzschild horizon. We consider a non-rotating background with non-magnetized and magnetized plasmas. The general relativistic magnetohydrodynamical equations for the Schwarzschild planar analogue spacetime with an isothermal state of the plasma are formulated. The perturbed form of these equations is linearized and Fourier analyzed by introducing simple harmonic waves. The determinant of these equations in each case leads to a complex dispersion relation, which gives complex values of the wave number. This has been used to discuss the nature of the waves and their characteristics near the horizon.
Luo, Ting
As optical communications approach more data bandwidth, longer transmission distance, and more reconfigurability, dispersion, nonlinearity and polarization-dependent effects are becoming key issues for future all-optical fiber optic systems and networks. For ≥10 Gbit/s optical fiber transmission systems, it is critical that chromatic dispersion and polarization-mode-dispersion be well monitored and compensated using some type of dispersion monitoring and compensation. On the other hand, dispersive and nonlinear effects in optical fiber systems can also be beneficial and have applications on pulse management, all-optical signal processing and network function, which will be essential for high bite-rate optical networks and replacing the expensive optical-electrical-optical (O/E/O) conversion. In this Ph.D. dissertation, we present a detailed research on dispersion, nonlinearity, and polarization-dependent effects in high-speed optical communication systems. We have demonstrated: (i) A dynamic channel-spacing tunable multi-wavelength Erbium-doped fiber laser; (ii) Chromatic-dispersion-insensitive PMD monitoring by tracking the radio-frequency extracted from the vestigial-sideband; (iii) A method for simultaneous chromatic and polarization-mode dispersions monitoring by adding a frequency-shifted carrier; (iv) Polarization-insensitive optical parametric amplification by depolarizing the pump; (v) All optical chromatic dispersion monitoring potential for ultra-high speed (>40 Gbit/s) optical systems using cross-phase modulation in a highly nonlinear fiber; (vi) A novel fiber-based autocorrelator using polarimetric four-wave mixing effect and a tunable differential-group-delay element; (vii) A simple all-fiber-based autocorrelator by measuring the degree-of-polarization; and (viii) Reduction of pattern dependent data distortion in a stimulated Brillouin scattering based slow light element. These techniques will play key roles in future high-speed dynamic WDM optical
Solitary Wave and Non-traveling Wave Solutions to Two Nonlinear Evolution Equations
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
By applying the extended homogeneous balance method, we find some new explicit solutions to two nonlinear evolution equations, which include n-resonance plane solitary wave and non-traveling wave solutions.
A fractional calculus model of anomalous dispersion of acoustic waves.
Wharmby, Andrew W
2016-09-01
An empirical formula based on viscoelastic analysis techniques that employs concepts from the fractional calculus that was used to model the dielectric behavior of materials exposed to oscillating electromagnetic fields in the radiofrequency, terahertz, and infrared bands. This work adapts and applies the formula to model viscoelastic behavior of materials that show an apparent increase of phase velocity of vibration with an increase in frequency, otherwise known as anomalous dispersion. A fractional order wave equation is derived through the application of the classic elastic-viscoelastic correspondence principle whose analytical solution is used to describe absorption and dispersion of acoustic waves in the viscoelastic material displaying anomalous dispersion in a specific frequency range. A brief discussion and comparison of an alternative fractional order wave equation recently formulated is also included.
Sasanpour, Pezhman; Shahmansouri, Afsaneh; Rashidian, Bizhan
2010-11-01
Third order nonlinear effects and its enhancement in gold nanostructures has been numerically studied. Analysis method is based on computationally solving nonlinear Maxwell's equations, considering dispersion behavior of permittivity described by Drude model and third order nonlinear susceptibility. Simulation is done by method of nonlinear finite difference time domain method, in which nonlinear equations of electric field are solved by Newton-Raphshon method. As the main outcomes of third order nonlinear susceptibility, four wave mixing and third harmonic generation terms are produced around gold nanostructures. Results of analysis on different geometries and structures show that third order nonlinearity products are more enhanced in places where electric field enhancement is occurred due to surface plasmons. Results indicates that enhancement of nonlinearities is strongly occurred in structures whose interface is dielectric. According to analysis results, nonlinear effects are highly concentrated in the vicinity of nanostructures. Hence this approach can be used in applications where localized ultraviolet light is required.
Dispersion of nonresonant third-order nonlinearities in Silicon Carbide
De Leonardis, Francesco; Soref, Richard A.; Passaro, Vittorio M. N.
2017-01-01
In this paper we present a physical discussion of the indirect two-photon absorption (TPA) occuring in silicon carbide with either cubic or wurtzite structure. Phonon-electron interaction is analyzed by finding the phonon features involved in the process as depending upon the crystal symmetry. Consistent physical assumptions about the phonon-electron scattering mechanisms are proposed in order to give a mathematical formulation to predict the wavelength dispersion of TPA and the Kerr nonlinear refractive index n2. The TPA spectrum is investigated including the effects of band nonparabolicity and the influence of the continuum exciton. Moreover, a parametric analysis is presented in order to fit the experimental measurements. Finally, we have estimated the n2 in a large wavelength range spanning the visible to the mid-IR region. PMID:28098223
Dispersion of nonresonant third-order nonlinearities in Silicon Carbide
de Leonardis, Francesco; Soref, Richard A.; Passaro, Vittorio M. N.
2017-01-01
In this paper we present a physical discussion of the indirect two-photon absorption (TPA) occuring in silicon carbide with either cubic or wurtzite structure. Phonon-electron interaction is analyzed by finding the phonon features involved in the process as depending upon the crystal symmetry. Consistent physical assumptions about the phonon-electron scattering mechanisms are proposed in order to give a mathematical formulation to predict the wavelength dispersion of TPA and the Kerr nonlinear refractive index n2. The TPA spectrum is investigated including the effects of band nonparabolicity and the influence of the continuum exciton. Moreover, a parametric analysis is presented in order to fit the experimental measurements. Finally, we have estimated the n2 in a large wavelength range spanning the visible to the mid-IR region.
Particle Scattering off of Right-handed Dispersive Waves
Schreiner, C.; Kilian, P.; Spanier, F.
2017-01-01
Resonant scattering of fast particles off low frequency plasma waves is a major process determining transport characteristics of energetic particles in the heliosphere and contributing to their acceleration. Usually, only Alfvén waves are considered for this process, although dispersive waves are also present throughout the heliosphere. We investigate resonant interaction of energetic electrons with dispersive, right-handed waves. For the interaction of particles and a single wave a variable transformation into the rest frame of the wave can be performed. Here, well-established analytic models derived in the framework of magnetostatic quasi-linear theory can be used as a reference to validate simulation results. However, this approach fails as soon as several dispersive waves are involved. Based on analytic solutions modeling the scattering amplitude in the magnetostatic limit, we present an approach to modify these equations for use in the plasma frame. Thereby we aim at a description of particle scattering in the presence of several waves. A particle-in-cell code is employed to study wave–particle scattering on a micro-physically correct level and to test the modified model equations. We investigate the interactions of electrons at different energies (from 1 keV to 1 MeV) and right-handed waves with various amplitudes. Differences between model and simulation arise in the case of high amplitudes or several waves. Analyzing the trajectories of single particles we find no microscopic diffusion in the case of a single plasma wave, although a broadening of the particle distribution can be observed.
Dispersion and nonlinear effects in OFDM-RoF system
Alhasson, Bader H.; Bloul, Albe M.; Matin, M.
2010-08-01
The radio-over-fiber (RoF) network has been a proven technology to be the best candidate for the wireless-access technology, and the orthogonal frequency division multiplexing (OFDM) technique has been established as the core technology in the physical layer of next generation wireless communication system, as a result OFDM-RoF has drawn attentions worldwide and raised many new research topics recently. At the present time, the trend of information industry is towards mobile, wireless, digital and broadband. The next generation network (NGN) has motivated researchers to study higher-speed wider-band multimedia communication to transmit (voice, data, and all sorts of media such as video) at a higher speed. The NGN would offer services that would necessitate broadband networks with bandwidth higher than 2Mbit/s per radio channel. Many new services emerged, such as Internet Protocol TV (IPTV), High Definition TV (HDTV), mobile multimedia and video stream media. Both speed and capacity have been the key objectives in transmission. In the meantime, the demand for transmission bandwidth increased at a very quick pace. The coming of 4G and 5G era will provide faster data transmission and higher bit rate and bandwidth. Taking advantages of both optical communication and wireless communication, OFDM Radio over Fiber (OFDM-RoF) system is characterized by its high speed, large capacity and high spectral efficiency. However, up to the present there are some problems to be solved, such as dispersion and nonlinearity effects. In this paper we will study the dispersion and nonlinearity effects and their elimination in OFDM-radio-over-fiber system.
Nonlinear plasmonic dispersion and coupling analysis in the symmetric graphene sheets waveguide
Jiang, Xiangqian; Yuan, Haiming; Sun, Xiudong
2016-12-01
We study the nonlinear dispersion and coupling properties of the graphene-bounded dielectric slab waveguide at near-THz/THz frequency range, and then reveal the mechanism of symmetry breaking in nonlinear graphene waveguide. We analyze the influence of field intensity and chemical potential on dispersion relation, and find that the nonlinearity of graphene affects strongly the dispersion relation. As the chemical potential decreases, the dispersion properties change significantly. Antisymmetric and asymmetric branches disappear and only symmetric one remains. A nonlinear coupled mode theory is established to describe the dispersion relations and its variation, which agrees with the numerical results well. Using the nonlinear couple model we reveal the reason of occurrence of asymmetric mode in the nonlinear waveguide.
Controlling near shore nonlinear surging waves through bottom boundary conditions
Mukherjee, Abhik; Kundu, Anjan
2016-01-01
Instead of taking the usual passive view for warning of near shore surging waves including extreme waves like tsunamis, we aim to study the possibility of intervening and controlling nonlinear surface waves through the feedback boundary effect at the bottom. It has been shown through analytic result that the controlled leakage at the bottom may regulate the surface solitary wave amplitude opposing the hazardous variable depth effect. The theoretical results are applied to a real coastal bathymetry in India.
Nonlinear Internal Waves in the South China Sea: Their generation and transformation
Farmer, D. M.; Qiang, L.; Park, J.
2008-12-01
Observations of thermocline motions using inverted echo-sounders in the South China Sea provide evidence of the generation and evolution of an internal tide which can ultimately steepen to form nonlinear internal waves. The sill topography is complex and the observations are primarily sensitive to the first internal mode, requiring care in the interpretation of measurements close to the source. However, a two dimensional analysis illustrates the sensitivity of the response to tidal forcing over the Luzon sill between Taiwan and the Philippines, which exhibits a strong diurnal inequality leading to great variability in the far-field response. Negative interfacial slopes in the internal tide steepen with time, their subsequent evolution depending on the competing effects of nonlinearity, non-hydrostatic and rotational dispersion. Large initial interfacial slopes steepen to form a nonlinear wave train. For weak initial slopes, rotational dispersion inhibits steepening and formation of waves of permanent form. Analysis of our observations with simplified models support a dynamical explanation of internal wave development in terms of the stratification, tidal forcing, nonlinearity, nonhydrostatic and rotational effects.
Periodic folded waves for a (2+1)-dimensional modified dispersive water wave equation
Institute of Scientific and Technical Information of China (English)
Huang Wen-Hua
2009-01-01
A general solution,including three arbitrary functions,is obtained for a (2+1)-dimensional modified dispersive water-wave (MDWW) equation by means of the WTC truncation method.Introducing proper multiple valued functions and Jacobi elliptic functions in the seed solution,special types of periodic folded waves are derived.In the long wave limit these periodic folded wave patterns may degenerate into single localized folded solitary wave excitations.The interactions of the periodic folded waves and the degenerated single folded solitary waves axe investigated graphically and found to be completely elastic.
Nonlinear Waves in an Inhomogeneous Fluid Filled Elastic Tube
Institute of Scientific and Technical Information of China (English)
DUAN Wen-Shan
2004-01-01
In a thin-walled, homogeneous, straight, long, circular, and incompressible fluid filled elastic tube, small but finite long wavelength nonlinear waves can be describe by a KdV (Korteweg de Vries) equation, while the carrier wave modulations are described by a nonlinear Schrodinger equation (NLSE). However if the elastic tube is slowly inhomogeneous, then it is found, in this paper, that the carrier wave modulations are described by an NLSE-like equation. There are soliton-like solutions for them, but the stability and instability regions for this soliton-like waves will change,depending on what kind of inhomogeneity the tube has.
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.
Variational principle for nonlinear wave propagation in dissipative systems.
Dierckx, Hans; Verschelde, Henri
2016-02-01
The dynamics of many natural systems is dominated by nonlinear waves propagating through the medium. We show that in any extended system that supports nonlinear wave fronts with positive surface tension, the asymptotic wave-front dynamics can be formulated as a gradient system, even when the underlying evolution equations for the field variables cannot be written as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front and changes monotonically over time.
New multisoliton solutions of the （2＋1） —dimensional dispersive long wave equations
Institute of Scientific and Technical Information of China (English)
JiefangZHANG; PingHAN
2001-01-01
Using the extension homogeneous balance method,we have obtained a nonlinear transformation to simplify the (2+1) dimensional dispersive long wave equations into a linear partial differential equation,and found some new special types of the multisoliton solutions and exact solutions of the linear partial differential equation.
Dispersion properties of helical waves in radially inhomogeneous elastic media.
