Helical localized wave solutions of the scalar wave equation.
Overfelt, P L
2001-08-01
A right-handed helical nonorthogonal coordinate system is used to determine helical localized wave solutions of the homogeneous scalar wave equation. Introducing the characteristic variables in the helical system, i.e., u = zeta - ct and v = zeta + ct, where zeta is the coordinate along the helical axis, we can use the bidirectional traveling plane wave representation and obtain sets of elementary bidirectional helical solutions to the wave equation. Not only are these sets bidirectional, i.e., based on a product of plane waves, but they may also be broken up into right-handed and left-handed solutions. The elementary helical solutions may in turn be used to create general superpositions, both Fourier and bidirectional, from which new solutions to the wave equation may be synthesized. These new solutions, based on the helical bidirectional superposition, are members of the class of localized waves. Examples of these new solutions are a helical fundamental Gaussian focus wave mode, a helical Bessel-Gauss pulse, and a helical acoustic directed energy pulse train. Some of these solutions have the interesting feature that their shape and localization properties depend not only on the wave number governing propagation along the longitudinal axis but also on the normalized helical pitch.
Localized modulated wave solutions in diffusive glucose–insulin systems
Mvogo, Alain, E-mail: mvogal_2009@yahoo.fr [Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, University of Yaounde (Cameroon); Centre d' Excellence Africain en Technologies de l' Information et de la Communication, University of Yaounde I (Cameroon); Tambue, Antoine [The African Institute for Mathematical Sciences (AIMS) and Stellenbosch University, 6-8 Melrose Road, Muizenberg 7945 (South Africa); Center for Research in Computational and Applied Mechanics (CERECAM), and Department of Mathematics and Applied Mathematics, University of Cape Town, 7701 Rondebosch (South Africa); Ben-Bolie, Germain H. [Centre d' Excellence Africain en Technologies de l' Information et de la Communication, University of Yaounde I (Cameroon); Laboratory of Nuclear Physics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, University of Yaounde (Cameroon); Kofané, Timoléon C. [Centre d' Excellence Africain en Technologies de l' Information et de la Communication, University of Yaounde I (Cameroon); Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, University of Yaounde (Cameroon)
2016-06-03
We investigate intercellular insulin dynamics in an array of diffusively coupled pancreatic islet β-cells. The cells are connected via gap junction coupling, where nearest neighbor interactions are included. Through the multiple scale expansion in the semi-discrete approximation, we show that the insulin dynamics can be governed by the complex Ginzburg–Landau equation. The localized solutions of this equation are reported. The results suggest from the biophysical point of view that the insulin propagates in pancreatic islet β-cells using both temporal and spatial dimensions in the form of localized modulated waves. - Highlights: • The dynamics of an array of diffusively coupled pancreatic islet beta-cells is investigated. • Through the multiple scale expansion, we show that the insulin dynamics can be governed by the complex Ginzburg–Landau equation. • Localized modulated waves are obtained for the insulin dynamics.
Localized modulated wave solutions in diffusive glucose-insulin systems
Mvogo, Alain; Tambue, Antoine; Ben-Bolie, Germain H.; Kofané, Timoléon C.
2016-06-01
We investigate intercellular insulin dynamics in an array of diffusively coupled pancreatic islet β-cells. The cells are connected via gap junction coupling, where nearest neighbor interactions are included. Through the multiple scale expansion in the semi-discrete approximation, we show that the insulin dynamics can be governed by the complex Ginzburg-Landau equation. The localized solutions of this equation are reported. The results suggest from the biophysical point of view that the insulin propagates in pancreatic islet β-cells using both temporal and spatial dimensions in the form of localized modulated waves.
Localized light waves: Paraxial and exact solutions of the wave equation (a review)
Kiselev, A. P.
2007-04-01
Simple explicit localized solutions are systematized over the whole space of a linear wave equation, which models the propagation of optical radiation in a linear approximation. Much attention has been paid to exact solutions (which date back to the Bateman findings) that describe wave beams (including Bessel-Gauss beams) and wave packets with a Gaussian localization with respect to the spatial variables and time. Their asymptotics with respect to free parameters and at large distances are presented. A similarity between these exact solutions and harmonic in time fields obtained in the paraxial approximation based on the Leontovich-Fock parabolic equation has been studied. Higher-order modes are considered systematically using the separation of variables method. The application of the Bateman solutions of the wave equation to the construction of solutions to equations with dispersion and nonlinearity and their use in wavelet analysis, as well as the summation of Gaussian beams, are discussed. In addition, solutions localized at infinity known as the Moses-Prosser “acoustic bullets”, as well as their harmonic in time counterparts, “ X waves”, waves from complex sources, etc., have been considered. Everywhere possible, the most elementary mathematical formalism is used.
Christov, Ivan C
2012-01-01
In classical continuum physics, a wave is a mechanical disturbance. Whether the disturbance is stationary or traveling and whether it is caused by the motion of atoms and molecules or the vibration of a lattice structure, a wave can be understood as a specific type of solution of an appropriate mathematical equation modeling the underlying physics. Typical models consist of partial differential equations that exhibit certain general properties, e.g., hyperbolicity. This, in turn, leads to the possibility of wave solutions. Various analytical techniques (integral transforms, complex variables, reduction to ordinary differential equations, etc.) are available to find wave solutions of linear partial differential equations. Furthermore, linear hyperbolic equations with higher-order derivatives provide the mathematical underpinning of the phenomenon of dispersion, i.e., the dependence of a wave's phase speed on its wavenumber. For systems of nonlinear first-order hyperbolic equations, there also exists a general ...
Ma Hong-Cai; Ge Dong-Jie; Yu Yao-Dong
2008-01-01
Based on the B(a)cklund method and the multilinear variable separation approach (MLVSA), this paper finds a general solution including two arbitrary functions for the (2+1)-dimensional Burgers equations. Then a class of new doubly periodic wave solutions for (2+1)-dimensional Burgers equations is obtained by introducing appropriate Jacobi elliptic functions, Weierstrass elliptic functions and their combination in the general solutions (which contains two arbitrary functions). Two types of limit cases are considered. Firstly, taking one of the moduli to be unity and the other zero, it obtains particular wave (called semi-localized) patterns, which is periodic in one direction, but localized in the other direction. Secondly, if both moduli are tending to 1 as a limit, it derives some novel localized excitations (two-dromion solution).
Chatzipetros, Argyrios Alexandros
1994-01-01
The synthesis of two types of Localized Wave (L W) pulses is considered; these are the 'Focus Wave Model (FWM) pulse and the X Wave pulse. First, we introduce the modified bidirectional representation where one can select new basis functions resulting in different representations for a solution to the scalar wave equation. Through this new representation, we find a new class of focused X Waves which can be extremely localized. The modified bidirectional decomposition is applied...
Hassan Kamil Jassim
2016-01-01
Full Text Available We used the local fractional variational iteration transform method (LFVITM coupled by the local fractional Laplace transform and variational iteration method to solve three-dimensional diffusion and wave equations with local fractional derivative operator. This method has Lagrange multiplier equal to minus one, which makes the calculations more easily. The obtained results show that the presented method is efficient and yields a solution in a closed form. Illustrative examples are included to demonstrate the high accuracy and fast convergence of this new method.
Ryo, Ikehata
Uniform energy and L2 decay of solutions for linear wave equations with localized dissipation will be given. In order to derive the L2-decay property of the solution, a useful device whose idea comes from Ikehata-Matsuyama (Sci. Math. Japon. 55 (2002) 33) is used. In fact, we shall show that the L2-norm and the total energy of solutions, respectively, decay like O(1/ t) and O(1/ t2) as t→+∞ for a kind of the weighted initial data.
Exact solitary wave solutions of nonlinear wave equations
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.
Nonlinear Localized Dissipative Structures for Long-Time Solution of Wave Equation
2009-07-01
interesting that the role of the second order term (£0) in equation (2.11) is different from typical nonlinear pde’s studied, such as KdV , that harbor...the commonly used form of the CH equation. An important point is that other nonlinear pde’s like Kdv , which can successfully propagate localized
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'.
Capretti, Antonio; Negro, Luca Dal; Miano, Giovanni
2013-01-01
We present a full-wave analytical solution for the problem of second-harmonic generation from spherical particles made of lossy centrosymmetric materials. Both the local-surface and nonlocalbulk nonlinear sources are included in the generation process, under the undepleted-pump approximation. The solution is derived in the framework of the Mie theory by expanding the pump field, the non-linear sources and the second-harmonic fields in series of spherical vector wave functions. We apply the proposed solution to the second-harmonic generation properties of noble metal nano-spheres as function of the polarization, the pump wavelength and the particle size. This approach provides a rigorous methodology to understand second-order optical processes in metal nanoparticles, and to design novel nanoplasmonic devices in the nonlinear regime.
Localized coherence of freak waves
Latifah, Arnida L.; van Groesen, E.
2016-09-01
This paper investigates in detail a possible mechanism of energy convergence leading to freak waves. We give examples of a freak wave as a (weak) pseudo-maximal wave to illustrate the importance of phase coherence. Given a time signal at a certain position, we identify parts of the time signal with successive high amplitudes, so-called group events, that may lead to a freak wave using wavelet transform analysis. The local coherence of the critical group event is measured by its time spreading of the most energetic waves. Four types of signals have been investigated: dispersive focusing, normal sea condition, thunderstorm condition and an experimental irregular wave. In all cases presented in this paper, it is shown that a high correlation exists between the local coherence and the appearance of a freak wave. This makes it plausible that freak waves can be developed by local interactions of waves in a wave group and that the effect of waves that are not in the immediate vicinity is minimal. This indicates that a local coherence mechanism within a wave group can be one mechanism that leads to the appearance of a freak wave.
Liu, Hai-Tao; Sang, Jian-Bing; Zhou, Zhen-Gong
2016-10-01
This paper investigates a functionally graded piezoelectric material (FGPM) containing two parallel cracks under harmonic anti-plane shear stress wave based on the non-local theory. The electric permeable boundary condition is considered. To overcome the mathematical difficulty, a one-dimensional non-local kernel is used instead of a two-dimensional one for the dynamic fracture problem to obtain the stress and the electric displacement fields near the crack tips. The problem is formulated through Fourier transform into two pairs of dual-integral equations, in which the unknown variables are jumps of displacements across the crack surfaces. Different from the classical solutions, that the present solution exhibits no stress and electric displacement singularities at the crack tips.
2007-01-01
In this paper, the dynamic stress field near crack tips in the functionally graded materials subjected to the harmonic anti-plane shear stress waves was investi- gated by means of the non-local theory. The traditional concepts of the non-local theory were extended to solve the fracture problem of functionally graded materials. To make the analysis tractable, it was assumed that the material properties vary exponentially with coordinate parallel to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of dual integral equations, in which the unknown variable was the displacement on the crack surfaces. To solve the dual integral equations, the displacement on the crack surfaces was expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips. The non-local elastic solutions yield a finite hoop stress at crack tips, thus allowing us to use the maximum stress as a fracture criterion. The magnitude of the finite dynamic stress field depends on the crack length, the parameter describing the functionally graded materials, the circular frequency of the incident waves and the lattice parameter of materials.
ZHANG PeiWei; ZHOU ZhenGong; WU LinZhi
2007-01-01
In this paper, the dynamic stress field near crack tips in the functionally graded materials subjected to the harmonic anti-plane shear stress waves was investigated by means of the non-local theory. The traditional concepts of the non-local theory were extended to solve the fracture problem of functionally graded materials.To make the analysis tractable, it was assumed that the material properties vary exponentially with coordinate parallel to the crack. By use of the Fourier transform,the problem can be solved with the help of a pair of dual integral equations, in which the unknown variable was the displacement on the crack surfaces. To solve the dual integral equations, the displacement on the crack surfaces was expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularities are present at crack tips. The non-local elastic solutions yield a finite hoop stress at crack tips, thus allowing us to use the maximum stress as a fracture criterion. The magnitude of the finite dynamic stress field depends on the crack length, the parameter describing the functionally graded materials, the circular frequency of the incident waves and the lattice parameter of materials.
Local fluctuations in solution mixtures
Ploetz, Elizabeth A.; Smith, Paul E.