Syresin, D E; Zharnikov, T V; Tyutekin, V V
2012-06-01
In this paper, a method describing dispersion curve calculation for waves propagating in radially layered, inhomogeneous isotropic elastic waveguides is developed. Particular emphasis is placed on the helical waves with noninteger azimuthal wavenumbers, which can be potentially applied in such fields as nondestructive evaluation, acoustic tomography, etc., stipulating their practical importance. To solve the problem under consideration, the matrix Riccati equation is formulated for an impedance matrix. The use of the latter yields a simple form of the dispersion equation. Numerical computation of dispersion curves can encounter difficulties, which are due to potential singularities of the impedance matrix and the necessity to separate roots of the dispersion equation. These difficulties are overcome by employing the Cayley transform and invoking the parametric continuation method. The method developed by the authors is demonstrated by calculating dispersion diagrams in support of helical waves for several models of practical interest. Such computations for an inhomogeneous layer and its approximation by a set of homogeneous layers using a transfer matrix and Riccati equation methods revealed higher computational accuracy of the latter. Dispersion curves calculated for layers with different types of inhomogeneity demonstrated significant discrepancies at low frequencies.
P wave dispersion is prolonged in patients with Wilson's disease
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
AIM: To investigate the P wave dispersion as a noninvasive marker of intra-atrial conduction disturbances in patients with Wilson's disease. METHODS: We compared Wilson's disease patients (n=18) with age matched healthy subjects (n=15) as controls. The diagnosis was based on clinical symptoms, laboratory tests (ceruloplasmin, urinary and hepatic copper concentrations). P wave dispersion, a measurement of the heterogeneity of atrial depolarization, was measured as the difference between the duration of the longest and the shortest P-waves in 12 lead electrocardiography. RESULTS: All the patients were asymptomatic on cardiological examination and have sinusal rhythm in electrocardiography. Left ventricular and left atrial diameters, left ventricular ejection fraction and left ventricular mass index were similar in both groups. The Wilson's disease patients had a significantly higher P wave dispersion compared with the controls (44.7+5.8vs 25.7±2.5,P＜0.01＝. CONCLUSION: There was an increase in P wave dispersion in cardiologically asymptomatic Wilson's disease patients which probably represents an early stage of cardiac involvement.
Indian Academy of Sciences (India)
Aiyong Chen; Jibin Li; Chunhai Li; Yuanduo Zhang
2010-01-01
The bifurcation theory of dynamical systems is applied to an integrable non-linear wave equation. As a result, it is pointed out that the solitary waves of this equation evolve from bell-shaped solitary waves to W/M-shaped solitary waves when wave speed passes certain critical wave speed. Under different parameter conditions, all exact explicit parametric representations of solitary wave solutions are obtained.
GLOBAL ATTRACTOR FOR THE NONLINEAR STRAIN WAVES IN ELASTIC WAVEGUIDES
Institute of Scientific and Technical Information of China (English)
戴正德; 杜先云
2001-01-01
In this paper the authors consider the initial boundary value problems of the generalized nonlinear strain waves in elastic waveguides and prove the existence of global attractors and thefiniteness of the Hausdorff and the fractal dimensions of the attractors.
Nonlinear waves in the terrestrial quasi-parallel foreshock
Hnat, B; O'Connell, D; Nakariakov, V M; Rowlands, G
2016-01-01
We study the applicability of the derivative nonlinear Schr\\"{o}dinger (DNLS) equation, for the evolution of high frequency nonlinear waves, observed at the foreshock region of the terrestrial quasi-parallel bow shock. The use of a pseudo-potential is elucidated and, in particular, the importance of canonical representation in the correct interpretation of solutions in this formulation is discussed. Numerical solutions of the DNLS equation are then compared directly with the wave forms observed by Cluster spacecraft. Non harmonic slow variations are filtered out by applying the empirical mode decomposition. We find large amplitude nonlinear wave trains at frequencies above the proton cyclotron frequency, followed in time by nearly harmonic low amplitude fluctuations. The approximate phase speed of these nonlinear waves, indicated by the parameters of numerical solutions, is of the order of the local Alfv\\'{e}n speed.
The periodic wave solutions for two systems of nonlinear wave equations
Institute of Scientific and Technical Information of China (English)
王明亮; 王跃明; 张金良
2003-01-01
The periodic wave solutions for the Zakharov system of nonlinear wave equations and a long-short-wave interaction system are obtained by using the F-expansion method, which can be regarded as an overall generalization of Jacobi elliptic function expansion proposed recently. In the limit cases, the solitary wave solutions for the systems are also obtained.
Numerical method of studying nonlinear interactions between long waves and multiple short waves
Institute of Scientific and Technical Information of China (English)
Xie Tao; Kuang Hai-Lan; William Perrie; Zou Guang-Hui; Nan Cheng-Feng; He Chao; Shen Tao; Chen Wei
2009-01-01
Although the nonlinear interactions between a single short gravity wave and a long wave can be solved analytically,the solution is less tractable in more general cases involving multiple short waves.In this work we present a numerical method of studying nonlinear interactions between a long wave and multiple short harmonic waves in infinitely deep water.Specifically,this method is applied to the calculation of the temporal and spatial evolutions of the surface elevations in which a given long wave interacts with several short harmonic waves.Another important application of our method is to quantitatively analyse the nonlinear interactions between an arbitrary short wave train and another short wave train.From simulation results,we obtain that the mechanism for the nonlinear interactions between one short wave train and another short wave train(expressed as wave train 2)leads to the energy focusing of the other short wave train(expressed as wave train 31.This mechanism Occurs on wave components with a narrow frequency bandwidth,whose frequencies are near that of wave train 3.
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.
Curvature-Induced Asymmetric Spin-Wave Dispersion
Otálora, Jorge A.; Yan, Ming; Schultheiss, Helmut; Hertel, Riccardo; Kákay, Attila
2016-11-01
In magnonics, spin waves are conceived of as electron-charge-free information carriers. Their wave behavior has established them as the key elements to achieve low power consumption, fast operative rates, and good packaging in magnon-based computational technologies. Hence, knowing alternative ways that reveal certain properties of their undulatory motion is an important task. Here, we show using micromagnetic simulations and analytical calculations that spin-wave propagation in ferromagnetic nanotubes is fundamentally different than in thin films. The dispersion relation is asymmetric regarding the sign of the wave vector. It is a purely curvature-induced effect and its fundamental origin is identified to be the classical dipole-dipole interaction. The analytical expression of the dispersion relation has the same mathematical form as in thin films with the Dzyalonshiinsky-Moriya interaction. Therefore, this curvature-induced effect can be seen as a "dipole-induced Dzyalonshiinsky-Moriya-like" effect.
Mitsotakis, Dimitrios; Assylbekuly, Aydar; Zhakebaev, Dauren
2016-01-01
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.
Baba, Toshitaka; Takahashi, Narumi; Kaneda, Yoshiyuki; Ando, Kazuto; Matsuoka, Daisuke; Kato, Toshihiro
2015-12-01
Because of improvements in offshore tsunami observation technology, dispersion phenomena during tsunami propagation have often been observed in recent tsunamis, for example the 2004 Indian Ocean and 2011 Tohoku tsunamis. The dispersive propagation of tsunamis can be simulated by use of the Boussinesq model, but the model demands many computational resources. However, rapid progress has been made in parallel computing technology. In this study, we investigated a parallelized approach for dispersive tsunami wave modeling. Our new parallel software solves the nonlinear Boussinesq dispersive equations in spherical coordinates. A variable nested algorithm was used to increase spatial resolution in the target region. The software can also be used to predict tsunami inundation on land. We used the dispersive tsunami model to simulate the 2011 Tohoku earthquake on the Supercomputer K. Good agreement was apparent between the dispersive wave model results and the tsunami waveforms observed offshore. The finest bathymetric grid interval was 2/9 arcsec (approx. 5 m) along longitude and latitude lines. Use of this grid simulated tsunami soliton fission near the Sendai coast. Incorporating the three-dimensional shape of buildings and structures led to improved modeling of tsunami inundation.
Absorption of ultrasound waves during dynamic processes in disperse systems
Kol'tsova, I. S.; Khomutova, A. S.
2016-11-01
Measurements of ultrasound wave absorption are conducted at a frequency of 3 MHz in 3% suspensions of starch, gelatin, and lactose. It is shown that the dynamics of the additional ultrasound wave absorption coefficient in the suspensions carries information on the processes of swelling, dissolution, and the phase and structural periods occurring in the interaction of the disperse and dispersoid phases; it also reflects the influence of the temperature field on these processes.
Nonlinear electrostatic drift Kelvin-Helmholtz instability
Sharma, Avadhesh C.; Srivastava, Krishna M.
1993-01-01
Nonlinear analysis of electrostatic drift Kelvin-Helmholtz instability is performed. It is shown that the analysis leads to the propagation of the weakly nonlinear dispersive waves, and the nonlinear behavior is governed by the nonlinear Burger's equation.
Nonlinear traveling waves for the skeleton of the Madden-Julian oscillation
Chen, Shengqian
2015-01-01
The Madden-Julian Oscillation (MJO) is the dominant component of intraseasonal (30-90 days) variability in the tropical atmosphere. Here, traveling wave solutions are presented for the MJO skeleton model of Majda and Stechmann. The model is a system of nonlinear partial differential equations that describe the evolution of the tropical atmosphere on planetary (10,000-40,000 km) spatial scales. The nonlinear traveling waves come in four types, corresponding to the four types of linear wave solutions, one of which has the properties of the MJO. In the MJO traveling wave, the convective activity has a pulse-like shape, with a narrow region of enhanced convection and a wide region of suppressed convection. Furthermore, an amplitude-dependent dispersion relation is derived, and it shows that the nonlinear MJO has a lower frequency and slower propagation speed than the linear MJO. By taking the small-amplitude limit, an analytic formula is also derived for the dispersion relation of linear waves. To derive all of t...
Ganesh, R.; Gonella, S.
2017-02-01
The motive of this work is to understand the complex spatial characteristics of finite-amplitude elastic wave propagation in periodic structures and leverage the unique opportunities offered by nonlinearity to activate complementary functionalities and design adaptive spatial wave manipulators. The underlying assumption is that the magnitude of wave propagation is small with respect to the length scale of the structure under consideration, albeit large enough to elicit the effects of finite deformation. We demonstrate that the interplay of dispersion, nonlinearity and modal complexity involved in the generation and propagation of higher harmonics gives rise to secondary wave packets that feature multiple characteristics, one of which conforms to the dispersion relation of the corresponding linear structure. This provides an opportunity to engineer desired wave characteristics through a geometric and topological design of the unit cell, and results in the ability to activate complementary functionalities, typical of high frequency regimes, while operating at low frequencies of excitation - an effect seldom observed in linear periodic structures. The ability to design adaptive switches is demonstrated here using lattice configurations whose response is characterized by geometric and/or material nonlinearities.
NONLINEAR BOUNDARY STABILIZATION OF WAVE EQUATIONS WITH VARIABLE C OEFFICIENTS
Institute of Scientific and Technical Information of China (English)
冯绍继; 冯德兴
2003-01-01
The wave equation with variable coefficients with a nonlinear dissipative boundary feedbackis studied. By the Riemannian geometry method and the multiplier technique, it is shown thatthe closed loop system decays exponentially or asymptotically, and hence the relation betweenthe decay rate of the system energy and the nonlinearity behavior of the feedback function isestablished.
Non-linear wave packet dynamics of coherent states
Indian Academy of Sciences (India)
J Banerji
2001-02-01
We have compared the non-linear wave packet dynamics of coherent states of various symmetry groups and found that certain generic features of non-linear evolution are present in each case. Thus the initial coherent structures are quickly destroyed but are followed by Schrödinger cat formation and revival. We also report important differences in their evolution.
New travelling wave solutions for nonlinear stochastic evolution equations
Indian Academy of Sciences (India)
Hyunsoo Kim; Rathinasamy Sakthivel
2013-06-01
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 Broer–Kaup equation and stochastic coupled Korteweg–de Vries (KdV) equation. The study highlights the significant features of the method employed and its capability of handling nonlinear stochastic problems.
Lamb Wave Technique for Ultrasonic Nonlinear Characterization in Elastic Plates
Energy Technology Data Exchange (ETDEWEB)
Lee, Tae Hun; Kim, Chung Seok; Jhang, Kyung Young [Hanyang University, Seoul (Korea, Republic of)
2010-10-15
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
Nonlinear spin-wave excitations at low magnetic bias fields
Woltersdorf, Georg
We investigate experimentally and theoretically the nonlinear magnetization dynamics in magnetic films at low magnetic bias fields. Nonlinear magnetization dynamics is essential for the operation of numerous spintronic devices ranging from magnetic memory to spin torque microwave generators. Examples are microwave-assisted switching of magnetic structures and the generation of spin currents at low bias fields by high-amplitude ferromagnetic resonance. In the experiments we use X-ray magnetic circular dichroism to determine the number density of excited magnons in magnetically soft Ni80Fe20 thin films. Our data show that the common Suhl instability model of nonlinear ferromagnetic resonance is not adequate for the description of the nonlinear behavior in the low magnetic field limit. Here we derive a model of parametric spin-wave excitation, which correctly predicts nonlinear threshold amplitudes and decay rates at high and at low magnetic bias fields. In fact, a series of critical spin-wave modes with fast oscillations of the amplitude and phase is found, generalizing the theory of parametric spin-wave excitation to large modulation amplitudes. For these modes, we also find pronounced frequency locking effects that may be used for synchronization purposes in magnonic devices. By using this effect, effective spin-wave sources based on parametric spin-wave excitation may be realized. Our results also show that it is not required to invoke a wave vector-dependent damping parameter in the interpretation of nonlinear magnetic resonance experiments performed at low bias fields.