2011-01-01
An extension of the traditional Kirkwood-Buff (KB) theory of solutions is outlined which provides additional fluctuating quantities that can be used to characterize and probe the behavior of solution mixtures. Particle-energy and energy-energy fluctuations for local regions of any multicomponent solution are expressed in terms of experimentally obtainable quantities, thereby supplementing the usual particle-particle fluctuations provided by the established KB inversion approach. The expressions are then used to analyze experimental data for pure water over a range of temperatures and pressures, a variety of pure liquids, and three binary solution mixtures – methanol and water, benzene and methanol, and aqueous sodium chloride. In addition to providing information on local properties of solutions it is argued that the particle-energy and energy-energy fluctuations can also be used to test and refine solute and solvent force fields for use in computer simulation studies. PMID:21806137
Travelling Wave Solutions to Stretched Beam's Equation: Phase Portraits Survey
Gambo Betchewe; Kuetche Kamgang Victor; Bouetou Bouetou Thomas; Timoleon Crepin Kofane
2011-01-01
In this paper, following the phase portraits analysis, we investigate the integrability of a system which physically describes the transverse oscillation of an elastic beam under end-thrust. As a result, we find that this system actually comprises two families of travelling waves: the sub- and super-sonic periodic waves of positive- and negative-definite velocities, respectively, and the localized sub-sonic loop-shaped waves of positive-definite velocity. Expressing the energy-like of this system while depicting its phase portrait dynamics, we show that these multivalued localized travelling waves appear as the boundary solutions to which the periodic travelling waves tend asymptotically.
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.
Local Scour Around Piles Under Wave Action
陈国平; 左其华; 黄海龙
2004-01-01
The model tests are performed with regular waves, and the effect of wave height, wave period, water depth, scdiment size and pile diameter is evaluated. The shape and size of local scour around piles are studied. There are three typical scour patterns due to wave action. It is found that a relationship exists between the erosion depth and the wave number. An empirical formula of the maximum local scour is thus derived.
On the Exact Solution of Wave Equations on Cantor Sets
Dumitru Baleanu
2015-09-01
Full Text Available The transfer of heat due to the emission of electromagnetic waves is called thermal radiations. In local fractional calculus, there are numerous contributions of scientists, like Mandelbrot, who described fractal geometry and its wide range of applications in many scientific fields. Christianto and Rahul gave the derivation of Proca equations on Cantor sets. Hao et al. investigated the Helmholtz and diffusion equations in Cantorian and Cantor-Type Cylindrical Coordinates. Carpinteri and Sapora studied diffusion problems in fractal media in Cantor sets. Zhang et al. studied local fractional wave equations under fixed entropy. In this paper, we are concerned with the exact solutions of wave equations by the help of local fractional Laplace variation iteration method (LFLVIM. We develop an iterative scheme for the exact solutions of local fractional wave equations (LFWEs. The efficiency of the scheme is examined by two illustrative examples.
Effect of wave localization on plasma instabilities
Levedahl, W.K.
1987-01-01
The Anderson model of wave localization in random media is invoked to study the effect of solar-wind density turbulence on plasma processes associated with the solar type-III radio burst. ISEE-3 satellite data indicate that a possible model for the type-III process is the parametric decay of Langmuir waves excited by solar-flare electron streams into daughter electromagnetic and ion-acoustic waves. The threshold for this instability, however, is much higher than observed Langmuir-wave levels because of rapid wave convection of the transverse electromagnetic daughter wave in the case where the solar wind is assumed homogeneous. Langmuir and transverse waves near critical density satisfy the Ioffe-Riegel criteria for wave localization in the solar wind with observed density fluctuations {approximately}1%. Computer simulations using a linearized hybrid code show that an electron beam will excite localized Langmuir waves in a plasma with density turbulence. An action-principle approach is used to develop a theory of nonlinear wave processes when waves are localized. A theory of resonant particles diffusion by localized waves is developed to explain the saturation of the beam-plasma instability.
Multicomponent integrable wave equations: II. Soliton solutions
Degasperis, A [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , and Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Rome (Italy); Lombardo, S [School of Mathematics, University of Manchester, Alan Turing Building, Upper Brook Street, Manchester M13 9EP (United Kingdom)], E-mail: antonio.degasperis@roma1.infn.it, E-mail: sara.lombardo@manchester.ac.uk, E-mail: sara@few.vu.nl
2009-09-25
The Darboux-dressing transformations developed in Degasperis and Lombardo (2007 J. Phys. A: Math. Theor. 40 961-77) are here applied to construct soliton solutions for a class of boomeronic-type equations. The vacuum (i.e. vanishing) solution and the generic plane wave solution are both dressed to yield one-soliton solutions. The formulae are specialized to the particularly interesting case of the resonant interaction of three waves, a well-known model which is of boomeronic type. For this equation a novel solution which describes three locked dark pulses (simulton) is introduced.
Scattering and Depolarization of Electromagnetic Waves--Full Wave Solutions.
1984-01-01
Analysis," Proceedings of the International Union of Radio Science URSI Conference at Ciudad Universitaria , Madrid, August 1983, in press. . . 13...rough land and seat3 J. The full wave approach was also used to determine the scattering and depolarization of radio waves in irregular spheroidal struc...Full Wave Solutions," Radio Science, Vol. 17, No. 5, September-October 1982, pp. 1055-1066. 4. "Scattering and Depolarization by Rough Surfaces: Full
Testing local Lorentz invariance with gravitational waves
Kostelecky, Alan
2016-01-01
The effects of local Lorentz violation on dispersion and birefringence of gravitational waves are investigated. The covariant dispersion relation for gravitational waves involving gauge-invariant Lorentz-violating operators of arbitrary mass dimension is constructed. The chirp signal from the gravitational-wave event GW150914 is used to place numerous first constraints on gravitational Lorentz violation.
Testing local Lorentz invariance with gravitational waves
Kostelecký, V. Alan, E-mail: kostelec@indiana.edu [Physics Department, Indiana University, Bloomington, IN 47405 (United States); Mewes, Matthew [Physics Department, California Polytechnic State University, San Luis Obispo, CA 93407 (United States)
2016-06-10
The effects of local Lorentz violation on dispersion and birefringence of gravitational waves are investigated. The covariant dispersion relation for gravitational waves involving gauge-invariant Lorentz-violating operators of arbitrary mass dimension is constructed. The chirp signal from the gravitational-wave event GW150914 is used to place numerous first constraints on gravitational Lorentz violation.
EXACT TRAVELLING WAVE SOLUTIONS TO BBM EQUATION
无
2009-01-01
Abundant new travelling wave solutions to the BBM (Benjamin-Bona-Mahoni) equation are obtained by the generalized Jacobian elliptic function method. This method can be applied to other nonlinear evolution equations.
EXACT SOLUTIONS TO NONLINEAR WAVE EQUATION
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.
Traveling Wave Solutions for Generalized Bretherton Equation
Amin Esfahani
2011-01-01
This paper studies the Generalized Bretherton equation using trigonometric function method including the sech-function method, the sine-cosine function method, and the tanh-function method, and He's semi-inverse method (He's variational method).Various traveling wave solutions are obtained, revealing an intrinsic relationship among the amplitude, frequency, and wave speed.
Localized travelling waves in the asymptotic suction boundary layer
Kreilos, Tobias; Schneider, Tobias M
2016-01-01
We present two spanwise-localized travelling wave solutions in the asymptotic suction boundary layer, obtained by continuation of solutions of plane Couette flow. One of the solutions has the vortical structures located close to the wall, similar to spanwise-localized edge states previously found for this system. The vortical structures of the second solution are located in the free stream far above the laminar boundary layer and are supported by a secondary shear gradient that is created by a large-scale low-speed streak. The dynamically relevant eigenmodes of this solution are concentrated in the free stream, and the departure into turbulence from this solution evolves in the free stream towards the walls. For invariant solutions in free-stream turbulence, this solution thus shows that that the source of energy of the vortical structures can be a dynamical structure of the solution itself, instead of the laminar boundary layer.
Exact periodic wave solutions for some nonlinear partial differential equations
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.
A generic travelling wave solution in dissipative laser cavity
BALDEEP KAUR; SOUMENDU JANA
2016-10-01
A large family of cosh-Gaussian travelling wave solution of a complex Ginzburg–Landau equation (CGLE), that describes dissipative semiconductor laser cavity is derived. Using perturbation method, the stability region is identified. Bifurcation analysis is done by smoothly varying the cavity loss coefficient to provide insight of the system dynamics. He’s variational method is adopted to obtain the standard sech-type and the notso-explored but promising cosh-Gaussian type, travelling wave solutions. For a given set of system parameters, only one sech solution is obtained, whereas several distinct solution points are derived for cosh-Gaussian case. These solutions yield a wide variety of travelling wave profiles, namely Gaussian, near-sech, flat-top and a cosh-Gaussian with variable central dip. A split-step Fourier method and pseudospectral method have been used for direct numerical solution of the CGLE and travelling wave profiles identical to the analytical profiles have been obtained. We also identified the parametric zone that promises an extremely large family of cosh-Gaussian travelling wave solutions with tunable shape. This suggests that the cosh-Gaussian profile is quite generic and would be helpful for further theoretical as well as experimental investigation on pattern formation, pulse dynamics and localization in semiconductor laser cavity.
Wei-guo Zhang; Shao-wei Li; Wei-zhong Tian; Lu Zhang
2008-01-01
By means of the undetermined assumption method, we obtain some new exact solitary-wave solutions with hyperbolic secant function fractional form and periodic wave solutions with cosine function form for the generalized modified Bonssinesq equation. We also discuss the boundedness of these solutions. More over,we study the correlative characteristic of the solitary-wave solutions and the periodic wave solutions along with the travelling wave velocity's variation.
Local energy decay for linear wave equations with variable coefficients
Ikehata, Ryo
2005-06-01
A uniform local energy decay result is derived to the linear wave equation with spatial variable coefficients. We deal with this equation in an exterior domain with a star-shaped complement. Our advantage is that we do not assume any compactness of the support on the initial data, and its proof is quite simple. This generalizes a previous famous result due to Morawetz [The decay of solutions of the exterior initial-boundary value problem for the wave equation, Comm. Pure Appl. Math. 14 (1961) 561-568]. In order to prove local energy decay, we mainly apply two types of ideas due to Ikehata-Matsuyama [L2-behaviour of solutions to the linear heat and wave equations in exterior domains, Sci. Math. Japon. 55 (2002) 33-42] and Todorova-Yordanov [Critical exponent for a nonlinear wave equation with damping, J. Differential Equations 174 (2001) 464-489].
CHENYong; YANZhen－Ya; 等
2002-01-01
In this paper,we study the generalized coupled Hirota-Satsuma KdV system by using the new generalized transformation in homogeneous balance method.As a result,many explicit exact solutions,which contain new solitary wave solutions,periodic wave solutions,and the combined formal solitary wave solutions,and periodic wave solutions ,are obtained.
New Exact Solutions and Localized Structures for (3+1)-Dimensional Burgers System
ZHANG Jing-Shang; LI Jiang-Bo; MA Song-Hua; REN Qing-Bao; FANG Jian-Ping; ZHENG Chun-Long
2008-01-01
With an extended mapping approach and a linear variable separation method, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions, and rational function solutions) with arbitrary functions for (3+1)-dimensional Burgers system is derived. Based on the derived excitations, we obtain some novel localized coherent structures and study the interactions between solitons.
SINGULAR AND RAREFACTIVE SOLUTIONS TO A NONLINEAR VARIATIONAL WAVE EQUATION
无
2001-01-01
Following a recent paper of the authors in Communications in Partial Differential Equations, this paper establishes the global existence of weak solutions to a nonlinear variational wave equation under relaxed conditions on the initial data so that the solutions can contain singularities (blow-up). Propagation of local oscillations along one family of characteristics remains under control despite singularity formation in the other family of characteristics.
Slanted snaking bifurcation of localized Faraday waves
Pradenas, Bastián; Clerc, Marcel G; Falcón, Claudio; Gandhi, Punit; Knobloch, Edgar
2016-01-01
We report on an experimental, theoretical and numerical study of slanted snaking of spatially localized parametrically excited waves on the surface of a water-surfactant mixture in a Hele-Shaw cell. We demonstrate experimentally the presence of a hysteretic transition to spatially extended parametrically excited surface waves when the acceleration amplitude is varied, as well as the presence of spatially localized waves exhibiting slanted snaking. The latter extend outside the hysteresis loop. We attribute this behavior to the presence of a conserved quantity, the liquid volume, and introduce a universal model which couples the wave amplitude with such a conserved quantity. The model captures both the observed slanted snaking and the presence of localized waves outside the hysteresis loop, as demonstrated by numerical integration of the model equations.
Exact Periodic Solitary Solutions to the Shallow Water Wave Equation
LI Dong-Long; ZHAO Jun-Xiao
2009-01-01
Exact solutions to the shallow wave equation are studied based on the idea of the extended homoclinic test and bilinear method. Some explicit solutions, such as the one soliton solution, the doubly-periodic wave solution and the periodic solitary wave solutions, are obtained. In addition, the properties of the solutions are investigated.
Traveling Wave Solutions of a Generalized Zakharov-Kuznetsov Equation
Wenbin Zhang; Jiangbo Zhou
2012-01-01
We employ the bifurcation theory of planar dynamical system to investigate the traveling-wave solutions of the generalized Zakharov-Kuznetsov equation. Four important types of traveling wave solutions are obtained, which include the solitary wave solutions, periodic solutions, kink solutions, and antikink solutions.
Zhou Yubin; Wang Mingliang; Miao Tiande
2004-03-15
The periodic wave solutions for a class of nonlinear partial differential equations, including the Davey-Stewartson equations and the generalized Zakharov equations, are obtained by using the F-expansion method, which can be regarded as an overall generalization of the Jacobi elliptic function expansion method recently proposed. In the limit cases the solitary wave solutions of the equations are also obtained.
Explicit solutions of nonlinear wave equation systems
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.
BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS IN VARIANT BOUSSINESQ EQUATIONS
YUAN Yu-bo; PU Dong-mei; LI Shu-min
2006-01-01
The bifurcations of solitary waves and kink waves for variant Boussinesq equations are studied by using the bifurcation theory of planar dynamical systems. The bifurcation sets and the numbers of solitary waves and kink waves for the variant Boussinesq equations are presented. Several types explicit formulas of solitary waves solutions and kink waves solutions are obtained. In the end, several formulas of periodic wave solutions are presented.
New exact travelling wave solutions of bidirectional wave equations
Jonu Lee; Rathinasamy Sakthivel
2011-06-01
The surface water waves in a water tunnel can be described by systems of the form [Bona and Chen, Physica D116, 191 (1998)] \\begin{equation*} \\begin{cases} v_t + u_x + (uv)_x + au_{x x x} − bv_{x x t} = 0,\\\\ u_t + v_x + u u_x + cv_{x x x} − d u_{x x t} = 0, \\end{cases} \\tag{1} \\end{equation*} where , , and d are real constants. In general, the exact travelling wave solutions will be helpful in the theoretical and numerical study of the nonlinear evolution systems. In this paper, we obtain exact travelling wave solutions of system (1) using the modiﬁed tanh–coth function method with computerized symbolic computation.
Traveling Wave Solutions for CH2 Equations
2015-01-01
In this paper, we use a method in order to find exact explicit traveling solutions in the subspace of the phase space for CH2equations. The key idea is removing a coupled relation for the given system so that the new systems can be solved. The existenceof solitary wave solutions is obtained. It is shown that bifurcation theory of dynamical systems provides a powerful mathematicaltool for solving a great many nonlinear partial differential equations in mathematical physics.
Solitary Wave Solutions for Zoomeron Equation
Amna IRSHAD
2013-04-01
Full Text Available Tanh-Coth Method is applied to find solitary wave solutions of the Zoomeron equation which is of extreme importance in mathematical physics. The proposed scheme is fully compatible with the complexity of the problem and is highly efficient. Moreover, suggested combination is capable to handle nonlinear problems of versatile physical nature.
Rational homoclinic solution and rogue wave solution for the coupled long-wave–short-wave system
Chen Wei; Chen Hanlin; Dai Zhengde
2016-03-01
In this paper, a rational homoclinic solution is obtained via the classical homoclinicsolution for the coupled long-wave–short-wave system. Based on the structures of ratinal homoclinic solution, the characteristics of homoclinic solution are discussed which might provide us with useful information on the dynamics of the relevant physical fields.
New multi-soliton solutions and travelling wave solutions of the dispersive long-wave equations
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.
CHEN Yong; YAN Zhen-Ya; LI Biao; ZHANG Hong-Qing
2002-01-01
In this paper, we study the generalized coupled Hirota Satsuma KdV system by using the new generalizedtransformation in homogeneous balance method. As a result, many explicit exact solutions, which contain new solitarywave solutions, periodic wave solutions, and the combined formal solitary wave solutions, and periodic wave solutions,are obtained.
INDOOR LOCALIZATION SOLUTION FOR GPS
Shreyanka B. Chougule; Dr.Sayed Abdulhayan
2017-01-01
GPS technology is used for positioning application and it is highly reliable and accurate when used outdoor. Due to multipath propagation, signal attenuation and blockage its performance is limited in indoor and dense urban environment. As a solution, technologies like Apple’s iBeacon, Radio-frequency identification (RFID), Ultrasonic and Wireless Fidelity (Wi-Fi) access points are used to improve performance in Indoor environment. We are having a look at all these technologies which are mean...
BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS TO A COUPLED NONLINEAR WAVE SYSTEM
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.
Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation[
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
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.
Travelling wave solutions for a second order wave equation of KdV type
无
2007-01-01
The theory of planar dynamical systems is used to study the dynamical behaviours of travelling wave solutions of a nonlinear wave equations of KdV type. In different regions of the parametric space, sufficient conditions to guarantee the existence of solitary wave solutions, periodic wave solutions, kink and anti-kink wave solutions are given. All possible exact explicit parametric representations are obtained for these waves.
Wave system and its approximate similarity solutions
Liu Ping; Fu Pei-Kai
2011-01-01
Recently,a new (2+1)-dimensional shallow water wave system,the (2+1)-dimensional displacement shallow water wave system (2DDSWWS),was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS,which is the same as the famous Kadomtsev-Petviashvili equation and Korteweg-de Vries equation. Applying dimensional analysis,we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS (M2DDSWWS) is studied and four similarity solutions are obtained. For the perfect fluids,the coefficient of kinematic viscosity is zero,then the M2DDSWWS will degenerate to the 2DDSWWS.
Participatory ergonomics that builds on local solutions.
Kogi, K
1995-06-01
Ergonomic interventions must be a local process that responds to the particular needs of local people. In view of the many constraints, a special attention is drawn to participatory ergonomics as an effective means of finding locally workable solutions. Recent experiences show that the best way to utilize its practical advantage is to focus on solutions. The practical steps in providing necessary support for participatory ergonomics should include (1) a good starting point for group discussion and subsequent participatory action based on locally achieved examples; (2) prioritizing different elements of the workplace by means of checklists of available solutions; and (3) making small improvements with a view to learning-by-doing through small wins. Good local examples that have been achieved in the given local conditions can show how improvements can be done in the local conditions and thus motivate people in making improvements. The next important step is to help the participants determine priority solutions by means of "action checklists" that list the available solutions. It is necessary to concentrate on those aspects in which both better working conditions and higher productivity are accessible simultaneously. They include operational, cognitive and organizational aspects. Through learning-by-doing, the participants must be able to base their judgement on the results of relative assessment of locally available solutions and to implement the chosen solutions. To sustain active initiatives of the participants, support and advice must be provided which are suitable for working in small groups, sharing experiences and identifying workable solutions.(ABSTRACT TRUNCATED AT 250 WORDS)
Localization of Waves in Fractals : Spatial Behavior
Vries, Pedro de; Raedt, Hans De; Lagendijk, Ad
1989-01-01
Localization of a quantum particle on two-dimensional percolating networks is investigated numerically. Solving the time-dependent Schrödinger equation for particular initial wave packets we study the spatial behavior of eigenstates for two tight-binding models: the quantum percolation model and the
Local Tensor Radiation Conditions For Elastic Waves
Krenk, S.; Kirkegaard, Poul Henning
2001-01-01
A local boundary condition is formulated, representing radiation of elastic waves from an arbitrary point source. The boundary condition takes the form of a tensor relation between the stress at a point on an arbitrarily oriented section and the velocity and displacement vectors at the point. The...
Modulated envelope localized wavepackets associated with electrostatic plasma waves
Kourakis, I; Kourakis, Ioannis; Shukla, Padma Kant
2004-01-01
The nonlinear amplitude modulation of known electrostatic plasma modes is examined in a generic manner, by applying a collisionless fluid model. Both cold (zero-temperature) and warm fluid descriptions are discussed and the results are compared. The moderately nonlinear oscillation regime is investigated by applying a multiple scale technique. The calculation leads to a Nonlinear Schrodinger-type Equation (NLSE), which describes the evolution of the slowly varying wave amplitude in time and space. The NLSE admits localized envelope (solitary wave) solutions of bright- (pulses) or dark- (holes, voids) type, whose characteristics (maximum amplitude, width) depend on intrinsic plasma parameters. Effects like amplitude perturbation obliqueness, finite temperature and defect (dust) concetration are explicitly considered. The relevance with similar highly localized modulated wave structures observed during recent satellite missions is discussed.
NONLINEAR WAVES AND PERIODIC SOLUTION IN FINITE DEFORMATION ELASTIC ROD
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.
Zhang, Guoqiang; Yan, Zhenya; Wen, Xiao-Yong; Chen, Yong
2017-04-01
We investigate the defocusing coupled nonlinear Schrödinger equations from a 3 ×3 Lax pair. The Darboux transformations with the nonzero plane-wave solutions are presented to derive the newly localized wave solutions including dark-dark and bright-dark solitons, breather-breather solutions, and different types of new vector rogue wave solutions, as well as interactions between distinct types of localized wave solutions. Moreover, we analyze these solutions by means of parameters modulation. Finally, the perturbed wave propagations of some obtained solutions are explored by means of systematic simulations, which demonstrates that nearly stable and strongly unstable solutions. Our research results could constitute a significant contribution to explore the distinct nonlinear waves (e.g., dark solitons, breather solutions, and rogue wave solutions) dynamics of the coupled system in related fields such as nonlinear optics, plasma physics, oceanography, and Bose-Einstein condensates.
The Peridic Wave Solutions for Two Nonlinear Evolution Equations
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.
New Exact Solutions to Long-Short Wave Interaction Equations
TIAN Ying-Hui; CHEN Han-Lin; LIU Xi-Qiang
2006-01-01
New exact solutions expressed by the Jacobi elliptic functions are obtained to the long-short wave interaction equations by using the modified F-expansion method. In the limit case, solitary wave solutions and triangular periodic wave solutions are obtained as well.
Folded localized excitations in the (2+1)-dimensional modified dispersive water-wave system
Lei Yan; Ma Song-Hua; Fang Jian-Ping
2013-01-01
By using a mapping approach and a linear variable separation approach,a new family of solitary wave solutions with arbitrary functions for the (2+1)-dimensional modified dispersive water-wave system (MDWW) is derived.Based on the derived solutions and using some multi-valued functions,we obtain some novel folded localized excitations of the system.
Periodic Wave Solutions and Their Limits for the Generalized KP-BBM Equation
Ming Song; Zhengrong Liu
2012-01-01
We use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the generalized KP-BBM equation. A number of explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain periodic wave solutions, kink wave solutions, unbounded wave solutions, blow-up wave solutions, and solitary wave solutions.
Bifurcations of travelling wave solutions for two generalized Boussinesq systems
2008-01-01
Using the methods of dynamical systems for two generalized Boussinesq systems, the existence of all possible solitary wave solutions and many uncountably infinite periodic wave solutions is obtained. Exact explicit parametric representations of the travelling solutions are given. To guarantee the existence of the above solutions, all parameter conditions are determined.
Localization and solitary waves in solid mechanics
Champneys, A R; Thompson, J M T
1999-01-01
This book is a collection of recent reprints and new material on fundamentally nonlinear problems in structural systems which demonstrate localized responses to continuous inputs. It has two intended audiences. For mathematicians and physicists it should provide useful new insights into a classical yet rapidly developing area of application of the rich subject of dynamical systems theory. For workers in structural and solid mechanics it introduces a new methodology for dealing with structural localization and the related topic of the generation of solitary waves. Applications range from classi
Oscillatory traveling wave solutions to an attractive chemotaxis system
Li, Tong; Liu, Hailiang; Wang, Lihe
2016-12-01
This paper investigates oscillatory traveling wave solutions to an attractive chemotaxis system. The convective part of this system changes its type when crossing a parabola in the phase space. The oscillatory nature of the traveling wave comes from the fact that one far-field state is in the elliptic region and another in the hyperbolic region. Such traveling wave solutions are shown to be linearly unstable. Detailed construction of some traveling wave solutions is presented.