Application of particle swarm optimization to interpret Rayleigh wave dispersion curves
Song, Xianhai; Tang, Li; Lv, Xiaochun; Fang, Hongping; Gu, Hanming
2012-09-01
Rayleigh waves have been used increasingly as an appealing tool to obtain near-surface shear (S)-wave velocity profiles. However, inversion of Rayleigh wave dispersion curves is challenging for most local-search methods due to its high nonlinearity and to its multimodality. In this study, we proposed and tested a new Rayleigh wave dispersion curve inversion scheme based on particle swarm optimization (PSO). PSO is a global optimization strategy that simulates the social behavior observed in a flock (swarm) of birds searching for food. A simple search strategy in PSO guides the algorithm toward the best solution through constant updating of the cognitive knowledge and social behavior of the particles in the swarm. To evaluate calculation efficiency and stability of PSO to inversion of surface wave data, we first inverted three noise-free and three noise-corrupted synthetic data sets. Then, we made a comparative analysis with genetic algorithms (GA) and a Monte Carlo (MC) sampler and reconstructed a histogram of model parameters sampled on a low-misfit region less than 15% relative error to further investigate the performance of the proposed inverse procedure. Finally, we inverted a real-world example from a waste disposal site in NE Italy to examine the applicability of PSO on Rayleigh wave dispersion curves. Results from both synthetic and field data demonstrate that particle swarm optimization can be used for quantitative interpretation of Rayleigh wave dispersion curves. PSO seems superior to GA and MC in terms of both reliability and computational efforts. The great advantages of PSO are fast in locating the low misfit region and easy to implement. Also there are only three parameters to tune (inertia weight or constriction factor, local and global acceleration constants). Theoretical results exist to explain how to tune these parameters.
Nonlinear and Dissipation Characteristics of Ocean Surface Waves in Estuarine Environments
2010-01-01
determines the time scale over which the interactions occur, in the manner of Hill and Foda (1998) and Jamali et al. (2003). RESULTS Contrary to...the intermediate-depth work of Hill and Foda (1998) and Jamali et al. (2003), the interactions in this wealky-dispersive, weakly-nonlinear model...The stability of oscillatory internal waves. Journal of Fluid Mechanics, 30, 723-736. Hill, D.F., and Foda , M.A., 1998. Subharmonic resonance of
Evolution of Modulated Dispersive Electron Waves in a Plasma
DEFF Research Database (Denmark)
Sugai, H.; Lynov, Jens-Peter; Michelsen, Poul
1979-01-01
The linear propagation of amplitude-modulated electron waves was examined in a low-density Q-machine plasma. Three effects of the strong dispersion on the modulated wave have been demonstrated: (i) a wavepacket expands along its direction of propagation, followed by a shift of the frequency through...... the wavepacket, (ii) the number of oscillations in the temporally observed packet is not identical with that in the spatially observed packet and (iii) continuously modulated waves exhibit recurrence of modulation. The experimental results agree with both a simple analysis based on the Schrodinger equation...
Statistical distribution of nonlinear random wave height in shallow water
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Here we present a statistical model of random wave,using Stokes wave theory of water wave dynamics,as well as a new nonlinear probability distribution function of wave height in shallow water.It is more physically logical to use the wave steepness of shallow water and the factor of shallow water as the parameters in the wave height distribution.The results indicate that the two parameters not only could be parameters of the distribution function of wave height but also could reflect the degree of wave height distribution deviation from the Rayleigh distribution.The new wave height distribution overcomes the problem of Rayleigh distribution that the prediction of big wave is overestimated and the general wave is underestimated.The prediction of small probability wave height value of new distribution is also smaller than that of Rayleigh distribution.The effect of wave steepness in shallow water is similar to that in deep water;but the factor of shallow water lowers the wave height distribution of the general wave with the reduced factor of wave steepness.It also makes the wave height distribution of shallow water more centralized.The results indicate that the new distribution fits the in situ measurements much better than other distributions.
Development of A Fully Nonlinear Numerical Wave Tank
Institute of Scientific and Technical Information of China (English)
陈永平; 李志伟; 张长宽
2004-01-01
A fully nonlinear numerical wave tank (NWT) based on the solution of the σ-transformed Navier-Stokes equation is developed in this study. The numerical wave is generated from the inflow boundary, where the surface elevation and/or velocity are specified by use of the analytical solution or the laboratory data. The Sommerfeld/Orlanski radiation condition in conjunction with an artificial damping zone is applied to reduce wave reflection from the outflow boundary. The whole numerical solution procedures are split into three steps, i.e., advection, diffusion and propagation, and a new method,the Lagrange-Euler Method, instead of the MAC or VOF method, is introduced to solve the free surface elevation at the new time step. Several typical wave cases, including solitary waves, regular waves and irregular waves, are simulated in the wave tank. The robustness and accuracy of the NWT are verified by the good agreement between the numerical results and the linear or nonlinear analytical solutions. This research will be further developed by study of wave-wave, wave-current, wave-structure or wave-jet interaction in the future.
Nonlinear evolution of parallel propagating Alfven waves: Vlasov - MHD simulation
Nariyuki, Y; Kumashiro, T; Hada, T
2009-01-01
Nonlinear evolution of circularly polarized Alfv\\'en waves are discussed by using the recently developed Vlasov-MHD code, which is a generalized Landau-fluid model. The numerical results indicate that as far as the nonlinearity in the system is not so large, the Vlasov-MHD model can validly solve time evolution of the Alfv\\'enic turbulence both in the linear and nonlinear stages. The present Vlasov-MHD model is proper to discuss the solar coronal heating and solar wind acceleration by Alfve\\'n waves propagating from the photosphere.
Nonlinear volume holography for wave-front engineering.
Hong, Xu-Hao; Yang, Bo; Zhang, Chao; Qin, Yi-Qiang; Zhu, Yong-Yuan
2014-10-17
The concept of volume holography is applied to the design of an optical superlattice for the nonlinear harmonic generation. The generated harmonic wave can be considered as a holographic image caused by the incident fundamental wave. Compared with the conventional quasi-phase-matching method, this new method has significant advantages when applied to complicated nonlinear processes such as the nonlinear generation of special beams. As an example, we experimentally realized a second-harmonic Airy beam, and the results are found to agree well with numerical simulations.
Exact travelling wave solutions for some important nonlinear physical models
Indian Academy of Sciences (India)
Jonu Lee; Rathinasamy Sakthivel
2013-05-01
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 studies. In this paper, the Kudryashov method is used to seek exact travelling wave solutions of such physical models. Further, three-dimensional plots of some of the solutions are also given to visualize the dynamics of the equations. The results reveal that the method is a very effective and powerful tool for solving nonlinear partial differential equations arising in mathematical physics.
Tombelaine, Vincent; Labruyère, Alexis; Kobelke, Jens; Schuster, Kay; Reichel, Volker; Leproux, Philippe; Couderc, Vincent; Jamier, Raphaël; Bartelt, Hartmut
2009-08-31
We report about a new type of nonlinear photonic crystal fibers allowing broadband four-wave mixing and supercontinuum generation. The microstructured optical fiber has a structured core consisting of a rod of highly nonlinear glass material inserted in a silica tube. This particular structure enables four wave mixing processes with very large frequency detuning (>135 THz), which permitted the generation of a wide supercontinuum spectrum extending over 1650 nm after 2.15 m of propagation length. The comparison with results obtained from germanium-doped holey fibers confirms the important role of the rod material properties regarding nonlinear process and dispersion.
Exact Nonlinear Internal Equatorial Waves in the f-plane
Hsu, Hung-Chu
2016-07-01
We present an explicit exact solution of the nonlinear governing equations for internal geophysical water waves propagating westward above the thermocline in the f-plane approximation near the equator. Moreover, the mass transport velocity induced by this internal equatorial wave is eastward and a westward current occurs in the transition zone between the great depth where the water is still and the thermocline.
Experimental observations of nonlinear effects of the Lamb waves
Institute of Scientific and Technical Information of China (English)
DENG Mingxi; D.C. Price; D.A.Scott
2004-01-01
The experimental observations of nonlinear effects of the primary Lamb waves have been reported. Firstly, the brief descriptions have been made for the nonlinear acoustic measurement system developed by Ritec. The detailed considerations for the acoustic experiment system established for observing of the nonlinear effects of the primary Lamb waves have been carried out. Especially, the analysis focuses on the time-domain responses of second harmonics of the primary Lame waves by employing a straightforward model. Based on the existence conditions of strong nonlinearity of the primary Lamb waves, the wedge transducers are designed to generate and detect the primary and secondary waves on the surface of an aluminum sheet. For the different distances between the transmitting and receiving wedge transducers,the amplitudes of the primary waves and the second harmonics on the sheet surface have been measured within a specified frequency range. In the immediate vicinity of the driving frequency,where the primary and the double frequency Lamb waves have the same phase velocities, the quantitative relations of second-harmonic amplitudes with the propagation distance have been analyzed. It is experimentally verified that the second harmonics of the primary Lamb waves do have a cumulative growth effect along with the propagation distance.
Elliptic Equation and New Solutions to Nonlinear Wave Equations
Institute of Scientific and Technical Information of China (English)
FU Zun-Tao; LIU Shi-Kuo; LIU Shi-Da
2004-01-01
The new solutions to elliptic equation are shown, and then the elliptic equation is taken as a transformationand is applied to solve nonlinear wave equations. It is shown that more kinds of solutions are derived, such as periodicsolutions of rational form, solitary wave solutions of rational form, and so on.
Wave dispersion and propagation in state-based peridynamics
Butt, Sahir N.; Timothy, Jithender J.; Meschke, Günther
2017-07-01
Peridynamics is a nonlocal continuum model which offers benefits over classical continuum models in cases, where discontinuities, such as cracks, are present in the deformation field. However, the nonlocal characteristics of peridynamics leads to a dispersive dynamic response of the medium. In this study we focus on the dispersion properties of a state-based linear peridynamic solid model and specifically investigate the role of the peridynamic horizon. We derive the dispersion relation for one, two and three dimensional cases and investigate the effect of horizon size, mesh size (lattice spacing) and the influence function on the dispersion properties. We show how the influence function can be used to minimize wave dispersion at a fixed lattice spacing and demonstrate it qualitatively by wave propagation analysis in one- and two-dimensional models of elastic solids. As a main contribution of this paper, we propose to associate peridynamic non-locality expressed by the horizon with a characteristic length scale related to the material microstructure. To this end, the dispersion curves obtained from peridynamics are compared with experimental data for two kinds of sandstone.
Engineering chromatic dispersion and effective nonlinearity in a dual-slot waveguide.
Liu, Yan; Yan, Jing; Han, Genquan
2014-09-20
In this paper, we propose a new dual slot based on rib-like structure, which exhibits a flat and near-zero dispersion over a 198 nm wide wavelength range. Chromatic dispersion of dual-slot silicon (Si) waveguide is mainly determined by waveguide dispersion due to the manipulating mode effective area rather than by the material dispersion. Moreover, the nonlinear coefficient and effective mode area of the waveguide are also explored in detail. A nonlinear coefficient of 1460/m/W at 1550 nm is achieved, which is 10 times larger than that of the Si rib waveguide. By changing different waveguide variables, both the dispersion and nonlinear coefficient can be tailored, thus enabling the potential for a highly nonlinear waveguide with uniform dispersion over a wide wavelength range, which could benefit the performance of broadband optical signal systems.
Some aspects of dispersive horizons: lessons from surface waves
Chaline, J; Maïssa, P; Rousseaux, G
2012-01-01
Hydrodynamic surface waves propagating on a moving background flow experience an effective curved space-time. We discuss experiments with gravity waves and capillary-gravity waves in which we study hydrodynamic black/white-hole horizons and the possibility of penetrating across them. Such possibility of penetration is due to the interaction with an additional "blue" horizon, which results from the inclusion of surface tension in the low-frequency gravity-wave theory. This interaction leads to a dispersive cusp beyond which both horizons completely disappear. We speculate the appearance of high-frequency "superluminal" corrections to be a universal characteristic of analogue gravity systems, and discuss their relevance for the trans-Planckian problem. We also discuss the role of Airy interference in hybridising the incoming waves with the flowing background (the effective spacetime) and blurring the position of the black/white-hole horizon.
Emergence of dispersive shocks and rarefaction waves in power-law contact models
Yasuda, H.; Chong, C.; Yang, J.; Kevrekidis, P. G.
2017-06-01
In the present work, motivated by generalized forms of the Hertzian dynamics associated with granular crystals, we consider the possibility of such models to give rise to both dispersive shock and rarefaction waves. Depending on the value p of the nonlinearity exponent, we find that both of these possibilities are realizable. We use a quasicontinuum approximation of a generalized inviscid Burgers model in order to predict the solution profile up to times near the formation of the dispersive shock, as well as to estimate when it will occur. Beyond that time threshold, oscillations associated with the highly dispersive nature of the underlying model emerge, which cannot be captured by the quasicontinuum approximation. Our analytical characterization of the above features is complemented by systematic numerical computations.
Energy Technology Data Exchange (ETDEWEB)
Berryman, J G; Pride, S R
2004-07-28
Laboratory experiments on wave propagation through saturated and partially saturated porous media have often been conducted on porous cylinders that were initially fully saturated and then allowed to dry while continuing to acquire data on the wave behavior. Since it is known that drying typically progresses from outside to inside, a sensible physical model of this process is concentric cylinders having different saturation levels--the simplest example being a fully dry outer cylindrical shell together with a fully wet inner cylinder. We use this model to formulate the equations for wave dispersion in porous cylinders for patchy saturation (i.e. drainage) conditions. In addition to multiple modes of propagation obtained numerically from these dispersion relations, we find two distinct analytical expressions for torsional wave modes. We solve the dispersion relation for torsional waves for two examples: Massillon sandstone and Sierra White granite. The drainage analysis appears to give improved agreement with the data for both these materials.
Linear and nonlinear propagation of water wave groups
Pierson, W. J., Jr.; Donelan, M. A.; Hui, W. H.
1992-01-01
Results are presented from a study of the evolution of waveforms with known analytical group shapes, in the form of both transient wave groups and the cloidal (cn) and dnoidal (dn) wave trains as derived from the nonlinear Schroedinger equation. The waveforms were generated in a long wind-wave tank of the Canada Centre for Inland Waters. It was found that the low-amplitude transients behaved as predicted by the linear theory and that the cn and dn wave trains of moderate steepness behaved almost as predicted by the nonlinear Schroedinger equation. Some of the results did not fit into any of the available theories for waves on water, but they provide important insight on how actual groups of waves propagate and on higher-order effects for a transient waveform.
Directory of Open Access Journals (Sweden)
V. I. Vlasenko
Full Text Available For many lakes the nonlinear transfer of energy from basin-scale internal waves to short-period motions, such as solitary internal waves (SIW and wave trains, their successive interaction with lake boundaries, as well as over-turning and breaking are important mechanisms for an enhanced mixing of the turbulent benthic boundary layer. In the present paper, the evolution of plane SIWs in a variable depth channel, typical of a lake of variable depth, is considered, with the basis being the Reynolds equations. The vertical fluid stratification, wave amplitudes and bottom parameters are taken close to those observed in Lake Constance, a typical mountain lake. The problem is solved numerically. Three different scenarios of a wave evolution over variable bottom topography are examined. It is found that the basic parameter controlling the mechanism of wave evolution is the ratio of the wave amplitude to the distance from the metalimnion to the bottom d. At sites with a gentle sloping bottom, where d is small, propagating (weak or strong internal waves adjust to the local ambient conditions and preserve their form. No secondary waves or wave trains arise during wave propagation from the deep part to the shallow water. If the amplitude of the propagating waves is comparable with the distance between the metalimnion and the top of the underwater obstacle ( d ~ 1, nonlinear dispersion plays a key role. A wave approaching the bottom feature splits into a sequence of secondary waves (solitary internal waves and an attached oscillating wave tail. The energy of the SIWs above the underwater obstacle is transmitted in parts from the first baroclinic mode, to the higher modes. Most crucially, when the internal wave propagates from the deep part of a basin to the shallow boundary, a breaking event can arise. The cumulative effects of the nonlinearity lead to a steepening and
Wave Propagation In Strongly Nonlinear Two-Mass Chains
Wang, Si Yin; Herbold, Eric B.; Nesterenko, Vitali F.
2010-05-01
We developed experimental set up that allowed the investigation of propagation of oscillating waves generated at the entrance of nonlinear and strongly nonlinear two-mass granular chains composed of steel cylinders and steel spheres. The paper represents the first experimental data related to the propagation of these waves in nonlinear and strongly nonlinear chains. The dynamic compressive forces were detected using gauges imbedded inside particles at depths equal to 4 cells and 8 cells from the entrance gauge detecting the input signal. At these relatively short distances we were able to detect practically perfect transparency at low frequencies and cut off effects at higher frequencies for nonlinear and strongly nonlinear signals. We also observed transformation of oscillatory shocks into monotonous shocks. Numerical calculations of signal transformation by non-dissipative granular chains demonstrated transparency of the system at low frequencies and cut off phenomenon at high frequencies in reasonable agreement with experiments. Systems which are able to transform nonlinear and strongly nonlinear waves at small sizes of the system are important for practical applications such as attenuation of high amplitude pulses.
Dynamics of optical rogue waves in inhomogeneous nonlinear waveguides
Institute of Scientific and Technical Information of China (English)
Zhang Jie-Fang; Jin Mei-Zhen; He Ji-Da; Lou Ji-Hui; Dai Chao-Qing
2013-01-01
We propose a unified theory to construct exact rogue wave solutions of the (2+1)-dimensional nonlinear Schr(o)dinger equation with varying coefficients.And then the dynamics of the first-and the second-order optical rogues are investigated.Finally,the controllability of the optical rogue propagating in inhomogeneous nonlinear waveguides is discussed.By properly choosing the distributed coefficients,we demonstrate analytically that rogue waves can be restrained or even be annihilated,or emerge periodically and sustain forever.We also figure out the center-of-mass motion of the rogue waves.
Thermal conductivity of nonlinear waves in disordered chains
Indian Academy of Sciences (India)
Sergej Flach; Mikhail Ivanchenko; Nianbei Li
2011-11-01
We present computational data on the thermal conductivity of nonlinear waves in disordered chains. Disorder induces Anderson localization for linear waves and results in a vanishing conductivity. Cubic nonlinearity restores normal conductivity, but with a strongly temperature-dependent conductivity (). We ﬁnd indications for an asymptotic low-temperature ∼ 4 and intermediate temperature ∼ 2 laws. These ﬁndings are in accord with theoretical studies of wave packet spreading, where a regime of strong chaos is found to be intermediate, followed by an asymptotic regime of weak chaos (Laptyeva et al, Europhys. Lett. 91, 30001 (2010)).
Nonlinear mixing of laser generated narrowband Rayleigh surface waves
Bakre, Chaitanya; Rajagopal, Prabhu; Balasubramaniam, Krishnan
2017-02-01
This research presents the nonlinear mixing technique of two co-directionally travelling Rayleigh surface waves generated and detected using laser ultrasonics. The optical generation of Rayleigh waves on the specimen is obtained by shadow mask method. In conventional nonlinear measurements, the inherently small higher harmonics are greatly influenced by the nonlinearities caused by coupling variabilities and surface roughness between the transducer and specimen interface. The proposed technique is completely contactless and it should be possible to eliminate this problem. Moreover, the nonlinear mixing phenomenon yields not only the second harmonics, but also the sum and difference frequency components, which can be used to measure the acoustic nonlinearity of the specimen. In this paper, we will be addressing the experimental configurations for this technique. The proposed technique is validated experimentally on Aluminum 7075 alloy specimen.
Time-reversed wave mixing in nonlinear optics.
Zheng, Yuanlin; Ren, Huaijin; Wan, Wenjie; Chen, Xianfeng
2013-11-19
Time-reversal symmetry is important to optics. Optical processes can run in a forward or backward direction through time when such symmetry is preserved. In linear optics, a time-reversed process of laser emission can enable total absorption of coherent light fields inside an optical cavity of loss by time-reversing the original gain medium. Nonlinearity, however, can often destroy such symmetry in nonlinear optics, making it difficult to study time-reversal symmetry with nonlinear optical wave mixings. Here we demonstrate time-reversed wave mixings for optical second harmonic generation (SHG) and optical parametric amplification (OPA) by exploring this well-known but underappreciated symmetry in nonlinear optics. This allows us to observe the annihilation of coherent beams. Our study offers new avenues for flexible control in nonlinear optics and has potential applications in efficient wavelength conversion, all-optical computing.
Analysis of nonlinear shallow water waves in a tank by concentrated mass model
Ishikawa, Satoshi; Kondou, Takahiro; Matsuzaki, Kenichiro; Yamamura, Satoshi
2016-06-01
The sloshing of liquid in a tank is an important engineering problem. For example, liquid storage tanks in industrial facilities can be damaged by earthquakes, and conversely liquid tanks, called tuned liquid damper, are often used as passive mechanical dampers. The water depth is less often than the horizontal length of the tank. In this case, shallow water wave theory can be applied, and the results indicate that the surface waveform in a shallow excited tank exhibits complex behavior caused by nonlinearity and dispersion of the liquid. This study aims to establish a practical analytical model for this phenomenon. A model is proposed that consists of masses, connecting nonlinear springs, connecting dampers, base support dampers, and base support springs. The characteristics of the connecting nonlinear springs are derived from the static and dynamic pressures. The advantages of the proposed model are that nonlinear dispersion is considered and that the problem of non-uniform water depth can be addressed. To confirm the validity of the model, numerical results obtained from the model are compared with theoretical values of the natural frequencies of rectangular and triangular tanks. Numerical results are also compared with experimental results for a rectangular tank. All computational results agree well with the theoretical and experimental results. Therefore, it is concluded that the proposed model is valid for the numerical analysis of nonlinear shallow water wave problems.
Nonlinear wave propagation in a rapidly-spun fiber.
McKinstrie, C J; Kogelnik, H
2006-09-04
Multiple-scale analysis is used to study linear wave propagation in a rapidly-spun fiber and its predictions are shown to be consistent with results obtained by other methods. Subsequently, multiple-scale analysis is used to derive a generalized Schroedinger equation for nonlinear wave propagation in a rapidly-spun fiber. The consequences of this equation for pulse propagation and four-wave mixing are discussed briefly.
Nonlinear propagation of planet-generated tidal waves
Rafikov, Roman
2001-01-01
The propagation and evolution of planet-generated density waves in protoplanetary disks is considered. The evolution of waves, leading to the shock formation and wake dissipation, is followed in the weakly nonlinear regime. The local approach of Goodman & Rafikov (2001) is extended to include the effects of surface density and temperature variations in the disk as well as the disk cylindrical geometry and nonuniform shear. Wave damping due to shocks is demonstrated to be a nonlocal process sp...
BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS TO A COUPLED NONLINEAR WAVE SYSTEM
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
Employ theory of bifurcations of dynamical systems to a system of coupled nonlin-ear equations, the existence of solitary wave solutions, kink wave solutions, anti-kink wave solutions and periodic wave solutions is obtained. Under different parametric conditions, various suffcient conditions to guarantee the existence of the above so-lutions are given. Some exact explicit parametric representations of travelling wave solutions are derived.
Institute of Scientific and Technical Information of China (English)
朱良生; 洪广文
2001-01-01
Based on the high order nonlinear and dispersive wave equation with a dissipative term, a numerical model for nonlinear waves is developed. It is suitable to calculate wave propagation in water areas with an arbitrarily varying bottom slope and a relative depth h/L0≤1. By the application of the completely implicit stagger grid and central difference algorithm, discrete governing equations are obtained. Although the central difference algorithm of second-order accuracy both in time and space domains is used to yield the difference equations, the order of truncation error in the difference equation is the same as that of the third-order derivatives of the Boussinesq equation. In this paper, the correction to the first-order derivative is made, and the accuracy of the difference equation is improved. The verifications of accuracy show that the results of the numerical model are in good agreement with those of analytical solutions and physical models.
Numerical simulation of nonlinear long waves interacting with arrays of emergent cylinders
Zainali, Amir; Weiss, Robert; Irish, Jennifer L; Yang, Yongqian
2016-01-01
We presented numerical simulation of long waves, interacting with arrays of emergent cylinders inside regularly spaced patches, representing discontinues patchy coastal vegetation. We employed the fully nonlinear and weakly dispersive Serre-Green-Naghdi equations (SGN) until the breaking process starts, while we changed the governing equations to nonlinear shallow water equations (NSW) at the vicinity of the breaking-wave peak and during the runup stage. We modeled the cylinders as physical boundaries rather than approximating them as macro-roughness friction. We showed that the cylinders provide protection for the areas behind them. However they might also cause amplification in local water depth in those areas. The presented results are extensively validated against the existing numerical and experimental data. Our results demonstrate the capability and reliability of our model in simulating wave interaction with emergent cylinders.
Nonlinear Whitham-Broer-Kaup Wave Equation in an Analytical Solution
Directory of Open Access Journals (Sweden)
S. A. Zahedi
2008-01-01
Full Text Available This study presented a new approach for the analysis of a nonlinear Whitham-Broer-Kaup equation dealing with propagation of shallow water waves with different dispersion relations. The analysis was based on a kind of analytical method, called Variational Iteration Method (VIM. To illustrate the capability of the approach, some numerical examples were given and the propagation and the error of solutions were shown in comparison to those of exact solution. In clear conclusion, the approach was efficient and capable to obtain the analytical approximate solution of this set of wave equations while these solutions could straightforwardly show some facts of the described process deeply such as the propagation. This method can be easily extended to other nonlinear wave equations and so can be found widely applicable in this field of science.
Dispersion-engineered and highly-nonlinear microstructured polymer optical fibres
DEFF Research Database (Denmark)
Frosz, Michael Henoch; Nielsen, Kristian; Hlubina, Petr;
2009-01-01
We demonstrate dispersion-engineering of microstructured polymer optical fibres (mPOFs) made of poly(methyl methacrylate) (PMMA). A significant shift of the total dispersion from the material dispersion is confirmed through measurement of the mPOF dispersion using white-light spectral....... To increase the nonlinearity of the mPOFs we investigated doping of PMMA with the highly-nonlinear dye Disperse Red 1. Both doping of a PMMA cane and direct doping of a PMMA mPOF was performed....
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...
Dam break problem for the focusing nonlinear Schrödinger equation and the generation of rogue waves
El, G. A.; Khamis, E. G.; Tovbis, A.
2016-09-01
We propose a novel, analytically tractable, scenario of the rogue wave formation in the framework of the small-dispersion focusing nonlinear Schrödinger (NLS) equation with the initial condition in the form of a rectangular barrier (a ‘box’). We use the Whitham modulation theory combined with the nonlinear steepest descent for the semi-classical inverse scattering transform, to describe the evolution and interaction of two counter-propagating nonlinear wave trains—the dispersive dam break flows—generated in the NLS box problem. We show that the interaction dynamics results in the emergence of modulated large-amplitude quasi-periodic breather lattices whose amplitude profiles are closely approximated by the Akhmediev and Peregrine breathers within certain space-time domain. Our semi-classical analytical results are shown to be in excellent agreement with the results of direct numerical simulations of the small-dispersion focusing NLS equation.
Energy Technology Data Exchange (ETDEWEB)
Xie, Xi-Yang; Tian, Bo, E-mail: tian_bupt@163.com; Wang, Yu-Feng; Sun, Ya; Jiang, Yan
2015-11-15
In this paper, we investigate a generalized nonautonomous nonlinear equation which describes the ultrashort optical pulse propagating in a nonlinear inhomogeneous fiber. By virtue of the generalized Darboux transformation, the first- and second-order rogue-wave solutions for the generalized nonautonomous nonlinear equation are obtained, under some variable–coefficient constraints. Properties of the first- and second-order rogue waves are graphically presented and analyzed: When the coefficients are all chosen as the constants, we can observe the some functions, the shapes of wave crests and troughs for the first- and second-order rogue waves change. Oscillating behaviors of the first- and second-order rogue waves are observed when the coefficients are the trigonometric functions.