Bifurcations and new exact travelling wave solutions for the bidirectional wave equations
HENG WANG; SHUHUA ZHENG; LONGWEI CHEN; XIAOCHUN HONG
2016-11-01
By using the method of dynamical system, the bidirectional wave equations are considered. Based on this method, all kinds of phase portraits of the reduced travelling wave system in the parametric space are given. All possible bounded travelling wave solutions such as dark soliton solutions, bright soliton solutions and periodic travelling wave solutions are obtained. With the aid of {\\it Maple} software, numerical simulations are conducted for dark soliton solutions, bright soliton solutions and periodic travelling wave solutions to the bidirectional waveequations. The results presented in this paper improve the related previous studies.
New Exact Travelling Wave Solutions to Kundu Equation
HUANG Ding-Jiang; LI De-Sheng; ZHANG Hong-Qing
2005-01-01
Based on a first-order nonlinear ordinary differential equation with six-degree nonlinear term, we first present a new auxiliary equation expansion method and its algorithm. Being concise and straightforward, the method is applied to the Kundu equation. As a result, some new exact travelling wave solutions are obtained, which include bright and dark solitary wave solutions, triangular periodic wave solutions, and singular solutions. This algorithm can also be applied to other nonlinear evolution equations in mathematical physics.
Solitary Wave and Non-traveling Wave Solutions to Two Nonlinear Evolution Equations
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.
TRAVELING WAVE SOLUTIONS FOR A CLASS OF NONLINEAR DISPERSIVE EQUATIONS
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.
The periodic wave solutions for two systems of nonlinear wave equations
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.
LOCAL STABILITY OF TRAVELLING FRONTS FOR A DAMPED WAVE EQUATION
Cao LUO
2013-01-01
The paper is concerned with the long-time behaviour of the travelling fronts of the damped wave equation αutt +ut =uxx-V'(u) on R.The long-time asymptotics of the solutions of this equation are quite similar to those of the corresponding reaction-diffusion equation ut =uxx-V'(u).Whereas a lot is known about the local stability of travelling fronts in parabolic systems,for the hyperbolic equations it is only briefly discussed when the potential V is of bistable type.However,for the combustion or monostable type of V,the problem is much more complicated.In this paper,a local stability result for travelling fronts of this equation with combustion type of nonlinearity is established.And then,the result is extended to the damped wave equation with a case of monostable pushed front.
Elliptic Equation and New Solutions to Nonlinear Wave Equations
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.
Travelling wave solutions for higher-order wave equations of kdv type (iii).
Li, Jibin; Rui, Weigou; Long, Yao; He, Bin
2006-01-01
By using the theory of planar dynamical systems to the travelling wave equation of a higher order nonlinear wave equations of KdV type, the existence of smooth solitary wave, kink wave and anti-kink wave solutions and uncountably infinite many smooth and non-smooth periodic wave solutions are proved. In different regions of the parametric space, the sufficient conditions to guarantee the existence of the above solutions are given. In some conditions, exact explicit parametric representations of these waves are obtain.
A Photonic mm-Wave Local Oscillator
Kimberk, R; Tong, C Y E; Blundell, R; Kimberk, Robert; Hunter, Todd R.; Blundell, Raymond
2006-01-01
A photonic millimeter wave local oscillator capable of producing two microwatts of radiated power at 224 GHz has been developed. The device was tested in one antenna of Smithsonian Institution's Submillimeter Array (SMA) and was found to produce stable phase on multiple baselines. Graphical data is presented of correlator output phase and amplitude stability. A description of the system is given in both open and closed loop modes. A model is given which is used to predict the operational behavior. A novel method is presented to determine the safe operating point of the automated system.
Exact Solitary Wave Solution in the ZK-BBM Equation
Juan Zhao
2014-01-01
Full Text Available The traveling wave solution for the ZK-BBM equation is considered, which is governed by a nonlinear ODE system. The bifurcation structure of fixed points and bifurcation phase portraits with respect to the wave speed c are analyzed by using the dynamical system theory. Furthermore, the exact solutions of the homoclinic orbits for the nonlinear ODE system are obtained which corresponds to the solitary wave solution curve of the ZK-BBM equation.
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.
Travelling-wave solutions bifurcating from relative periodic orbits in plane Poiseuille flow
Rawat, Subhendu; Rincon, François
2016-01-01
Travelling-wave solutions are shown to bifurcate from relative periodic orbits in plane Poiseuille flow at Re = 2000 in a saddle-node infinite period bifurcation. These solutions consist in self-sustaining sinuous quasi-streamwise streaks and quasi- streamwise vortices located in the bulk of the flow. The lower branch travelling-wave solutions evolve into spanwise localized states when the spanwise size Lz of the domain in which they are computed is increased. On the contrary, upper branch of travelling-wave solutions develop multiple streaks when Lz is increased. Upper branch travelling-wave solutions can be continued into coherent solutions of the filtered equations used in large-eddy simulations where they represent turbulent coherent large-scale motions.
Dynamics and Bifurcations of Travelling Wave Solutions of (, ) Equations
Dahe Feng; Jibin Li
2007-11-01
By using the bifurcation theory and methods of planar dynamical systems to (, ) equations, the dynamical behavior of different physical structures like smooth and non-smooth solitary wave, kink wave, smooth and non-smooth periodic wave, and breaking wave is obtained. The qualitative change in the physical structures of these waves is shown to depend on the systemic parameters. Under different regions of parametric spaces, various sufficient conditions to guarantee the existence of the above waves are given. Moreover, some explicit exact parametric representations of travelling wave solutions are listed.
Asymptotic traveling wave solution for a credit rating migration problem
Liang, Jin; Wu, Yuan; Hu, Bei
2016-07-01
In this paper, an asymptotic traveling wave solution of a free boundary model for pricing a corporate bond with credit rating migration risk is studied. This is the first study to associate the asymptotic traveling wave solution to the credit rating migration problem. The pricing problem with credit rating migration risk is modeled by a free boundary problem. The existence, uniqueness and regularity of the solution are obtained. Under some condition, we proved that the solution of our credit rating problem is convergent to a traveling wave solution, which has an explicit form. Furthermore, numerical examples are presented.
Launching transverse-electric Localized Waves from a circular waveguide
Salem, Mohamed
2011-07-01
Axially symmetric transverse electric (TE) modes of a circular waveguide section are used to synthesize the vector TE Localized Wave (LW) field at the open end of the waveguide section. The necessary excitation coefficients of these modes are obtained by the method of matching, taking advantage of the modal power orthogonality relations. The necessary excitation of modes provided by a number of coaxial loop antennas inserted inside the waveguide section. The antennas currents are computed from the solution of the waveguide excitation inverse problem. The accuracy of the synthesized wave field (compared to the mathematical model) and the power efficiency of the generation technique are evaluated in order to practically realize a launcher for LWs in the microwave regime. © 2011 IEEE.
Explicit Traveling Wave Solutions to Nonlinear Evolution Equations
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.
Travelling wave solution of the Buckley-Leverett equation
Tychkov, Sergey
2016-09-01
A two-dimensional Buckley-Leverett system governing motion of two-phase flow is considered. Travelling-wave solutions for these equations are found. Wavefronts of these solutions may be circles, lines and parabolae. Values of pressure and saturation on the wave fronts are found.
Peaked Periodic Wave Solutions to the Broer–Kaup Equation
Jiang, Bo; Bi, Qin-Sheng
2017-01-01
By qualitative analysis method, a sufficient condition for the existence of peaked periodic wave solutions to the Broer–Kaup equation is given. Some exact explicit expressions of peaked periodic wave solutions are also presented. Supported by National Nature Science Foundation of China under Grant No. 11102076 and Natural Science Fund for Colleges and Universities in Jiangsu Province under Grant No. 15KJB110005
Effect of wave localization on plasma instabilities. Ph. D. Thesis
Levedahl, W.K.
1987-10-01
The Anderson model of wave localization in random media is involved to study the effect of solar wind density turbulence on plasma processes associated with the solar type III radio burst. ISEE-3 satellite data indicate that a possible model for the type III process is the parametric decay of Langmuir waves excited by solar flare electron streams into daughter electromagnetic and ion acoustic waves. The threshold for this instability, however, is much higher than observed Langmuir wave levels because of rapid wave convection of the transverse electromagnetic daughter wave in the case where the solar wind is assumed homogeneous. Langmuir and transverse waves near critical density satisfy the Ioffe-Reigel criteria for wave localization in the solar wind with observed density fluctuations -1 percent. Numerical simulations of wave propagation in random media confirm the localization length predictions of Escande and Souillard for stationary density fluctations. For mobile density fluctuations localized wave packets spread at the propagation velocity of the density fluctuations rather than the group velocity of the waves. Computer simulations using a linearized hybrid code show that an electron beam will excite localized Langmuir waves in a plasma with density turbulence. An action principle approach is used to develop a theory of non-linear wave processes when waves are localized. A theory of resonant particles diffusion by localized waves is developed to explain the saturation of the beam-plasma instability. It is argued that localization of electromagnetic waves will allow the instability threshold to be exceeded for the parametric decay discussed above.
Enhancing propagation characteristics of truncated localized waves in silica
Salem, Mohamed
2011-07-01
The spectral characteristics of truncated Localized Waves propagating in dispersive silica are analyzed. Numerical experiments show that the immunity of the truncated Localized Waves propagating in dispersive silica to decay and distortion is enhanced as the non-linearity of the relation between the transverse spatial spectral components and the wave vector gets stronger, in contrast to free-space propagating waves, which suffer from early decay and distortion. © 2011 IEEE.
Localized waves in three-component coupled nonlinear Schrödinger equation
Xu, Tao; Chen, Yong
2016-09-01
We study the generalized Darboux transformation to the three-component coupled nonlinear Schrödinger equation. First- and second-order localized waves are obtained by this technique. In first-order localized wave, we get the interactional solutions between first-order rogue wave and one-dark, one-bright soliton respectively. Meanwhile, the interactional solutions between one-breather and first-order rogue wave are also given. In second-order localized wave, one-dark-one-bright soliton together with second-order rogue wave is presented in the first component, and two-bright soliton together with second-order rogue wave are gained respectively in the other two components. Besides, we observe second-order rogue wave together with one-breather in three components. Moreover, by increasing the absolute values of two free parameters, the nonlinear waves merge with each other distinctly. These results further reveal the interesting dynamic structures of localized waves in the three-component coupled system. Project supported by the Global Change Research Program of China (Grant No. 2015CB953904), the National Natural Science Foundation of China (Grant Nos. 11275072 and 11435005), the Doctoral Program of Higher Education of China (Grant No. 20120076110024), the Network Information Physics Calculation of Basic Research Innovation Research Group of China (Grant No. 61321064), and Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things, China (Grant No. ZF1213).
A multimodal wave spectrum-based approach for statistical downscaling of local wave climate
Hegermiller, Christie; Antolinez, Jose A A; Rueda, Ana C; Camus, Paula; Perez, Jorge; Erikson, Li; Barnard, Patrick; Mendez, Fernando J.
2017-01-01
Characterization of wave climate by bulk wave parameters is insufficient for many coastal studies, including those focused on assessing coastal hazards and long-term wave climate influences on coastal evolution. This issue is particularly relevant for studies using statistical downscaling of atmospheric fields to local wave conditions, which are often multimodal in large ocean basins (e.g. the Pacific). Swell may be generated in vastly different wave generation regions, yielding complex wave spectra that are inadequately represented by a single set of bulk wave parameters. Furthermore, the relationship between atmospheric systems and local wave conditions is complicated by variations in arrival time of wave groups from different parts of the basin. Here, we address these two challenges by improving upon the spatiotemporal definition of the atmospheric predictor used in statistical downscaling of local wave climate. The improved methodology separates the local wave spectrum into “wave families,” defined by spectral peaks and discrete generation regions, and relates atmospheric conditions in distant regions of the ocean basin to local wave conditions by incorporating travel times computed from effective energy flux across the ocean basin. When applied to locations with multimodal wave spectra, including Southern California and Trujillo, Peru, the new methodology improves the ability of the statistical model to project significant wave height, peak period, and direction for each wave family, retaining more information from the full wave spectrum. This work is the base of statistical downscaling by weather types, which has recently been applied to coastal flooding and morphodynamic applications.