Nonlinear Pressure Wave Analysis by Concentrated Mass Model
Ishikawa, Satoshi; Kondou, Takahiro; Matsuzaki, Kenichiro
A pressure wave propagating in a tube often changes to a shock wave because of the nonlinear effect of fluid. Analyzing this phenomenon by the finite difference method requires high computational cost. To lessen the computational cost, a concentrated mass model is proposed. This model consists of masses, connecting nonlinear springs, connecting dampers, and base support dampers. The characteristic of a connecting nonlinear spring is derived from the adiabatic change of fluid, and the equivalent mass and equivalent damping coefficient of the base support damper are derived from the equation of motion of fluid in a cylindrical tube. Pressure waves generated in a hydraulic oil tube, a sound tube and a plane-wave tube are analyzed numerically by the proposed model to confirm the validity of the model. All numerical computational results agree very well with the experimental results carried out by Okamura, Saenger and Kamakura. Especially, the numerical analysis reproduces the phenomena that a pressure wave with large amplitude propagating in a sound tube or in a plane tube changes to a shock wave. Therefore, it is concluded that the proposed model is valid for the numerical analysis of nonlinear pressure wave problem.
Galiev, Sh. U.
2003-08-01
A non-linear theory of transresonant wave phenomena based on consideration of perturbed wave equations is presented. In particular, the waves in a surface layer of a porous compressible viscoelastoplastic material are considered. For such layers the 3-D equations of deformable media are reduced to 1-D or 2-D perturbed wave equations. A set of approximate, closed-form, general solutions of these equations are presented, which take into account non-linear, dissipative, dispersive, topographic and boundary effects. Then resonant, site and liquefaction effects are analysed. Resonance is considered as a global parameter. Transresonant evolution of the equations is studied. Within the resonant band, utt~a20∇2u and the perturbed wave equations transform into non-linear diffusion equations, either to a basic highly non-linear ordinary differential equation or to the basic algebraic equation for travelling waves. Resonances can destroy predictability and wave reversibility. Surface topography (valleys, islands, etc.) is considered as a series of earthquake-induced resonators. A non-linear transresonant evolution of smooth seismic waves into shock-, jet- and mushroom-like waves and vortices is studied. The amplitude of the resonant waves may be of the order of the square or cube root of the exciting amplitude. Therefore, seismic waves with a moderate amplitude can be amplified very strongly in natural resonators, whereas strong seismic waves can be attenuated. Reports of the 1835 February 20 Chilean earthquake given by Charles Darwin are qualitatively examined using the non-linear theory. The theory qualitatively describes the `shivering' of islands and ridges, volcano spouts and generation of tsunami-like waves and supports Darwin's opinion that these events were part of a single phenomenon. Same-day earthquake/eruption events and catastrophic amplification of seismic waves near the edge of sediment layers are discussed. At the same time the theory can account for recent
Wave-equation dispersion inversion of surface waves recorded on irregular topography
Li, Jing
2017-08-17
Significant topographic variations will strongly influence the amplitudes and phases of propagating surface waves. Such effects should be taken into account, otherwise the S-velocity model inverted from the Rayleigh dispersion curves will contain significant inaccuracies. We now show that the recently developed wave-equation dispersion inversion (WD) method naturally takes into account the effects of topography to give accurate S-velocity tomograms. Application of topographic WD to demonstrates that WD can accurately invert dispersion curves from seismic data recorded over variable topography. We also apply this method to field data recorded on the crest of mountainous terrain and find with higher resolution than the standard WD tomogram.
Nonlinear internal wave penetration via parametric subharmonic instability
Ghaemsaidi, S J; Dauxois, T; Odier, P; Peacock, T
2016-01-01
We present the results of a laboratory experimental study of an internal wave field generated by harmonic, spatially-periodic boundary forcing from above of a density stratification comprising a strongly-stratified, thin upper layer sitting atop a weakly-stratified, deep lower layer. In linear regimes, the energy flux associated with relatively high frequency internal waves excited in the upper layer is prevented from entering the lower layer by virtue of evanescent decay of the wave field. In the experiments, however, we find that the development of parametric subharmonic instability (PSI) in the upper layer transfers energy from the forced primary wave into a pair of subharmonic daughter waves, each capable of penetrating the weakly-stratified lower layer. We find that around $10\\%$ of the primary wave energy flux penetrates into the lower layer via this nonlinear wave-wave interaction for the regime we study.
Indian Academy of Sciences (India)
R Ganapathy; V C Kuriakose
2002-04-01
We obtain conditions for the occurrence of cross-phase modulational instability in the normal dispersion regime for the coupled higher order nonlinear Schrödinger equation with higher order dispersion and nonlinear terms.
Efficient computation method for two-dimensional nonlinear waves
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
The theory and simulation of fully-nonlinear waves in a truncated two-dimensional wave tank in time domain are presented. A piston-type wave-maker is used to generate gravity waves into the tank field in finite water depth. A damping zone is added in front of the wave-maker which makes it become one kind of absorbing wave-maker and ensures the prescribed Neumann condition. The efficiency of nmerical tank is further enhanced by installation of a sponge layer beach (SLB) in front of downtank to absorb longer weak waves that leak through the entire wave train front. Assume potential flow, the space- periodic irrotational surface waves can be represented by mixed Euler- Lagrange particles. Solving the integral equation at each time step for new normal velocities, the instantaneous free surface is integrated following time history by use of fourth-order Runge- Kutta method. The double node technique is used to deal with geometric discontinuity at the wave- body intersections. Several precise smoothing methods have been introduced to treat surface point with high curvature. No saw-tooth like instability is observed during the total simulation.The advantage of proposed wave tank has been verified by comparing with linear theoretical solution and other nonlinear results, excellent agreement in the whole range of frequencies of interest has been obtained.
Prieur, Fabrice; Vilenskiy, Gregory; Holm, Sverre
2012-10-01
A corrected derivation of nonlinear wave propagation equations with fractional loss operators is presented. The fundamental approach is based on fractional formulations of the stress-strain and heat flux definitions but uses the energy equation and thermodynamic identities to link density and pressure instead of an erroneous fractional form of the entropy equation as done in Prieur and Holm ["Nonlinear acoustic wave equations with fractional loss operators," J. Acoust. Soc. Am. 130(3), 1125-1132 (2011)]. The loss operator of the obtained nonlinear wave equations differs from the previous derivations as well as the dispersion equation, but when approximating for low frequencies the expressions for the frequency dependent attenuation and velocity dispersion remain unchanged.
Dispersion analysis for waves propagated in fractured media
Energy Technology Data Exchange (ETDEWEB)
Lesniak, A.; Niitsuma, H. [Tohoku University, Sendai (Japan). Faculty of Engineering
1996-05-01
Dispersion of velocity is defined as a variation of the phase velocity with frequency. This paper describes the dispersion analysis of compressional body waves propagated in the heterogeneous fractured media. The new method proposed and discussed here permitted the evaluation of the variation in P wave arrival with frequency. For this processing method, any information about the attenuation of the medium are not required, and only an assumption of weak heterogeneity is important. It was shown that different mechanisms of dispersion can be distinguished and its value can be quantitatively estimated. Although the frequency used in this study was lower than those in most previous experiments reported in literature, the evaluated dispersion was large. It was suggested that such a large dispersion may be caused by the velocity structure of the media studied and by frequency dependent processes in a highly fractured zone. It was demonstrated that the present method can be used in the evaluation of subsurface fracture systems or characterization of any kind of heterogeneities. 10 refs., 6 figs.
Dispersion of guided waves in composite laminates and sandwich panels
Schaal, Christoph; Mal, Ajit
2015-03-01
In composite structures, damages are often invisible from the surface and can grow to reach a critical size, potentially causing catastrophic failure of the entire structure. Thus safe operation of these structures requires careful monitoring of the initiation and growth of such defects. Ultrasonic methods using guided waves offer a reliable and cost-effective method for structural health monitoring in advanced structures. Guided waves allow for long monitoring ranges and are very sensitive to defects within their propagation path. In this work, the relevant properties of guided Lamb waves for damage detection in composite structures are investigated. An efficient numerical approach is used to determine their dispersion characteristics, and these results are compared to those from laboratory experiments. The experiments are based on a pitch-catch method, in which a pair of movable transducers is placed on one surface of the structure to induce and detect guided Lamb waves. The specific cases considered include an aluminum plate and an aluminum honeycomb sandwich panel with woven composite face sheets. In addition, a disbond of the interface between one of the face sheets and the honeycomb core of the sandwich panel is also considered, and the dispersion characteristics of the two resultant waveguides are determined. Good agreement between numerical and experimental dispersion results is found, and suggestions on the applicability of the pitch-catch system for structural health monitoring are made.
Increased P wave dispersion in patients with liver steatosis
Directory of Open Access Journals (Sweden)
Mustafa Aparci
2010-08-01
Full Text Available Aim Hepatic steatosis is associated with metabolic and hemodynamicabnormalities induced by insulin resistance and inflammatory state. Since abnormalities of P wave dispersion may be accompanied with latter issues we evaluated this subject in patients with hepatic steatosis. Methods Total of 106 patients and 56 healthy subjects were enrolled and performed hepatic ultrasonography, echocardiography, electrocardiogram, and biochemistry tests. Clinical features, laboratory and echocardiographic parameters, P wave dispersion were compared between groups and analyzed for any correlation among parameters. Results Body mass index (BMI, waist circumference, systolic and diastolic blood pressure, levels of total and LDL cholesterol, and fasting blood glucose (FBG, and left atrial diameter were significantly higher in patients with hepatic steatosis. Peak velocities of mitral E and A waves and their ratio were abnormally changed in patients compared to normals. In multiple linear regression analysis, approximately all of the variables previously correlated within Pearsons’ correlation test were found to be significantly correlated with P wave dispersion [ waist circumference (ß=0.151, p=0.048, LDL cholesterol (ß=0.234, p=0.000, FBG (ß=0.402, p= 0.000, alanine aminotransferase (ALT (ß=0.205, p= 0.006, alkaline phosphatase (ALP (ß=0.277, p=0.000, γ-glutamyl transferase (γ-GT (ß=0.240, p=0.000, left atrial diameter (ß=0.204, p=0.003, heart rate (ß=0.123, p=0.037]. Conclusion Increased P wave dispersion may indicate a risk of atrial arrhythmia which may be complicated with disabling symptoms and thromboembolism in patients with hepatic steatosis. Consequently, hepatic steatosis is associated with increased risk for cardiovascular disease due to metabolic and hemodynamic abnormalitiesprobably induced by insulin resistance and inflammatory state.
Linear and Nonlinear MHD Wave Processes in Plasmas. Final Report
Energy Technology Data Exchange (ETDEWEB)
Tataronis, J. A.
2004-06-01
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 Alfvkn 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.
Emergent geometries and nonlinear-wave dynamics in photon fluids.
Marino, F; Maitland, C; Vocke, D; Ortolan, A; Faccio, D
2016-03-22
Nonlinear waves in defocusing media are investigated in the framework of the hydrodynamic description of light as a photon fluid. The observations are interpreted in terms of an emergent curved spacetime generated by the waves themselves, which fully determines their dynamics. The spacetime geometry emerges naturally as a result of the nonlinear interaction between the waves and the self-induced background flow. In particular, as observed in real fluids, different points of the wave profile propagate at different velocities leading to the self-steepening of the wave front and to the formation of a shock. This phenomenon can be associated to a curvature singularity of the emergent metric. Our analysis offers an alternative insight into the problem of shock formation and provides a demonstration of an analogue gravity model that goes beyond the kinematic level.
Simulation of Fully Nonlinear 3-D Numerical Wave Tank
Institute of Scientific and Technical Information of China (English)
张晓兔; 滕斌; 宁德志
2004-01-01
A fully nonlinear numerical wave tank (NWT) has been simulated by use of a three-dimensional higher order boundary element method (HOBEM) in the time domain. Within the frame of potential flow and the adoption of simply Rankine source, the resulting boundary integral equation is repeatedly solved at each time step and the fully nonlinear free surface boundary conditions are integrated with time to update its position and boundary values. A smooth technique is also adopted in order to eliminate the possible saw-tooth numerical instabilities. The incident wave at the uptank is given as theoretical wave in this paper. The outgoing waves are absorbed inside a damping zone by spatially varying artificial damping on the free surface at the wave tank end. The numerical results show that the NWT developed by these approaches has a high accuracy and good numerical stability.
Time-Reversal of Nonlinear Waves - Applicability and Limitations
Ducrozet, G; Chabchoub, A
2016-01-01
Time-reversal (TR) refocusing of waves is one of fundamental principles in wave physics. Using the TR approach, "Time-reversal mirrors" can physically create a time-reversed wave that exactly refocus back, in space and time, to its original source regardless of the complexity of the medium as if time were going backwards. Lately, laboratory experiments proved that this approach can be applied not only in acoustics and electromagnetism but also in the field of linear and nonlinear water waves. Studying the range of validity and limitations of the TR approach may determine and quantify its range of applicability in hydrodynamics. In this context, we report a numerical study of hydrodynamic TR using a uni-directional numerical wave tank, implemented by the nonlinear high-order spectral method, known to accurately model the physical processes at play, beyond physical laboratory restrictions. The applicability of the TR approach is assessed over a variety of hydrodynamic localized and pulsating structures' configu...