New traveling wave solutions for nonlinear evolution equations
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.
ON TRANSMISSION PROBLEM FOR VISCOELASTIC WAVE EQUATION WITH A LOCALIZED A NONLINEAR DISSIPATION
Jeong Ja BAE; Seong Sik KIM
2013-01-01
In this article,we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physically different types of materials,one component being a Kirchhoff type wave equation with time dependent localized dissipation which is effective only on a neighborhood of certain part of boundary,while the other being a Kirchhoff type viscoelastic wave equation with nonlinear memory.
Jeong Ja Bae
2012-01-01
In this article,we consider the global existence and decay rates of solutions for the transmission problem of Kirchhoff type wave equations consisting of two physically different types of materials,one component is a Kirchhoff type wave equation with nonlinear time dependent localized dissipation which is effective only on a neighborhood of certain part of the boundary,while the other is a Kirchhoff type wave equation with nonlinear memory.
Stability of traveling wave solutions to the Whitham equation
Sanford, Nathan, E-mail: nathansanford2013@u.northwestern.edu [Mathematics Department, Seattle University, 901 12th Avenue, Seattle, WA 98122 (United States); Kodama, Keri, E-mail: kodamak@seattleu.edu [Mathematics Department, Seattle University, 901 12th Avenue, Seattle, WA 98122 (United States); Carter, John D., E-mail: carterj1@seattleu.edu [Mathematics Department, Seattle University, 901 12th Avenue, Seattle, WA 98122 (United States); Kalisch, Henrik, E-mail: Henrik.Kalisch@math.uib.no [Department of Mathematics, University of Bergen, Postbox 7800, 5020 Bergen (Norway)
2014-06-13
The Whitham equation was proposed as an alternate model equation for the simplified description of unidirectional wave motion at the surface of an inviscid fluid. An advantage of the Whitham equation over the KdV equation is that it provides a more faithful description of short waves of small amplitude. Recently, Ehrnström and Kalisch [19] established that the Whitham equation admits periodic traveling-wave solutions. The focus of this work is the stability of these solutions. The numerical results presented here suggest that all large-amplitude solutions are unstable, while small-amplitude solutions with large enough wavelength L are stable. Additionally, periodic solutions with wavelength smaller than a certain cut-off period always exhibit modulational instability. The cut-off wavelength is characterized by kh{sub 0}=1.145, where k=2π/L is the wave number and h{sub 0} is the mean fluid depth. - Highlights: • The Whitham equation is used as a model for waves on shallow water. • The Whitham equation admits periodic traveling-wave solutions. • All large-amplitude traveling-wave Whitham solutions are unstable. • Small-amplitude solutions with sufficient period are stable.
Localized standing waves in inhomogeneous Schrodinger equations
Marangell, R; Susanto, H
2010-01-01
A nonlinear Schrodinger equation arising from light propagation down an inhomogeneous medium is considered. The inhomogeneity is reflected through a non-uniform coefficient of the non-linear term in the equation. In particular, a combination of self-focusing and self-defocusing nonlinearity, with the self-defocusing region localized in a finite interval, is investigated. Using numerical computations, the extension of linear eigenmodes of the corresponding linearized system into nonlinear states is established, particularly nonlinear continuations of the fundamental state and the first excited state. The (in)stability of the states is also numerically calculated, from which it is obtained that symmetric nonlinear solutions become unstable beyond a critical threshold norm. Instability of the symmetric states is then investigated analytically through the application of a topological argument. Determination of instability of positive symmetric states is reduced to simple geometric properties of the composite phas...
BIFURCATIONS OF TRAVELLING WAVE SOLUTIONS FOR GENERALIZED DRINFELD-SOKOLOV EQUATIONS
LONG Yao; RUI Wei-guo; HE Bin; CHEN Can
2006-01-01
Ansatz method and the theory of dynamical systems are used to study the traveling wave solutions for the generalized Drinfeld-Sokolov equations. Under two groups .of the parametric conditions, more solitary wave solutions, kink and anti-kink wave solutions and periodic wave solutions are obtained. Exact explicit parametric representations of these travelling wave solutions are given.
Stability of traveling wave solutions to the Whitham equation
Sanford, Nathan; Kodama, Keri; Carter, John D.; Kalisch, Henrik
2014-06-01
The Whitham equation was proposed as an alternate model equation for the simplified description of unidirectional wave motion at the surface of an inviscid fluid. An advantage of the Whitham equation over the KdV equation is that it provides a more faithful description of short waves of small amplitude. Recently, Ehrnström and Kalisch [19] established that the Whitham equation admits periodic traveling-wave solutions. The focus of this work is the stability of these solutions. The numerical results presented here suggest that all large-amplitude solutions are unstable, while small-amplitude solutions with large enough wavelength L are stable. Additionally, periodic solutions with wavelength smaller than a certain cut-off period always exhibit modulational instability. The cut-off wavelength is characterized by kh0=1.145, where k=2π/L is the wave number and h0 is the mean fluid depth.
S S Ghosh; A Sen; G S Lakhina
2000-11-01
The nonlinear evolution of an electron acoustic wave is shown to obey the Davey–Stewartson I equation which admits so called dromion solutions. The importance of these two dimensional localized solutions for recent satellite observations of wave structures in the day side polar cap regions is discussed and the parameter regimes for their existence is delineated.
YANG Qiu-Ying; MA Song-Hua; ZHANG Ying-Yue; FANG Jian-Ping; CHEN Tian-Lun; HONG Bi-Hai; ZHENG Chun-Long
2008-01-01
By means of an extended mapping approach and a linear variable separation approach, a new family of exact solutions of the (3+1)-dimensional Jimbo-Miwa system is derived. Based on the derived solitary wave solution, we obtain some special localized excitations and study the interactions between two solitary waves of the system.
Standing Wave Solutions in Nonhomogeneous Delayed Synaptically Coupled Neuronal Networks
ZHANG Linghai; STONER Melissa Anne
2012-01-01
The authors establish the existence and stability of standing wave solutions of a nonlinear singularly perturbed system of integral differential equations and a nonlinear scalar integral differential equation.It will be shown that there exist six standing wave solutions ((u(x,t),w(x,t)) =(U(x),W(x)) to the nonlinear singularly perturbed system of integral differential equations.Similarly,there exist six standing wave solutions u(x,t) =U(x) to the nonlinear scalar integral differential equation.The main idea to establish the stability is to construct Evans functions corresponding to several associated eigenvalue problems.
Full Wave Solution for Hydrodynamic Behaviors of Pile Breakwater
ZHU Da-tong
2013-01-01
Rayleigh expansion is used to study the water-wave interaction with a row of pile breakwater in finite water depth.Evanescent waves,the wave energy dissipated on the fluid resistance and the thickness of the breakwater are totally included in the model.The formulae of wave reflection and transmission coefficients are obtained.The accuracy of the present model is verified by a comparison with existing results.It is found that the predicted wave reflection and transmission coefficients for the zero order are all highly consistent with the experimental data (Hagiwara,1984;Isaacson et al.,1998) and plane wave solutions (Zhu,2011).The losses of the wave energy for the fluid passing through slits play an important role,which removes the phenomena of enhanced wave transmission.
Finite difference solutions to shocked acoustic waves
Walkington, N. J.; Eversman, W.
1983-01-01
The MacCormack, Lambda and split flux finite differencing schemes are used to solve a one dimensional acoustics problem. Two duct configurations were considered, a uniform duct and a converging-diverging nozzle. Asymptotic solutions for these two ducts are compared with the numerical solutions. When the acoustic amplitude and frequency are sufficiently high the acoustic signal shocks. This condition leads to a deterioration of the numerical solutions since viscous terms may be required if the shock is to be resolved. A continuous uniform duct solution is considered to demonstrate how the viscous terms modify the solution. These results are then compared with a shocked solution with and without viscous terms. Generally it is found that the most accurate solutions are those obtained using the minimum possible viscosity coefficients. All of the schemes considered give results accurate enough for acoustic power calculations with no one scheme performing significantly better than the others.
Global infinite energy solutions for the cubic wave equation
Burq, N.; L. Thomann; Tzvetkov, N.
2012-01-01
International audience; We prove the existence of infinite energy global solutions of the cubic wave equation in dimension greater than 3. The data is a typical element on the support of suitable probability measures.
Cantor families of periodic solutions for completely resonant wave equations
2008-01-01
We present recent existence results of Cantor families of small amplitude periodic solutions for completely resonant nonlinear wave equations. The proofs rely on the Nash-Moser implicit function theory and variational methods.
SOLUTION OF A KIND OF LINEAR INTERNAL WAVE EQUATION
WANG Gang; HOU Yi-jun; ZHENG Quan-an
2005-01-01
Considering the effect of horizontal Coriolis parameter and the density compactness of seawater, which were often neglected in internal waves discussion, the governing equation of linear internal waves presented by vertical velocity only will be proposed. Under the assumption that the Brunt-Visl frequency is exponential, an accurate analytic solution of it is obtained. Finally, the expressions of wave functions are also given.
Traveling wave front solutions in lateral-excitatory neuronal networks
Sittipong Ruktamatakul
2008-05-01
Full Text Available In this paper, we discuss the shape of traveling wave front solutions to a neuronal model with the connection function to be of lateral excitation type. This means that close connecting cells have an inhibitory influence, while cells that aremore distant have an excitatory influence. We give results on the shape of the wave fronts solutions, which exhibit different shapes depend ing on the size of a threshold parameter.
Travelling wave solutions for ( + 1)-dimensional nonlinear evolution equations
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.
Travelling wave-like solutions of the Zakharov-Kuznetsov equation with variable coefficients
Yan-Ze Peng; E V Krishnan; Hui Feng
2008-07-01
Travelling wave-like solutions of the Zakharov-Kuznetsov equation with variable coefficients are studied using the solutions of Raccati equation. The solitary wave-like solution, the trigonometric periodic wave solution and the rational wave solution are obtained with a constraint between coefficients. The property of the solutions is numerically investigated. It is shown that the coefficients of the equation do not change the wave amplitude, but may change the wave velocity.
Exact Solitary Wave and Periodic Wave Solutions of a Class of Higher-Order Nonlinear Wave Equations
Lijun Zhang
2015-01-01
Full Text Available We study the exact traveling wave solutions of a general fifth-order nonlinear wave equation and a generalized sixth-order KdV equation. We find the solvable lower-order subequations of a general related fourth-order ordinary differential equation involving only even order derivatives and polynomial functions of the dependent variable. It is shown that the exact solitary wave and periodic wave solutions of some high-order nonlinear wave equations can be obtained easily by using this algorithm. As examples, we derive some solitary wave and periodic wave solutions of the Lax equation, the Ito equation, and a general sixth-order KdV equation.
Luchko, Yuri; Povstenko, Yuriy
2012-01-01
In this paper, the one-dimensional time-fractional diffusion-wave equation with the fractional derivative of order $1 \\le \\alpha \\le 2$ is revisited. This equation interpolates between the diffusion and the wave equations that behave quite differently regarding their response to a localized disturbance: whereas the diffusion equation describes a process, where a disturbance spreads infinitely fast, the propagation speed of the disturbance is a constant for the wave equation. For the time fractional diffusion-wave equation, the propagation speed of a disturbance is infinite, but its fundamental solution possesses a maximum that disperses with a finite speed. In this paper, the fundamental solution of the Cauchy problem for the time-fractional diffusion-wave equation, its maximum location, maximum value, and other important characteristics are investigated in detail. To illustrate analytical formulas, results of numerical calculations and plots are presented. Numerical algorithms and programs used to produce pl...
Xu Chang-Zhi; He Bao-Gang; Zhang Jie-Fang
2004-01-01
A variable separation approach is proposed and extended to the (1+1)-dimensional physical system. The variable separation solutions of (1+1)-dimensional equations of long-wave-short-wave resonant interaction are obtained. Some special type of solutions such as soliton solution, non-propagating solitary wave solution, propagating solitary wave solution, oscillating solitary wave solution are found by selecting the arbitrary function appropriately.
EVANS FUNCTIONS AND ASYMPTOTIC STABILITY OF TRAVELING WAVE SOLUTIONS
无
2001-01-01
This paper studies the asymptotic stability of traveling wave solutions of nonlinear systems of integral-differential equations. It has been established that linear stability of traveling waves is equivalent to nonlinear stability and some “nice structure” of the spectrum of an associated operator implies the linear stability. By using the method of variation of parameter, the author defines some complex analytic function, called the Evans function. The zeros of the Evans function corresponds to the eigenvalues of the associated linear operator. By calculating the zeros of the Evans function, the asymptotic stability of the travling wave solutions is established.
Wave localization in randomly disordered periodic layered piezoelectric structures
Fengming Li; Yuesheng Wang; Chao Hu; Wenhu Huang
2006-01-01
Considering the mechnoelectrical coupling,the localization of SH-waves in disordered periodic layered piezoelectric structures is studied.The waves propagating in directions normal and tangential to the layers are considered.The transfer matrices between two consecutive unit cells are obtained according to the continuity conditions.The expressions of localization factor and localization length in the disordered periodic structures are presented.For the disordered periodic piezoelectric structures,the numerical results of localization factor and localization length are presented and discussed.It can be seen from the results that the fequency passbands and stopbands appear for the ordered periodic structures and the wave localization phenomenon occurs in the disordered periodic ones,and the larger the coefficient of variation is,the greater the degree of wave localization is.The widths of stopbands in the ordered periodic structures are very narrow when the properties of the consecutive piezoelectric materials are similar and the intervals of stopbands become broader when a certain material parameter has large changes.For the wave propagating in the direction normal to the layers the localization length has less dependence on the frequency,but for the wave propagating in the direction tangential to the layers the localization length is strongly dependent on the frequency.
Numerical Modelling of Wind Waves. Problems, Solutions, Verifications, and Applications
Polnikov, Vladislav
2011-01-01
The time-space evolution of the field is described by the transport equation for the 2-dimensional wave energy spectrum density, S(x,t), spread in the space, x, and time, t. This equation has the forcing named the source function, F, depending on both the wave spectrum, S, and the external wave-making factors: local wind, W(x, t), and local current, U(x, t). The source function contains certain physical mechanisms responsible for a wave spectrum evolution. It is used to distinguish three terms in function F: the wind-wave energy exchange mechanism, In; the energy conservative mechanism of nonlinear wave-wave interactions, Nl; and the wave energy loss mechanism, Dis. Differences in mathematical representation of the source function terms determine general differences between wave models. The problem is to derive analytical representations for the source function terms said above from the fundamental wave equations. Basing on publications of numerous authors and on the last two decades studies of the author, th...
New exact wave solutions for Hirota equation
M Eslami; M A Mirzazadeh; A Neirameh
2015-01-01
In this paper, we construct the topological or dark solitons of Hirota equation by using the first integral method. This approach provides first integrals in polynomial form with a high accuracy for two-dimensional plane autonomous systems. Exact soliton solution is constructed through the established first integrals. This method is a powerful tool for searching exact travelling solutions of nonlinear partial differential equations (NPDEs) in mathematical physics.
Frank, Scott D; Collis, Jon M; Odom, Robert I
2015-06-01
Oceanic T-waves are earthquake signals that originate when elastic waves interact with the fluid-elastic interface at the ocean bottom and are converted to acoustic waves in the ocean. These waves propagate long distances in the Sound Fixing and Ranging (SOFAR) channel and tend to be the largest observed arrivals from seismic events. Thus, an understanding of their generation is important for event detection, localization, and source-type discrimination. Recently benchmarked seismic self-starting fields are used to generate elastic parabolic equation solutions that demonstrate generation and propagation of oceanic T-waves in range-dependent underwater acoustic environments. Both downward sloping and abyssal ocean range-dependent environments are considered, and results demonstrate conversion of elastic waves into water-borne oceanic T-waves. Examples demonstrating long-range broadband T-wave propagation in range-dependent environments are shown. These results confirm that elastic parabolic equation solutions are valuable for characterization of the relationships between T-wave propagation and variations in range-dependent bathymetry or elastic material parameters, as well as for modeling T-wave receptions at hydrophone arrays or coastal receiving stations.
NEW EXACT TRAVELLING WAVE SOLUTIONS TO THREE NONLINEAR EVOLUTION EQUATIONS
Sirendaoreji
2004-01-01
Based on the computerized symbolic computation, some new exact travelling wave solutions to three nonlinear evolution equations are explicitly obtained by replacing the tanhξ in tanh-function method with the solutions of a new auxiliary ordinary differential equation.
Exponential decay for solutions to semilinear damped wave equation
Gerbi, Stéphane
2011-10-01
This paper is concerned with decay estimate of solutions to the semilinear wave equation with strong damping in a bounded domain. Intro- ducing an appropriate Lyapunov function, we prove that when the damping is linear, we can find initial data, for which the solution decays exponentially. This result improves an early one in [4].
AdS Waves as Exact Solutions to Quadratic Gravity
Gullu, Ibrahim; Sisman, Tahsin Cagri; Tekin, Bayram
2011-01-01
We give an exact solution of the quadratic gravity in D dimensions. The solution is a plane fronted wave metric with a cosmological constant. This metric solves not only the full quadratic gravity field equations but also the linearized ones which include the linearized equations of the recently found critical gravity.
Peralta, J.; López-Valverde, M. A. [Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía, 18008 Granada (Spain); Imamura, T. [Institute of Space and Astronautical Science-Japan Aerospace Exploration Agency 3-1-1, Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210 (Japan); Read, P. L. [Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford (United Kingdom); Luz, D. [Centro de Astronomia e Astrofísica da Universidade de Lisboa (CAAUL), Observatório Astronómico de Lisboa, Tapada da Ajuda, 1349-018 Lisboa (Portugal); Piccialli, A., E-mail: peralta@iaa.es [LATMOS, UVSQ, 11 bd dAlembert, 78280 Guyancourt (France)
2014-07-01
This paper is the second in a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases where the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the background wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this second part, we study the waves' solutions when several atmospheric approximations are applied: Lamb, surface, and centrifugal waves. Lamb and surface waves are found to be quite similar to those in a geostrophic regime. By contrast, centrifugal waves turn out to be a special case of Rossby waves that arise in atmospheres in cyclostrophic balance. Finally, we use our results to identify the nature of the waves behind atmospheric periodicities found in polar and lower latitudes of Venus's atmosphere.
Exact travelling wave solutions for some important nonlinear physical models
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.
Stokes Waves Revisited: Exact Solutions in the Asymptotic Limit
Davies, Megan
2016-01-01
Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The weakling in this structure though is the presence of aperiodic secular variation in the solution that does not agree with the known periodic propagation of surface waves. This has historically necessitated increasingly higher ordered (perturbative) approximations in the representation of the velocity profile. The present article ameliorates this long standing theoretical insufficiency by invoking a compact exact $n$-ordered solution in the asymptotic infinite depth limit, primarily based on a representation structured around the third ordered perturbative solution, that leads to a seamless extension to higher order (e.g. fifth order) forms existing in the literature. The result from this study is expected to improve phenomenological engineering estimates, now that any desir...
Solitary wave solutions to nonlinear evolution equations in mathematical physics
Anwar Ja’afar Mohamad Jawad; M Mirzazadeh; Anjan Biswas
2014-10-01
This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan–cot method and functional variable approaches. The soliton solutions can be used in the further study of shallow water waves in (1+1) as well as (2+1) dimensions.
Symmetry groups and spiral wave solution of a wave propagation equation
张全举; 屈长征
2002-01-01
We study a third-order nonlinear evolution equation, which can be transformed to the modified KdV equation,using the Lie symmetry method. The Lie point symmetries and the one-dimensional optimal system of the symmetryalgebras are determined. Those symmetries are some types of nonlocal symmetries or hidden symmetries of the modifiedKdV equation. The group-invariant solutions, particularly the travelling wave and spiral wave solutions, are discussedin detail, and a type of spiral wave solution which is smooth in the origin is obtained.
Local Runup Amplification By Resonant Wave Interactions
Stefanakis, Themistoklis; Dutykh, Denys
2011-01-01
Until now the analysis of long wave runup on a plane beach has been focused on finding its maximum value, failing to capture the existence of resonant regimes. One-dimensional numerical simulations in the framework of the Nonlinear Shallow Water Equations (NSWE) are used to investigate the Boundary Value Problem (BVP) for plane and non-trivial beaches. Monochromatic waves, as well as virtual wave-gage recordings from real tsunami simulations, are used as forcing conditions to the BVP. Resonant phenomena between the incident wavelength and the beach slope are found to occur, which result in enhanced runup of non-leading waves. The evolution of energy reveals the existence of a quasi-periodic state for the case of sinusoidal waves, the energy level of which, as well as the time required to reach that state, depend on the incident wavelength for a given beach slope. Dispersion is found to slightly reduce the value of maximum runup, but not to change the overall picture. Runup amplification occurs for both leadin...
Wang, Ying; Guo, Yunxi
2017-09-01
In this paper, we developed, for the first time, the exact expressions of several periodic travelling wave solutions and a solitary wave solution for a shallow water wave model of moderate amplitude. Then, we present the existence theorem of the global weak solutions. Finally, we prove the stability of solution in L1(R) space for the Cauchy problem of the equation.
Wang, Ying; Guo, Yunxi
2016-07-01
In this paper, we developed, for the first time, the exact expressions of several periodic travelling wave solutions and a solitary wave solution for a shallow water wave model of moderate amplitude. Then, we present the existence theorem of the global weak solutions. Finally, we prove the stability of solution in L1(R) space for the Cauchy problem of the equation.
Kink-Like Wave and Compacton-Like Wave Solutions for a Two-Component Fornberg-Whitham Equation
Shaoyong Li
2014-01-01
systems, we study a two-component Fornberg-Whitham equation. Two types of bounded traveling wave solutions are found, that is, the kink-like wave and compacton-like wave solutions. The planar graphs of these solutions are simulated by using software Mathematica; meanwhile, two new phenomena are revealed; that is, the periodic wave solution can become the kink-like wave or compacton-like wave solution under some conditions, respectively. Exact implicit or parameter expressions of these solutions are given.
Localized Pulsating Solutions of the Generalized Complex Cubic-Quintic Ginzburg-Landau Equation
Ivan M. Uzunov; Georgiev, Zhivko D.
2014-01-01
We study the dynamics of the localized pulsating solutions of generalized complex cubic-quintic Ginzburg-Landau equation (CCQGLE) in the presence of intrapulse Raman scattering (IRS). We present an approach for identification of periodic attractors of the generalized CCQGLE. Using ansatz of the travelling wave and fixing some relations between the material parameters, we derive the strongly nonlinear Lienard-Van der Pol equation for the amplitude of the nonlinear wave. Next, we apply the Meln...
Xu, Jian-Jun
1989-01-01
The complicated dendritic structure of a growing needle crystal is studied on the basis of global interfacial wave theory. The local dispersion relation for normal modes is derived in a paraboloidal coordinate system using the multiple-variable-expansion method. It is shown that the global solution in a dendrite growth process incorporates the morphological instability factor and the traveling wave factor.
Traveling wave solutions for reaction-diffusion systems
Pedersen, Michael; Lin, Zhigui; Tian, Canrong
2010-01-01
This paper is concerned with traveling waves of reaction–diffusion systems. The definition of coupled quasi-upper and quasi-lower solutions is introduced for systems with mixed quasimonotone functions, and the definition of ordered quasi-upper and quasi-lower solutions is also given for systems...... with quasimonotone nondecreasing functions. By the monotone iteration method, it is shown that if the system has a pair of coupled quasi-upper and quasi-lower solutions, then there exists at least a traveling wave solution. Moreover, if the system has a pair of ordered quasi-upper and quasi-lower solutions......, then there exists at least a traveling wavefront. As an application we consider the delayed system of a mutualistic model....
On Mooring Solutions for Large Wave Energy Converters
Thomsen, Jonas Bjerg; Kofoed, Jens Peter; Ferri, Francesco
2017-01-01
The present paper describes the work carried out in the project ’Mooring Solutions for Large Wave Energy Converters’, which is a Danish research project carried out in a period of three years from September 2014, with the aim of reducing cost of the moorings for four wave energy converters......-model based optimization process with the aim of optimizing the mooring layout for each WEC according to cost of the systems....