Nonlinear diffraction of water waves by offshore stuctures
Directory of Open Access Journals (Sweden)
Matiur Rahman
1986-01-01
Full Text Available This paper is concerned with a variational formulation of a nonaxisymmetric water wave problem. The full set of equations of motion for the problem in cylindrical polar coordinates is derived. This is followed by a review of the current knowledge on analytical theories and numerical treatments of nonlinear diffraction of water waves by offshore cylindrical structures. A brief discussion is made on water waves incident on a circular harbor with a narrow gap. Special emphasis is given to the resonance phenomenon associated with this problem. A new theoretical analysis is also presented to estimate the wave forces on large conical structures. Second-order (nonlinear effects are included in the calculation of the wave forces on the conical structures. A list of important references is also given.
Demi, L; van Dongen, K W A; Verweij, M D
2011-03-01
Experimental data reveals that attenuation is an important phenomenon in medical ultrasound. Attenuation is particularly important for medical applications based on nonlinear acoustics, since higher harmonics experience higher attenuation than the fundamental. Here, a method is presented to accurately solve the wave equation for nonlinear acoustic media with spatially inhomogeneous attenuation. Losses are modeled by a spatially dependent compliance relaxation function, which is included in the Westervelt equation. Introduction of absorption in the form of a causal relaxation function automatically results in the appearance of dispersion. The appearance of inhomogeneities implies the presence of a spatially inhomogeneous contrast source in the presented full-wave method leading to inclusion of forward and backward scattering. The contrast source problem is solved iteratively using a Neumann scheme, similar to the iterative nonlinear contrast source (INCS) method. The presented method is directionally independent and capable of dealing with weakly to moderately nonlinear, large scale, three-dimensional wave fields occurring in diagnostic ultrasound. Convergence of the method has been investigated and results for homogeneous, lossy, linear media show full agreement with the exact results. Moreover, the performance of the method is demonstrated through simulations involving steered and unsteered beams in nonlinear media with spatially homogeneous and inhomogeneous attenuation.
Energy Technology Data Exchange (ETDEWEB)
Romeo, Francesco [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail: francesco.romeo@uniromal.it; Rega, Giuseppe [Dipartimento di Ingegneria Strutturale e Geotecnica, Universita di Roma ' La Sapienza' , Via Gramsci 53, 00197 Rome (Italy)] e-mail: giuseppe.rega@uniromal.it
2006-02-01
Free wave propagation properties in one-dimensional chains of nonlinear oscillators are investigated by means of nonlinear maps. In this realm, the governing difference equations are regarded as symplectic nonlinear transformations relating the amplitudes in adjacent chain sites (n, n + 1) thereby considering a dynamical system where the location index n plays the role of the discrete time. Thus, wave propagation becomes synonymous of stability: finding regions of propagating wave solutions is equivalent to finding regions of linearly stable map solutions. Mechanical models of chains of linearly coupled nonlinear oscillators are investigated. Pass- and stop-band regions of the mono-coupled periodic system are analytically determined for period-q orbits as they are governed by the eigenvalues of the linearized 2D map arising from linear stability analysis of periodic orbits. Then, equivalent chains of nonlinear oscillators in complex domain are tackled. Also in this case, where a 4D real map governs the wave transmission, the nonlinear pass- and stop-bands for periodic orbits are analytically determined by extending the 2D map analysis. The analytical findings concerning the propagation properties are then compared with numerical results obtained through nonlinear map iteration.
Relativistic warm plasma theory of nonlinear laser-driven electron plasma waves.
Schroeder, C B; Esarey, E
2010-05-01
A relativistic, warm fluid model of a nonequilibrium, collisionless plasma is developed and applied to examine nonlinear Langmuir waves excited by relativistically intense, short-pulse lasers. Closure of the covariant fluid theory is obtained via an asymptotic expansion assuming a nonrelativistic plasma temperature. The momentum spread is calculated in the presence of an intense laser field and shown to be intrinsically anisotropic. Coupling between the transverse and longitudinal momentum variances is enabled by the laser field. A generalized dispersion relation is derived for Langmuir waves in a thermal plasma in the presence of an intense laser field. Including thermal fluctuations in three-velocity-space dimensions, the properties of the nonlinear electron plasma wave, such as the plasma temperature evolution and nonlinear wavelength, are examined and the maximum amplitude of the nonlinear oscillation is derived. The presence of a relativistically intense laser pulse is shown to strongly influence the maximum plasma wave amplitude for nonrelativistic phase velocities owing to the coupling between the longitudinal and transverse momentum variances.
The interaction of long and short waves in dispersive media
Deconinck, Bernard; Nguyen, Nghiem V.; Segal, Benjamin L.
2016-10-01
The KdV equation models the propagation of long waves in dispersive media, while the NLS equation models the dynamics of narrow-bandwidth wave packets consisting of short dispersive waves. A system that couples the two equations to model the interaction of long and short waves is mathematically attractive and such a system has been studied over the last decades. We evaluate the validity of this system as a physical model, discussing two main problems. First, only the system coupling the linear Schrödinger equation with KdV has been derived in the literature. Second, the time variables appearing in the equations are of a different order. It appears that in the manuscripts that study the coupled NLS-KdV system, an assumption has been made that the coupled system can be derived, justifying its mathematical study. In fact, this is true even for the papers where the asymptotic derivation with the problems described above is presented. In addition to discussing these inconsistencies, we present an alternative system describing the interaction of long and short waves.
Diffractive optics based four-wave, six-wave, ..., nu-wave nonlinear spectroscopy.
Miller, R J Dwayne; Paarmann, Alexander; Prokhorenko, Valentyn I
2009-09-15
A detailed understanding of chemical processes requires information about both structure and dynamics. By definition, a reaction involves nonstationary states and is a dynamic process. Structure describes the atomic positions at global minima in the nuclear potential energy surface. Dynamics are related to the anharmonicities in this potential that couple different minima and lead to changes in atomic positions (reactions) and correlations. Studies of molecular dynamics can be configured to directly access information on the anharmonic interactions that lead to chemical reactions and are as central to chemistry as structural information. In this regard, nonlinear spectroscopies have distinct advantages over more conventional linear spectroscopies. Because of this potential, nonlinear spectroscopies could eventually attain a comparable level of importance for studying dynamics on the relevant time scales to barrier crossings and reactive processes as NMR has for determining structure. Despite this potential, nonlinear spectroscopy has not attained the same degree of utility as linear spectroscopy largely because nonlinear studies are more technically challenging. For example, unlike the linear spectrometers that exist in almost all chemistry departments, there are no "black box" four-wave mixing spectrometers. This Account describes recent advances in the application of diffractive optics (DOs) to nonlinear spectroscopy, which reduces the complexity level of this technology to be closer to that of linear spectroscopy. The combination of recent advances in femtosecond laser technology and this single optic approach could bring this form of spectroscopy out of the exclusive realm of specialists and into the general user community. However, the real driving force for this research is the pursuit of higher sensitivity limits, which would enable new forms of nonlinear spectroscopy. This Account chronicles the research that has now extended nonlinear spectroscopy to six-wave
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.
Dispersion-Engineered Traveling Wave Kinetic Inductance Parametric Amplifier
Zmuidzinas, Jonas (Inventor); Day, Peter K. (Inventor)
2014-01-01
A traveling wave kinetic inductance parametric amplifier comprises a superconducting transmission line and a dispersion control element. The transmission line can include periodic variations of its dimension along its length. The superconducting material can include a high normal state resistivity material. In some instances the high normal state resistivity material includes nitrogen and a metal selected from the group consisting of titanium, niobium and vanadium. The traveling wave kinetic inductance parametric amplifier is expected to exhibit a noise temperature below 100 mK/GHz.
Traveling wave dispersal in partially sedentary age-structured populations
Le, Thuc Manh; Van Minh, Nguyen
2010-01-01
In this paper we present a thorough study on the existence of traveling waves in a mathematical model of dispersal in a partially sedentary age-structured population. This type of model was first proposed by Veit and Lewis in [{\\it Am. Nat.}, {\\bf 148} (1996), 255-274]. We choose the fecundity function to be the Beverton-Holt type function. We extend the theory of traveling waves in the population genetics model of Weinberger in [{\\it SIAM J. Math. Anal.}, {\\bf 13} (1982), 353-396] to the case when migration depends on age groups and a fraction of the population does not migrate.
Enhanced four-wave mixing with nonlinear plasmonic metasurfaces
Jin, Boyuan
2016-01-01
Plasmonic metasurfaces provide an effective way to increase the efficiency of several nonlinear processes while maintaining nanoscale dimensions. In this work, nonlinear metasurfaces based on film-coupled silver nanostripes loaded with Kerr nonlinear material are proposed to achieve efficient four-wave mixing (FWM). Highly localized plasmon resonances are formed in the nanogap between the metallic film and nanostripes. The local electric field is dramatically enhanced in this subwavelength nanoregion. These properties combined with the relaxed phase matching condition due to the ultrathin area lead to a giant FWM efficiency, which is enhanced by nineteen orders of magnitude compared to a bare silver screen. In addition, efficient visible and low-THz sources can be constructed based on the proposed nonlinear metasurfaces. The FWM generated coherent wave has a directional radiation pattern and its output power is relatively insensitive to the incident angles of the excitation sources. This radiated power can be...
Numerical modelling of nonlinear full-wave acoustic propagation
Energy Technology Data Exchange (ETDEWEB)
Velasco-Segura, Roberto, E-mail: roberto.velasco@ccadet.unam.mx; Rendón, Pablo L., E-mail: pablo.rendon@ccadet.unam.mx [Grupo de Acústica y Vibraciones, Centro de Ciencias Aplicadas y Desarrollo Tecnológico, Universidad Nacional Autónoma de México, Ciudad Universitaria, Apartado Postal 70-186, C.P. 04510, México D.F., México (Mexico)
2015-10-28
The various model equations of nonlinear acoustics are arrived at by making assumptions which permit the observation of the interaction with propagation of either single or joint effects. We present here a form of the conservation equations of fluid dynamics which are deduced using slightly less restrictive hypothesis than those necessary to obtain the well known Westervelt equation. This formulation accounts for full wave diffraction, nonlinearity, and thermoviscous dissipative effects. A two-dimensional, finite-volume method using Roe’s linearisation has been implemented to obtain numerically the solution of the proposed equations. This code, which has been written for parallel execution on a GPU, can be used to describe moderate nonlinear phenomena, at low Mach numbers, in domains as large as 100 wave lengths. Applications range from models of diagnostic and therapeutic HIFU, to parametric acoustic arrays and nonlinear propagation in acoustic waveguides. Examples related to these applications are shown and discussed.
Nonlinear scattering of radio waves by metal objects
Shteynshleyger, V. B.
1984-07-01
Nonlinear scattering of radio waves by metal structures with resulting harmonic and intermodulation interference is analyzed from both theoretical and empirical standpoints, disregarding nonlinear effects associated with the nonlinear dependence of the electric or magnetic polarization vector on respectively the electric or magnetic field intensity in the wave propagating medium. Nonlinear characteristics of metal-oxide-metal contacts where the thin oxide film separation two metal surfaces has properties approximately those of a dielectric or a high-resistivity semiconductor are discussed. Tunneling was found to be the principal mechanism of charge carrier transfer through such a contact with a sufficiently thin film, the contact having usually a cubic or sometimes an integral sign current-voltage characteristic at 300 K and usually S-form or sometimes a cubic current-voltage characteristic at 77 K.
Nonlinear surface waves in soft, weakly compressible elastic media.
Zabolotskaya, Evgenia A; Ilinskii, Yurii A; Hamilton, Mark F
2007-04-01
Nonlinear surface waves in soft, weakly compressible elastic media are investigated theoretically, with a focus on propagation in tissue-like media. The model is obtained as a limiting case of the theory developed by Zabolotskaya [J. Acoust. Soc. Am. 91, 2569-2575 (1992)] for nonlinear surface waves in arbitrary isotropic elastic media, and it is consistent with the results obtained by Fu and Devenish [Q. J. Mech. Appl. Math. 49, 65-80 (1996)] for incompressible isotropic elastic media. In particular, the quadratic nonlinearity is found to be independent of the third-order elastic constants of the medium, and it is inversely proportional to the shear modulus. The Gol'dberg number characterizing the degree of waveform distortion due to quadratic nonlinearity is proportional to the square root of the shear modulus and inversely proportional to the shear viscosity. Simulations are presented for propagation in tissue-like media.
Modeling Gravitational Waves to Test GR Dispersion and Polarization
Tso, Rhondale; Chen, Yanbei; Isi, Maximilliano
2017-01-01
Given continued observation runs from the Laser Interferometer Gravitational-Wave Observatory Scientific Collaboration, further gravitational wave (GW) events will provide added constraints on beyond-general relativity (b-GR) theories. One approach, independent of the GW generation mechanism at the source, is to look at modification to the GW dispersion and propagation, which can accumulate over vast distances. Generic modification of GW propagation can also, in certain b-GR theories, impact the polarization content of GWs. To this end, a comprehensive approach to testing the dispersion and polarization content is developed by modeling anisotropic deformations to the waveforms' phase, along with birefringence effects and corollary consequences for b-GR polarizations, i.e., breathing, vector, and longitudinal modes. Such an approach can be mapped to specific theories like Lorentz violation, amplitude birefringence in Chern-Simons, and provide hints at additional theories to be included. An overview of data analysis routines to be implemented will also be discussed.
Zhao, Tongtong; Lou, Shuqin; Su, Wei; Wang, Xin
2016-01-01
We propose an As2Se3-based highly nonlinear photonic quasi-crystal fiber with dual zero-dispersion wavelengths (ZDWs). Using a full-vector finite element method, the proposed fiber is optimized to obtain high nonlinear coefficient, low confinement loss and two zero-dispersion points by optimizing the structure parameters. Numerical results demonstrate that the proposed photonic quasi-crystal fiber (PQF) has dual ZDWs and the nonlinear coefficient up to 2600 W-1 km-1 within the wavelength range from 2 to 5.5 μm. Due to the introduction of the large air holes in the third ring of the proposed fiber, the ability of confining the fundamental mode field can be improved effectively and thus the low confinement loss can be obtained. The proposed PQF with high nonlinearity and dual ZDWs will have a number of potential applications in four-wave mixing, super-continuum generation, and higher-order dispersion effects.