AN ASYMPTOTIC SOLUTION OF VELOCITY FIELD IN SHIP WAVES
WU Yun-gang; TAO Ming-de
2006-01-01
The stationary phase method in conventional Lighthill's two-stage scheme to get the expressions of the velocity field was given up in this paper. The method that Ursell had used in deducing the elevation expression of ship wave was adopted, and an asymptotic solution of velocity field of ship waves on an inviscid fluid that is perfectly fit for the region inside and outside the critical lines was obtained. It is very convenient to be used in SAR technique.
Traveling Wave Solutions of the Benjamin-Bona-Mahony Water Wave Equations
A. R. Seadawy
2014-01-01
Full Text Available The modeling of unidirectional propagation of long water waves in dispersive media is presented. The Korteweg-de Vries (KdV and Benjamin-Bona-Mahony (BBM equations are derived from water waves models. New traveling solutions of the KdV and BBM equations are obtained by implementing the extended direct algebraic and extended sech-tanh methods. The stability of the obtained traveling solutions is analyzed and discussed.
Peralta, J.; López-Valverde, M. A. [Instituto de Astrofísica de Andalucía (CSIC), Glorieta de la Astronomía, 18008 Granada (Spain); Imamura, T. [Institute of Space and Astronautical Science-Japan Aerospace Exploration Agency 3-1-1, Yoshinodai, Chuo-ku, Sagamihara, Kanagawa 252-5210 (Japan); Read, P. L. [Department of Physics, University of Oxford, Clarendon Laboratory, Parks Road, Oxford (United Kingdom); Luz, D. [Centro de Astronomia e Astrofísica da Universidade de Lisboa (CAAUL), Observatório Astronómico de Lisboa, Tapada da Ajuda, 1349-018 Lisboa (Portugal); Piccialli, A., E-mail: peralta@iaa.es [LATMOS, UVSQ, 11 bd dAlembert, 78280 Guyancourt (France)
2014-07-01
This paper is the first of a two-part study devoted to developing tools for a systematic classification of the wide variety of atmospheric waves expected on slowly rotating planets with atmospheric superrotation. Starting with the primitive equations for a cyclostrophic regime, we have deduced the analytical solution for the possible waves, simultaneously including the effect of the metric terms for the centrifugal force and the meridional shear of the background wind. In those cases when the conditions for the method of the multiple scales in height are met, these wave solutions are also valid when vertical shear of the background wind is present. A total of six types of waves have been found and their properties were characterized in terms of the corresponding dispersion relations and wave structures. In this first part, only waves that are direct solutions of the generic dispersion relation are studied—acoustic and inertia-gravity waves. Concerning inertia-gravity waves, we found that in the cases of short horizontal wavelengths, null background wind, or propagation in the equatorial region, only pure gravity waves are possible, while for the limit of large horizontal wavelengths and/or null static stability, the waves are inertial. The correspondence between classical atmospheric approximations and wave filtering has been examined too, and we carried out a classification of the mesoscale waves found in the clouds of Venus at different vertical levels of its atmosphere. Finally, the classification of waves in exoplanets is discussed and we provide a list of possible candidates with cyclostrophic regimes.
Kink wave determined by parabola solution of a nonlinear ordinary differential equation
LI Ji-bin; LI Ming; NA Jing
2007-01-01
By finding a parabola solution connecting two equilibrium points of a planar dynamical system, the existence of the kink wave solution for 6 classes of nonlinear wave equations is shown. Some exact explicit parametric representations of kink wave solutions are given. Explicit parameter conditions to guarantee the existence of kink wave solutions are determined.
Dynamics of localized structures in vector waves
Hernández-García, E; Colet, P; San Miguel, M; Hernandez-Garcia, Emilio; Hoyuelos, Miguel; Colet, Pere; Miguel, Maxi San
1999-01-01
Dynamical properties of topological defects in a twodimensional complex vector field are considered. These objects naturally arise in the study of polarized transverse light waves. Dynamics is modeled by a Vector Complex Ginzburg-Landau Equation with parameter values appropriate for linearly polarized laser emission. Creation and annihilation processes, and selforganization of defects in lattice structures, are described. We find "glassy" configurations dominated by vectorial defects and a melting process associated to topological-charge unbinding.
Extended Long Wave Hindcast inside Port Solutions to Minimize Resonance
Gabriel Diaz-Hernandez
2016-02-01
Full Text Available The present study shows a methodology to carry out a comprehensive study of port agitation and resonance analysis in Geraldton Harbor (Western Australia. The methodology described and applied here extends the short and long wave hindcast outside the harbor and towards the main basin. To perform such an analysis, and as the first stage of the methodology, it is necessary to determine, in detail, both the long and short wave characteristics, through a comprehensive methodology to obtain and to hindcast the full spectral data (short waves + long waves, for frequencies between 0.005 and 1 Hz. Twelve-year spectral hindcast wave data, at a location before the reef, have been modified analytically to include the energy input associated with infragravity waves. A decomposition technique based on the energy balance of the radiation stress of short waves is followed. Predictions for long wave heights and periods at different harbor locations are predicted and validated with data recorded during 2004 to 2009. This new database will ensure an accurate and reliable assessment of long wave hourly data (height, period and currents in any area within the main basin of the Port of Geraldton, for its present geometry. With this information, two main task will be completed: (1 undertake a forensic diagnosis of the present response of the harbor, identifying those forcing characteristics related to inoperability events; and (2 propose any layout solutions to minimize, change, dissipate/fade/vanish or positively modify the effects of long waves in the harbor, proposing different harbor geometry modifications. The goal is to identify all possible combinations of solutions that would minimize the current inoperability in the harbor. Different pre-designs are assessed in this preliminary study in order to exemplify the potential of the methodology.
Exact Solutions for a Local Fractional DDE Associated with a Nonlinear Transmission Line
Aslan, İsmail
2016-09-01
Of recent increasing interest in the area of fractional calculus and nonlinear dynamics are fractional differential-difference equations. This study is devoted to a local fractional differential-difference equation which is related to a nonlinear electrical transmission line. Explicit traveling wave solutions (kink/antikink solitons, singular, periodic, rational) are obtained via the discrete tanh method coupled with the fractional complex transform.
On the minimal speed and asymptotics of the wave solutions for the lotka volterra system
Hou, Xiaojie
2010-01-01
e study the minimal wave speed and the asymptotics of the traveling wave solutions of a competitive Lotka Volterra system. The existence of the traveling wave solutions is derived by monotone iteration. The asymptotic behaviors of the wave solutions are derived by comparison argument and the exponential dichotomy, which seems to be the key to understand the geometry and the stability of the wave solutions. Also the uniqueness and the monotonicity of the waves are investigated via a generalized sliding domain method.
Enhanced localization of Dyakonov-like surface waves in left-handed materials
Crasovan, L. C.; Takayama, O.; Artigas, D.;
2006-01-01
We address the existence and properties of hybrid surface waves forming at interfaces between left-handed materials and dielectric birefringent media. The existence conditions of such waves are found to be highly relaxed in comparison to Dyakonov waves existing in right-handed media. We show...... that left-handed materials cause the coexistence of several surface solutions, which feature an enhanced degree of localization. Remarkably, we find that the hybrid surface modes appear for large areas in the parameter space, a key property in view of their experimental observation. © 2006 The American...
Local integration: a durable solution for refugees?
Ana Low
2006-05-01
Full Text Available UNHCR supports local integration as one possiblesolution for refugees who cannot return home. Experiencein Mexico, Uganda and Zambia indicates that integrationcan benefi t refugee-hosting communities as well asrefugees.
Local integration: reviving a forgotten solution
Alexandra Fielden
2008-04-01
Full Text Available A combination of historical trends, the changing policies ofgovernments and renewed efforts by UNHCR have all begunto strengthen the potential of local integration as a lastingsolution for refugees.
An Analytical Method of Auxiliary Sources Solution for Plane Wave Scattering by Impedance Cylinders
Larsen, Niels Vesterdal; Breinbjerg, Olav
2004-01-01
Analytical Method of Auxiliary Sources solutions for plane wave scattering by circular impedance cylinders are derived by transformation of the exact eigenfunction series solutions employing the Hankel function wave transformation. The analytical Method of Auxiliary Sources solution thus obtained...
Exact solution of equations for proton localization in neutron star matter
Kubis, Sebastian
2016-01-01
The rigorous treatment of proton localization phenomenon in asymmetric nuclear matter is presented. The solution of proton wave function and neutron background distribution is found by the use of the extended Thomas-Fermi approach. The minimum of energy is obtained in the Wigner- Seitz approximation of spherically symmetric cell. The analysis of three different nuclear models suggests that the proton localization is likely to take place in the interior of neutron star.
LOCAL CLASSICAL SOLUTIONS TO THE EQUATIONS OF RELATIVISTIC HYDRODYNAMICS
史一蓬
2001-01-01
In this paper, we prove that the convexity of the negative thermodynamical entropy of the equations of relativistic hydrodynamics for ideal gas keeps its invariance under the Lorentz transformation if and only if the local sound speed is less than the light speed in vacuum. Then a symmetric form for the equations of relativistic hydrodynamics is presented and the local classical solution is obtained. Based on this,we prove that the nonrelativistic limit of the local classical solution to the relativistic hydrodynamics equations for relativistic gas is the local classical solution of the Euler equations for polytropic gas.
EXACT SOLITARY WAVE SOLUTIONS OF THETWO NONLINEAR EVOLUTION EQUATIONS
ZhuYanjuan; ZhangChunhua
2005-01-01
The solitary wave solutions of the combined KdV-mKdV-Burgers equation and the Kolmogorov-Petrovskii-Piskunov equation are obtained by means of the direct algebra method, which can be generalized to deal with high dimensional nonlinear evolution equations.
Gravitational waves as exact solutions of Einstein field equations
Vilasi, G [Dipartimento di Fisica, Universita di Salerno Istituto Nazionale di Fisica Nucleare, Sezione di Napoli, Gruppo Collegato di Salerno Via S. Allende, I-84081 Baronissi (Salerno) (Italy)
2007-11-15
Exact solutions of Einstein field equations invariant for a non-Abelian 2-dimensional Lie algebra of Killing fields are described. A sub-class of these gravitational fields have a wave-like character; it is shown that they have spin-1.
Local Dynamics of Baroclinic Waves in the Martian Atmosphere
Kavulich, Michael J.
2013-11-01
The paper investigates the processes that drive the spatiotemporal evolution of baroclinic transient waves in the Martian atmosphere by a simulation experiment with the Geophysical Fluid Dynamics Laboratory (GFDL) Mars general circulation model (GCM). The main diagnostic tool of the study is the (local) eddy kinetic energy equation. Results are shown for a prewinter season of the Northern Hemisphere, in which a deep baroclinic wave of zonal wavenumber 2 circles the planet at an eastward phase speed of about 70° Sol-1 (Sol is a Martian day). The regular structure of the wave gives the impression that the classical models of baroclinic instability, which describe the underlying process by a temporally unstable global wave (e.g., Eady model and Charney model), may have a direct relevance for the description of the Martian baroclinic waves. The results of the diagnostic calculations show, however, that while the Martian waves remain zonally global features at all times, there are large spatiotemporal changes in their amplitude. The most intense episodes of baroclinic energy conversion, which take place in the two great plain regions (Acidalia Planitia and Utopia Planitia), are strongly localized in both space and time. In addition, similar to the situation for terrestrial baroclinic waves, geopotential flux convergence plays an important role in the dynamics of the downstream-propagating unstable waves. © 2013 American Meteorological Society.
Exact travelling wave solutions for four forms of nonlinear Klein-Gordon equations
Sirendaoreji [College of Mathematical Science, Inner Mongolia Normal University, Huhhot 010022, Inner Mongolia (China)]. E-mail: siren@imnu.edu.cn
2007-04-09
A variable separated equation and its solutions are used to construct the exact travelling wave solutions for four forms of nonlinear Klein-Gordon equations. The solutions previously obtained by the tanh and sech method are recovered. New and more exact travelling wave solutions including solitons, kink and anti-kink, bell and anti-bell solitary wave solutions, periodic solutions, singular solutions and exponential solutions are found.