The dispersion relations of dispersive Alfvén waves in superthermal plasmas
Gaelzer, Rudi; Ziebell, Luiz F.
2014-12-01
The effects of velocity distribution functions (VDFs) that exhibit a power law dependence on the high-energy tail have been the subject of intense research by the space plasma community. Such functions, known as superthermal or kappa distributions, have been found to provide a better fitting to the VDF measured by several spacecraft in the plasma environment of the solar wind. In the literature, the general treatment for waves excited by (bi-)Maxwellian plasmas is well established. However, for kappa distributions, either isotropic or anisotropic, the wave characteristics have been studied mostly for the limiting cases of purely parallel or perpendicular propagation. Contributions for the general case of obliquely propagating waves have been scarcely reported so far. In this work we introduce a mathematical formalism that provides expressions for the dielectric tensor components and subsequent dispersion relations for oblique propagating dispersive Alfvén waves (DAWs) resulting from a kappa VDF. We employ an isotropic distribution, but the methods used here can be easily applied to more general anisotropic distributions, such as the bi-kappa or product-bi-kappa. The effect of the kappa index and thermal corrections on the dispersion relations of DAW is discussed.
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
Kinetic equation for nonlinear resonant wave-particle interaction
Artemyev, A. V.; Neishtadt, A. I.; Vasiliev, A. A.; Mourenas, D.
2016-09-01
We investigate the nonlinear resonant wave-particle interactions including the effects of particle (phase) trapping, detrapping, and scattering by high-amplitude coherent waves. After deriving the relationship between probability of trapping and velocity of particle drift induced by nonlinear scattering (phase bunching), we substitute this relation and other characteristic equations of wave-particle interaction into a kinetic equation for the particle distribution function. The final equation has the form of a Fokker-Planck equation with peculiar advection and collision terms. This equation fully describes the evolution of particle momentum distribution due to particle diffusion, nonlinear drift, and fast transport in phase-space via trapping. Solutions of the obtained kinetic equation are compared with results of test particle simulations.
The Gouy phase shift in nonlinear interactions of waves
Lastzka, Nico; Schnabel, Roman
2007-06-01
We theoretically analyze the influence of the Gouy phase shift on the nonlinear interaction between waves of different frequencies. We focus on χ(2)interaction of optical fields, e.g. through birefringent crystals, and show that focussing, stronger than suggested by the Boyd-Kleinman factor, can further improve nonlinear processes. An increased value of 3.32 for the optimal focussing parameter for a single pass process is found. The new value builds on the compensation of the Gouy phase shift by a spatially varying, instead constant, wave vector phase mismatch. We analyze the single-ended, singly resonant standing wave nonlinear cavity and show that in this case the Gouy phase shift leads to an additional phase during backreflection. Our numerical simulations may explain ill-understood experimental observations in such devices.
Comment on "Dispersion relation for MHD waves in homogeneous plasma"
Chandra, Suresh; Kumthekar, B K; Sharma, Monika
2009-01-01
Pandey & Dwivedi (2007) again tried to claim that the dispersion relation for the given set of equations must be a sixth degree polynomial. Through a series of papers, they are unnecessarily creating confusion. In the present communication, we have shown how Pandey & Dwivedi (2007) are introducing an additional root, which is insignificant. Moreover, five roots of both the polynomials are common and they are sufficient for the discussion of propagation of slow-mode and fast-mode waves.
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
Energy Technology Data Exchange (ETDEWEB)
Alka, W.; Goyal, Amit [Department of Physics, Panjab University, Chandigarh-160014 (India); Nagaraja Kumar, C., E-mail: cnkumar@pu.ac.i [Department of Physics, Panjab University, Chandigarh-160014 (India)
2011-01-17
We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
Alka, W.; Goyal, Amit; Nagaraja Kumar, C.
2011-01-01
We study the nonlinear dynamics of DNA, for longitudinal and transverse motions, in the framework of the microscopic model of Peyrard and Bishop. The coupled nonlinear partial differential equations for dynamics of DNA model, which consists of two long elastic homogeneous strands connected with each other by an elastic membrane, have been solved for solitary wave solution which is further generalized using Riccati parameterized factorization method.
Hopkins, James; Gaudette, Jamie; Mehta, Priyanth
2013-10-01
With the advent of digital signal processing (DSP) in optical transmitters and receivers, the ability to finely tune the ratio of pre and post dispersion compensation can be exploited to best mitigate the nonlinear penalties caused by the Kerr effect. A portion of the nonlinear penalty in optical communication channels has been explained by an increase in peak to average power ratio (PAPR) inherent in highly dispersed signals. The standard approach for minimizing these impairments applies 50% pre dispersion compensation and 50% post dispersion compensation, thereby decreasing average PAPR along the length of the cable, as compared with either 100% pre or post dispersion compensation. In this paper we demonstrate that simply considering the net accumulated dispersion, and applying 50/50 pre/post dispersion is not necessarily the best way to minimize PAPR and subsequent Kerr nonlinearities. Instead, we consider the cumulative dispersion along the entire length of the cable, and, taking into account this additional information, derive an analytic formula for the minimization of PAPR. Alignment with simulation and experimental measurements is presented using a commercially available 100Gb/s dual-polarization binary phase-shift-keying (DP-BPSK) coherent modem, with transmitter and receiver DSP. Measurements are provided from two different 5000km dispersion managed Submarine test-beds, as well as a 3800km terrestrial test-bed with a mixture of SMF-28 and TWRS optical fiber. This method is shown to deviate significantly from the conventional 50/50 method described above, in dispersion managed communications systems, and more closely aligns with results obtained from simulation and data collected from laboratory test-beds.
NONLINEAR APPROXIMATION WITH GENERAL WAVE PACKETS
Institute of Scientific and Technical Information of China (English)
L. Borup; M. Nielsen
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 characterization of the approximation spaces is derived.
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...... characterization of the approximation spaces is derived....
Enhanced four-wave mixing with nonlinear plasmonic metasurfaces.
Jin, Boyuan; Argyropoulos, Christos
2016-06-27
Plasmonic metasurfaces provide an effective way to increase the efficiency of several nonlinear processes while maintaining nanoscale dimensions. In this work, nonlinear metasurfaces based on film-coupled silver nanostripes loaded with Kerr nonlinear material are proposed to achieve efficient four-wave mixing (FWM). Highly localized plasmon resonances are formed in the nanogap between the metallic film and nanostripes. The local electric field is dramatically enhanced in this subwavelength nanoregion. These properties combined with the relaxed phase matching condition due to the ultrathin area lead to a giant FWM efficiency, which is enhanced by nineteen orders of magnitude compared to a bare silver screen. In addition, efficient visible and low-THz sources can be constructed based on the proposed nonlinear metasurfaces. The FWM generated coherent wave has a directional radiation pattern and its output power is relatively insensitive to the incident angles of the excitation sources. This radiated power can be further enhanced by increasing the excitation power. The dielectric nonlinear material placed in the nanogap is mainly responsible for the ultrastrong FWM response. Compact and efficient wave mixers and optical sources spanning different frequency ranges are envisioned to be designed based on the proposed nonlinear metasurface designs.
New traveling wave solutions for nonlinear evolution equations
Energy Technology Data Exchange (ETDEWEB)
El-Wakil, S.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Madkour, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt); Abdou, M.A. [Theoretical Research Group, Physics Department, Faculty of Science, Mansoura University, 35516 Mansoura (Egypt)]. E-mail: m_abdou_eg@yahoo.com
2007-06-11
The generalized Jacobi elliptic function expansion method is used with a computerized symbolic computation for constructing the new exact traveling wave solutions. The validity and reliability of the method is tested by its applications on a class of nonlinear evolution equations of special interest in mathematical physics. As a result, many exact traveling wave solutions are obtained which include the kink-shaped solutions, bell-shaped solutions, singular solutions and periodic solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.
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.
Nonlinear fast sausage waves in homogeneous magnetic flux tubes
Mikhalyaev, Badma B.; Ruderman, Michael S.
2015-12-01
> We consider fast sausage waves in straight homogeneous magnetic tubes. The plasma motion is described by the ideal magnetohydrodynamic equations in the cold plasma approximation. We derive the nonlinear Schrödinger equation describing the nonlinear evolution of an envelope of a carrier wave. The coefficients of this equation are expressed in terms Bessel and modified Bessel functions. They are calculated numerically for various values of parameters. In particular, we show that the criterion for the onset of the modulational or Benjamin-Fair instability is satisfied. The implication of the obtained results for solar physics is discussed.
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...
Fully Nonlinear Boussinesq-Type Equations with Optimized Parameters for Water Wave Propagation
Institute of Scientific and Technical Information of China (English)
荆海晓; 刘长根; 龙文; 陶建华
2015-01-01
For simulating water wave propagation in coastal areas, various Boussinesq-type equations with improved properties in intermediate or deep water have been presented in the past several decades. How to choose proper Boussinesq-type equations has been a practical problem for engineers. In this paper, approaches of improving the characteristics of the equations, i.e. linear dispersion, shoaling gradient and nonlinearity, are reviewed and the advantages and disadvantages of several different Boussinesq-type equations are compared for the applications of these Boussinesq-type equations in coastal engineering with relatively large sea areas. Then for improving the properties of Boussinesq-type equations, a new set of fully nonlinear Boussinseq-type equations with modified representative velocity are derived, which can be used for better linear dispersion and nonlinearity. Based on the method of minimizing the overall error in different ranges of applications, sets of parameters are determined with optimized linear dispersion, linear shoaling and nonlinearity, respectively. Finally, a test example is given for validating the results of this study. Both results show that the equations with optimized parameters display better characteristics than the ones obtained by matching with padé approximation.
Fully nonlinear Boussinesq-type equations with optimized parameters for water wave propagation
Jing, Hai-xiao; Liu, Chang-gen; Long, Wen; Tao, Jian-hua
2015-06-01
For simulating water wave propagation in coastal areas, various Boussinesq-type equations with improved properties in intermediate or deep water have been presented in the past several decades. How to choose proper Boussinesq-type equations has been a practical problem for engineers. In this paper, approaches of improving the characteristics of the equations, i.e. linear dispersion, shoaling gradient and nonlinearity, are reviewed and the advantages and disadvantages of several different Boussinesq-type equations are compared for the applications of these Boussinesq-type equations in coastal engineering with relatively large sea areas. Then for improving the properties of Boussinesq-type equations, a new set of fully nonlinear Boussinseq-type equations with modified representative velocity are derived, which can be used for better linear dispersion and nonlinearity. Based on the method of minimizing the overall error in different ranges of applications, sets of parameters are determined with optimized linear dispersion, linear shoaling and nonlinearity, respectively. Finally, a test example is given for validating the results of this study. Both results show that the equations with optimized parameters display better characteristics than the ones obtained by matching with padé approximation.
Nonlinear waves in a fluid-filled thin viscoelastic tube
Zhang, Shan-Yuan; Zhang, Tao
2010-11-01
In the present paper the propagation property of nonlinear waves in a thin viscoelastic tube filled with incompressible inviscid fluid is studied. The tube is considered to be made of an incompressible isotropic viscoelastic material described by Kelvin—Voigt model. Using the mass conservation and the momentum theorem of the fluid and radial dynamic equilibrium of an element of the tube wall, a set of nonlinear partial differential equations governing the propagation of nonlinear pressure wave in the solid—liquid coupled system is obtained. In the long-wave approximation the nonlinear far-field equations can be derived employing the reductive perturbation technique (RPT). Selecting the exponent α of the perturbation parameter in Gardner—Morikawa transformation according to the order of viscous coefficient η, three kinds of evolution equations with soliton solution, i.e. Korteweg—de Vries (KdV)—Burgers, KdV and Burgers equations are deduced. By means of the method of traveling-wave solution and numerical calculation, the propagation properties of solitary waves corresponding with these evolution equations are analysed in detail. Finally, as a example of practical application, the propagation of pressure pulses in large blood vessels is discussed.
Nonlinear waves in a fluid-filled thin viscoelastic tube
Institute of Scientific and Technical Information of China (English)
Zhang Shan-Yuan; Zhang Tao
2010-01-01
In the present paper the propagation property of nonlinear waves in a thin viscoelastic tube filled with incom-pressible inviscid fluid is studied. The tube is considered to be made of an incompressible isotropic viscoelastic material described by Kelvin-Voigt model. Using the mass conservation and the momentum theorem of the fluid and radial dynamic equilibrium of an element of the tube wall, a set of nonlinear partial differential equations governing the prop-agation of nonlinear pressure wave in the solid-liquid coupled system is obtained. In the long-wave approximation the nonlinear far-field equations can be derived employing the reductive perturbation technique (RPT). Selecting the expo-η, three kinds of evolution equations with soliton solution, i.e. Korteweg-de Vries (KdV)-Burgers, KdV and Burgers equations are deduced. By means of the method of traveling-wave solution and numerical calculation, the propagation properties of solitary waves corresponding with these evolution equations are analysed in detail. Finally, as a example of practical application, the propagation of pressure pulses in large blood vessels is discussed.
Properties of GH4169 Superalloy Characterized by Nonlinear Ultrasonic Waves
Directory of Open Access Journals (Sweden)
Hongjuan Yan
2015-01-01
Full Text Available The nonlinear wave motion equation is solved by the perturbation method. The nonlinear ultrasonic coefficients β and δ are related to the fundamental and harmonic amplitudes. The nonlinear ultrasonic testing system is used to detect received signals during tensile testing and bending fatigue testing of GH4169 superalloy. The results show that the curves of nonlinear ultrasonic parameters as a function of tensile stress or fatigue life are approximately saddle. There are two stages in relationship curves of relative nonlinear coefficients β′ and δ′ versus stress and fatigue life. The relative nonlinear coefficients β′ and δ′ increase with tensile stress when tensile stress is lower than 65.8% of the yield strength, and they decrease with tensile stress when tensile stress is higher than 65.8% of the yield strength. The nonlinear coefficients have the extreme values at 53.3% of fatigue life. For the second order relative nonlinear coefficient β′, there is good agreement between the experimental data and the comprehensive model. For the third order relative nonlinear coefficient δ′, however, the experiment data does not accord with the theoretical model.
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)
Shallow water modal evolution due to nonlinear internal waves
Badiey, Mohsen; Wan, Lin; Luo, Jing
2017-09-01
Acoustic modal behavior is reported for an L-shape hydrophone array during the passage of a strong nonlinear internal wave packet. Acoustic track is nearly parallel to the front of nonlinear internal waves. Through modal decomposition at the vertical array, acoustic modes are identified. Modal evolution along the horizontal array then is examined during a passing internal wave. Strong intensity fluctuations of individual modes are observed before and during the internal waves packet passes the fixed acoustic track showing a detailed evolution of the waveguide modal behavior. Acoustic refraction created either uneven distribution of modal energy over the horizontal array or additional returns observable at the entire L-shape array. Acoustic ray-mode simulations are used to phenomenologically explain the observed modal behavior.
Doppler effect of nonlinear waves and superspirals in oscillatory media.
Brusch, Lutz; Torcini, Alessandro; Bär, Markus
2003-09-01
Nonlinear waves emitted from a moving source are studied. A meandering spiral in a reaction-diffusion medium provides an example in which waves originate from a source exhibiting a back-and-forth movement in a radial direction. The periodic motion of the source induces a Doppler effect that causes a modulation in wavelength and amplitude of the waves ("superspiral"). Using direct simulations as well as numerical nonlinear analysis within the complex Ginzburg-Landau equation, we show that waves subject to a convective Eckhaus instability can exhibit monotonic growth or decay as well as saturation of these modulations depending on the perturbation frequency. Our findings elucidate recent experimental observations concerning superspirals and their decay to spatiotemporal chaos.
Electromagnetic Cyclotron Waves in the Solar Wind: Wind Observation and Wave Dispersion Analysis
Jian, L. K.; Moya, P. S.; Vinas, A. F.; Stevens, M.
2016-01-01
Wind observed long-lasting electromagnetic cyclotron waves near the proton cyclotron frequency on 11 March 2005, in the descending part of a fast wind stream. Bi-Maxwellian velocity distributions are fitted for core protons, beam protons, and alpha-particles. Using the fitted plasma parameters we conduct kinetic linear dispersion analysis and find ion cyclotron and/or firehose instabilities grow in six of 10 wave intervals. After Doppler shift, some of the waves have frequency and polarization consistent with observation, thus may be correspondence to the cyclotron waves observed.
Localization of Dispersive Alfvén Wave in Solar wind plasmas and Turbulent Spectrum
Sharma, Swati; Sharma, R. P.
2016-07-01
Solar wind turbulence at large inertial scales is well known for decades and believed to consist of Alfvén cascade. The inertial range of Solar wind turbulence can be described by a magnetohydrodynamic model. But at small scales the MHD description is not valid. At scales of the order of proton inertial length, Alfvén cascade excites kinetic Alfvén wave or fast wave or whistler wave that carries wave energy to smaller scales. On the other hand, parallel propagating right(R) and left(L) circularly polarized Alfvén/ ion cyclotron wave in the framework of Hall MHD are also thought to be essential ingredients of the solar wind turbulence. Recently, He et.al[1] have used the magnetic field data from the STEREO spacecraft to calculate the magnetic helicities in the solar wind turbulence and reported the possible existence of Alfvén -cyclotron waves and their coexistence with the right handed polarized fluctuations. In the present article we intend to study the right circularly polarized dispersive Alfvén wave (DAW) and their role in the solar wind turbulence. The inclusion of the Hall term causes the dispersion of the AW which, in the present study, is considered on account of the finite frequency (frequency comparable to ion gyro frequency) of the pump wave. Filamentation instability has been reported to occur for the case of circularly polarized dispersive Alfvén wave (DAW) propagating parallel to ambient magnetic field. In the present study, the instability arises on account of the transverse density perturbations of the acoustic wave that may couple nonlinearly with the Alfvén wave and the driven ponderomotive force sequentially leads to growth of density perturbations. Numerical simulation involves finite difference method for the time domain and pseudo spectral method for the spatial domain. The power spectrum is investigated which shows a steepening for scales larger than the proton inertial length. These findings have been reported by Alexandrova et al
Nonlinear reflection of internal gravity wave onto a slope
Raja, Keshav; Sommeria, Joel; Staquet, Chantal; Leclair, Matthieu; Grisouard, Nicolas; Gostiaux, Louis
2016-04-01
The interaction of internal waves on sloping topography is one of the processes that cause mixing and transport in oceans. The mixing caused by internal waves is considered to be an important source of energy that is needed to bring back deep, dense water from the abyss to the surface of the ocean, across constant density surfaces. Apart from the vertical transport of heat (downwards) and mass (upwards), internal waves are also observed to irreversibly induce a mean horizontal flow. Mixing and wave induced mean flow may be considered as the processes that transfer wave induced energy to smaller and larger scales respectively. The process of mixing has been a subject of intense research lately. However, the process of wave induced mean flow and their dynamic impact await thorough study. The present study involves this wave induced mean flow, its generation and energetics. The nonlinear subcritical reflection of internal waves from a sloping boundary is studied using laboratory experiments carried out on the Coriolis Platform at Grenoble and, 2D and 3D numerical simulations done using a non-hydrostatic code. In the experiment, a plane wave is produced using a wave generator and is made to reflect normally on a sloping bottom in a uniformly stratified fluid. We consider both rotating and non-rotating cases. The numerical simulation mimicks the laboratory setup with an initial condition of an analytical plane wave solution in a vertical plane limited by a smooth envelope to simulate the finite wave generator. The interaction of the incident and reflected waves produce, apart from higher harmonics, an irreversible wave induced mean flow which grows in time and is localised in the interacting region. The finite extent of the wave generator allows the mean flow to recirculate in the horizontal plane, resulting in a dipolar potential vorticity field. Moreover, the generation of mean flow and higher harmonics, along with dissipative effects, diminishes the amplitude of
2011-01-01
International audience; We study theoretically, numerically and experimentally the nonlinear propagation of partially incoherent optical waves in single mode optical fibers. We revisit the traditional treatment of the wave turbulence theory to provide a statistical kinetic description of the integrable scalar NLS equation. In spite of the formal reversibility and of the integrability of the NLS equation, the weakly nonlinear dynamics reveals the existence of an irreversible evolution toward a...
Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential
Institute of Scientific and Technical Information of China (English)
化存才; 刘延柱
2002-01-01
For the nonlinear wave equation with quartic polynomial potential, bifurcation and solitary waves are investigated. Based on the bifurcation and the energy integral of the two-dimensional dynamical system satisfied by the travelling waves, it is very interesting to find different sufficient and necessary conditions in terms of the bifurcation parameter for the existence and coexistence of bright, dark solitary waves and shock waves. The method of direct integration is developed to give all types of solitary wave solutions. Our method is simpler than other newly developed ones. Some results are similar to those obtained recently for the combined KdV-mKdV equation.
Lamb waves dispersion curves for diamond based piezoelectric layered structure
Sorokin, B. P.; Kvashnin, G. M.; Telichko, A. V.; Novoselov, A. S.; Burkov, S. I.
2016-03-01
The presence of spurious peaks in the amplitude-frequency response of diamond based piezoelectric layered structure was shown. Excitation of such peaks results in deterioration of an useful acoustical signal. It was shown that such spurious peaks should be associated with Lamb waves in a layered structure. By means of FEM analysis, the propagation of acoustic waves of different types in the piezoelectric layered structure "Al/AlN/Mo/(100) diamond" has been investigated in detail. By analyzing the elastic displacement patterns at frequencies from 0 up to 250 MHz, a set of all the possible acoustic waves, especially Lamb modes, have been studied, and dispersive curves of phase velocity have been plotted. A revised classification of Lamb modes has been introduced.
Non-linear high-frequency waves in the magnetosphere
Indian Academy of Sciences (India)
S Moolla; R Bharuthram; S V Singh; G S Lakhina
2003-12-01
Using ﬂuid theory, a set of equations is derived for non-linear high-frequency waves propagating oblique to an external magnetic ﬁeld in a three-component plasma consisting of hot electrons, cold electrons and cold ions. For parameters typical of the Earth’s magnetosphere, numerical solutions of the governing equations yield sinusoidal, sawtooth or bipolar wave-forms for the electric ﬁeld.
Nonlinear Dynamic Characteristics of Combustion Wave in SHS Process
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
The characteristic of combustion wave and its change were analyzed by numerical value calculation and computer simulation,based on the combustion dynamical model of SHS process. It is shown that with the change of condition parameters in SHS process various time-space order combustion waves appear.It is concluded from non-liner dynamical mechanism analysis that the strong coupling of two non-linear dynamical processes is the dynamical mechanism causing the time-space order dissipation structures.
Travelling wave solutions for ( + 1)-dimensional nonlinear evolution equations
Indian Academy of Sciences (India)
Jonu Lee; Rathinasamy Sakthivel
2010-10-01
In this paper, we implement the exp-function method to obtain the exact travelling wave solutions of ( + 1)-dimensional nonlinear evolution equations. Four models, the ( + 1)-dimensional generalized Boussinesq equation, ( + 1)-dimensional sine-cosine-Gordon equation, ( + 1)-double sinh-Gordon equation and ( + 1)-sinh-cosinh-Gordon equation, are used as vehicles to conduct the analysis. New travelling wave solutions are derived.
Nonlinear Pulse Compression and Reshaping Using Cross-Phase Modulation in a Dispersion-Shifted Fiber
Institute of Scientific and Technical Information of China (English)
S.; W.; Chan; K.; K.; Chow; C.; Shu
2003-01-01
Nonlinear pulse compression has been demonstrated by cross-phase modulation in a dispersion-shifted fiber. The output is obtained from filtering of the broadened optical spectrum and a pulse width reduction from 61 to 28 ps is achieved.
Optical gyroscope with controllable dispersion in four wave mixing regime.
Mikhailov, Eugeniy; Wolfe, Owen; Du, Shuangli; Rochester, Simon; Budker, Dmitry; Novikova, Irina
2016-05-01
We present our work towards realization of the fast-light gyroscope prototype, in which the sensitivity enhancement (compared to a regular laser gyroscopes) is achieved by adjusting the intra-cavity dispersion. We discuss schematics and underlying nonlinear effects leading to the negative dispersion in Rb vapor: level structure, optically addressed transitions, and configuration of the resonant cavity. We investigate dependence of the pulling factor (i.e., the ratio of the lasing frequency shift with the change of the cavity length to the equivalent resonance frequency shift in the empty cavity) on pump lasers detunings, power, and density of the atomic vapor. The observation of the pulling factor exceeding unity implies the gyroscope sensitivity improvement over the regular system This work is supported by Naval Air Warfare Center STTR program N68335-11-C-0428.
Energy Technology Data Exchange (ETDEWEB)
He, J.S. [Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211 (China); Charalampidis, E.G., E-mail: charalamp@math.umass.edu [School of Civil Engineering, Faculty of Engineering, Aristotle University of Thessaloniki, Thessaloniki 54124 (Greece); Institut für Physik, Universität Oldenburg, Postfach 2503, D-26111 Oldenburg (Germany); Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Kevrekidis, P.G. [Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003-4515 (United States); Frantzeskakis, D.J. [Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784 (Greece)
2014-01-24
We explore the form of rogue wave solutions in a select set of case examples of nonlinear Schrödinger equations with variable coefficients. We focus on systems with constant dispersion, and present three different models that describe atomic Bose–Einstein condensates in different experimentally relevant settings. For these models, we identify exact rogue wave solutions. Our analytical findings are corroborated by direct numerical integration of the original equations, performed by two different schemes. Very good agreement between numerical results and analytical predictions for the emergence of the rogue waves is identified. Additionally, the nontrivial fate of small numerically induced perturbations to the exact rogue wave solutions is also discussed.
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.
Analysis of nonlinear internal waves in the New York Bight
Liu, Antony K.
1988-01-01
An analysis of the nonlinear-internal-wave evolution in the New York Bight was performed on the basis of current meter mooring data obtained in the New York Bight during the SAR Internal Wave Signature Experiment (SARSEX). The solitary wave theory was extended to include dissipation and shoaling effects, and a series of numerical experiments were performed by solving the wave evolution equation, with waveforms observed in the SARSEX area as initial conditions. The results of calculations demonstrate that the relative balance of dissipation and shoaling effects is crucial to the detailed evolution of internal wave packets. From an observed initial wave packet at the upstream mooring, the numerical evolution simulation agreed reasonably well with the measurements at the distant mooring for the leading two large solitons.
Nonlinear dynamics of Airy-Vortex 3D wave packets: Emission of vortex light waves
Driben, Rodislav
2014-01-01
The dynamics of 3D Airy-vortex wave packets is studied under the action of strong self-focusing Kerr nonlinearity. Emissions of nonlinear 3D waves out of the main wave packets with the topological charges were demonstrated. Due to the conservation of the total angular momentum, charges of the emitted waves are equal to those carried by the parental light structure. The rapid collapse imposes a severe limitation on the propagation of multidimensional waves in Kerr media. However, the structure of the Airy beam carrier allows the coupling of light from the leading, most intense peak into neighboring peaks and consequently strongly postpones the collapse. The dependence of the critical input amplitude for the appearance of a fast collapse on the beam width is studied for wave packets with zero and non-zero topological charges. Wave packets carrying angular momentum are found to be much more resistant to the rapid collapse, especially those having small width.