Full-wave solution of short impulses in inhomogeneous plasma
Orsolya E Ferencz
2005-02-01
In this paper the problem of real impulse propagation in arbitrarily inhomogeneous media will be presented on a fundamentally new, general, theoretical way. The general problem of wave propagation of monochromatic signals in inhomogeneous media was enlightened in [1]. The earlier theoretical models for spatial inhomogeneities have some errors regarding the structure of the resultant signal originated from backward and forward propagating parts. The application of the method of inhomogeneous basic modes (MIBM) and the complete full-wave solution of arbitrarily shaped non-monochromatic plane waves in plasmas made it possible to obtain a better description of the problem, on a fully analytical way, directly from Maxwell's equations. The model investigated in this paper is inhomogeneous of arbitrary order (while the wave pattern can exist), anisotropic (magnetized), linear, cold plasma, in which the gradient of the one-dimensional spatial inhomogeneity is parallel to the direction of propagation.
Local Martingale and Pathwise Solutions for an Abstract Fluids Model
Debussche, Arnaud; Glatt-Holtz, Nathan; Temam, Roger
2010-01-01
We establish the existence and uniqueness of both local martingale and local pathwise solutions of an abstract nonlinear stochastic evolution system. The primary application of this abstract framework is to infer the local existence of strong, pathwise solutions to the 3D primitive equations of the oceans and atmosphere forced by a nonlinear multiplicative white noise. Instead of developing our results specifically for the 3D primitive equations we choose to develop them in a slightly abstrac...
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.
Exact travelling wave solutions of nonlinear partial differential equations
Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish) Suez Canal University, AL-Arish 45111 (Egypt)]. E-mail: asoliman_99@yahoo.com; Abdou, M.A. [Theoretical Research Group, Department of Physics, Faculty of Science, Mansoura University, Mansoura 35516 (Egypt)]. E-mail: m_abdou_eg@yahoo.com
2007-04-15
An extended Fan-sub equation method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. The key idea of this method is to take full advantage of the general elliptic equation, involving five parameters, which has more new solutions and whose degeneracies can lead to special sub equation involving three parameters. As an illustration of the extended Fan method, more new solutions are obtained for three models namely, generalized KdV, Drinfeld-Sokolov system and RLW equation.
Introduction to wave scattering, localization, and mesoscopic phenomena
Sheng, Ping
1995-01-01
This book gives readers a coherent picture of waves in disordered media, including multiple scattered waves. The book is intended to be self-contained, with illustrated problems and solutions at the end of each chapter to serve the double purpose of filling out the technical and mathematical details and giving the students exercises if used as a course textbook.The study of wave behavior in disordered media has applications in:Condensed matter physics (semi and superconductor nanostructures and mesoscopic phenomena)Materials science/analytical chemistry (analysis of composite and crystalline structures and properties)Optics and electronics (microelectronic and optoelectronic devices)Geology (seismic exploration of Earths subsurface)
Dynamical understanding of loop soliton solution for several nonlinear wave equations
Ji-bin LI
2007-01-01
It has been found that some nonlinear wave equations have one-loop soliton solutions. What is the dynamical behavior of the so-called one-loop soliton solution? To answer this question, the travelling wave solutions for four nonlinear wave equations are discussed. Exact explicit parametric representations of some special travelling wave solutions are given. The results of this paper show that a loop solution consists of three different breaking travelling wave solutions. It is not one real loop soliton travelling wave solution.
Hoeke, Ron; Hemer, Mark; Contardo, Stephanie; Symonds, Graham; Mcinnes, Kathy
2016-04-01
As demonstrated by the Australian Wave Energy Atlas (AWavEA), the southern and western margins of the country possess considerable wave energy resources. The Australia Government has made notable investments in pre-commercial wave energy developments in these areas, however little is known about how this technology may impact local wave climate and subsequently affect neighbouring coastal environments, e.g. altering sediment transport, causing shoreline erosion or accretion. In this study, a network of in-situ wave measurement devices have been deployed surrounding the 3 wave energy converters of the Carnegie Wave Energy Limited's Perth Wave Energy Project. This data is being used to develop, calibrate and validate numerical simulations of the project site. Early stage results will be presented and potential simulation strategies for scaling-up the findings to larger arrays of wave energy converters will be discussed. The intended project outcomes are to establish zones of impact defined in terms of changes in local wave energy spectra and to initiate best practice guidelines for the establishment of wave energy conversion sites.
Yong, Peng; Huang, Jianping; Li, Zhenchun; Liao, Wenyuan; Qu, Luping; Li, Qingyang; Liu, Peijun
2017-02-01
In finite-difference (FD) method, numerical dispersion is the dominant factor influencing the accuracy of seismic modelling. Various optimized FD schemes for scalar wave modelling have been proposed to reduce grid dispersion, while the optimized time-space domain FD schemes for elastic wave modelling have not been fully investigated yet. In this paper, an optimized FD scheme with Equivalent Staggered Grid (ESG) for elastic modelling has been developed. We start from the constant P- and S-wave speed elastic wave equations and then deduce analytical plane wave solutions in the wavenumber domain with eigenvalue decomposition method. Based on the elastic plane wave solutions, three new time-space domain dispersion relations of ESG elastic modelling are obtained, which are represented by three equations corresponding to P-, S- and converted-wave terms in the elastic equations, respectively. By using these new relations, we can study the dispersion errors of different spatial FD terms independently. The dispersion analysis showed that different spatial FD terms have different errors. It is therefore suggested that different FD coefficients to be used to approximate the three spatial derivative terms. In addition, the relative dispersion error in L2-norm is minimized through optimizing FD coefficients using Newton's method. Synthetic examples have demonstrated that this new optimal FD schemes have superior accuracy for elastic wave modelling compared to Taylor-series expansion and optimized space domain FD schemes.
Snakes and ladders: localized solutions of plane Couette flow
Schneider, Tobias M; Burke, John
2009-01-01
We demonstrate the existence of a large number of exact solutions of plane Couette flow, which share the topology of known periodic solutions but are localized in space. Solutions of different size are organized in a snakes-and-ladders structure strikingly similar to that observed for simpler pattern-forming PDE systems. These new solutions are a step towards extending the dynamical systems view of transitional turbulence to spatially extended flows.
Wave Propagation in Stochastic Spacetimes Localization, Amplification and Particle Creation
Hu, B L
1998-01-01
Here we study novel effects associated with electromagnetic wave propagation in a Robertson-Walker universe and the Schwarzschild spacetime with a small amount of metric stochasticity. We find that localization of electromagnetic waves occurs in a Robertson-Walker universe with time-independent metric stochasticity, while time-dependent metric stochasticity induces exponential instability in the particle production rate. For the Schwarzschild metric, time-independent randomness can decrease the total luminosity of Hawking radiation due to multiple scattering of waves outside the black hole and gives rise to event horizon fluctuations and thus fluctuations in the Hawking temperature.
Symmetry and decay of traveling wave solutions to the Whitham equation
Bruell, Gabriele; Ehrnström, Mats; Pei, Long
2017-04-01
This paper is concerned with decay and symmetry properties of solitary-wave solutions to a nonlocal shallow-water wave model. An exponential decay result for supercritical solitary-wave solutions is given. Moreover, it is shown that all such solitary-wave solutions are symmetric and monotone on either side of the crest. The proof is based on the method of moving planes. Furthermore, a close relation between symmetric and traveling-wave solutions is established.
Travelling Wave Solutions to a Special Type of Nonlinear Evolution Equation
XU Gui-Qiong; LI Zhi-Bin
2003-01-01
A unified approach is presented for finding the travelling wave solutions to one kind of nonlinear evolution equation by introducing a concept of "rank". The key idea of this method is to make use of the arbitrariness of the manifold in Painleve analysis. We selected a new expansion variable and thus obtained a rich variety of travelling wave solutions to nonlinear evolution equation, which covered solitary wave solutions, periodic wave solutions, Weierstrass elliptic function solutions, and rational solutions. Three illustrative equations are investigated by this means, and abundant travelling wave solutions are obtained in a systematic way. In addition, some new solutions are firstly reported here.
Barker, Blake; Noble, Pascal; Rodrigues, L Miguel; Zumbrun, Kevin
2012-01-01
In this paper we consider the spectral and nonlinear stability of periodic traveling wave solutions of a generalized Kuramoto-Sivashinsky equation. In particular, we resolve the long-standing question of nonlinear modulational stability by demonstrating that spectrally stable waves are nonlinearly stable when subject to small localized (integrable) perturbations. Our analysis is based upon detailed estimates of the linearized solution operator, which are complicated by the fact that the (necessarily essential) spectrum of the associated linearization intersects the imaginary axis at the origin. We carry out a numerical Evans function study of the spectral problem and find bands of spectrally stable periodic traveling waves, in close agreement with previous numerical studies of Frisch-She-Thual, Bar-Nepomnyashchy, Chang-Demekhin-Kopelevich, and others carried out by other techniques. We also compare predictions of the associated Whitham modulation equations, which formally describe the dynamics of weak large s...
MULTICOMPONENT SOLUTION FOR LOCAL ANAESTHESIA IN OPERATIONS ON EXTREMITIES
V.I. Sobolev
2008-03-01
Full Text Available The analysis of the results of local anaesthesia (LA in 89 patients aged 18 to 68 years with trauma and diseases of extremities has been carried out. The efficiency of perineural injected multicomponent solution of clonidine added to conventional mixture oflidocaine and phentanyl has been assessed. The multicomponent method has significantly prolonged the duration of local anaesthesia of 1% lidocaine solution providing reliable anaesthesia of plexus and peripheral nerves alongside the sufficient regional myoplegia and prolonged postoperative anesthetization. When there is no need of deep myoplegia Hallows to lower the concentration of lidocaine solution twofold, maintaining its efficiency, and to realize local anaesthesia of patients with high risk.
New Exact Explicit Nonlinear Wave Solutions for the Broer-Kaup Equation
Zhenshu Wen
2014-01-01
Full Text Available We study the nonlinear wave solutions for the Broer-Kaup equation. Many exact explicit expressions of the nonlinear wave solutions for the equation are obtained by exploiting the bifurcation method and qualitative theory of dynamical systems. These solutions contain solitary wave solutions, singular solutions, periodic singular solutions, and kink-shaped solutions, most of which are new. Some previous results are extended.
TRAVELING WAVE SOLUTIONS OF SOME FRACTIONAL DIFFERENTIAL EQUATIONS
SERIFE MUGE EGE
2016-07-01
Full Text Available The modified Kudryashov method is powerful, efficient and can be used as an alternative to establish new solutions of different type of fractional differential equations applied in mathematical physics. In this article, we’ve constructed new traveling wave solutions including symmetrical Fibonacci function solutions, hyperbolic function solutions and rational solutions of the space-time fractional Cahn Hillihard equation D_t^α u − γD_x^α u − 6u(D_x^α u^2 − (3u^2 − 1D_x^α (D_x^α u + D_x^α(D_x^α(D_x^α(D_x^α u = 0 and the space-time fractional symmetric regularized long wave (SRLW equation D_t^α(D_t^α u + D_x^α(D_x^α u + uD_t^α(D_x^α u + D_x^α u D_t^α u + D_t^α(D_t^α(D_x^α(D_x^α u = 0 via modified Kudryashov method. In addition, some of the solutions are described in the figures with the help of Mathematica.
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.
Bifurcations of traveling wave solutions of a generalized Dullin-Gottwald-Holm equation
Fan, Xinghua; Li, Shasha
2015-01-01
The bifurcations of traveling wave solutions of a generalized Dullin-Gottwald-Holm equation ut-α2uxxt+2ωux+βumux+γuxxx = α2(2uxuxx+uxxx) is studied by using the method of planardynamical systems. Different kinds of traveling wave solutions, such as the solitary wave solution, thepeakon wave solution and the periodic cusp wave solution are found to exist under certain parameterconditions. Results show that types of bounded traveling wave solutions are kept in the gener...
Guided Wave Based Crack Detection in the Rivet Hole Using Global Analytical with Local FEM Approach
Md Yeasin Bhuiyan
2016-07-01
Full Text Available In this article, ultrasonic guided wave propagation and interaction with the rivet hole cracks has been formulated using closed-form analytical solution while the local damage interaction, scattering, and mode conversion have been obtained from finite element analysis. The rivet hole cracks (damage in the plate structure gives rise to the non-axisymmetric scattering of Lamb wave, as well as shear horizontal (SH wave, although the incident Lamb wave source (primary source is axisymmetric. The damage in the plate acts as a non-axisymmetric secondary source of Lamb wave and SH wave. The scattering of Lamb and SH waves are captured using wave damage interaction coefficient (WDIC. The scatter cubes of complex-valued WDIC are formed that can describe the 3D interaction (frequency, incident direction, and azimuth direction of Lamb waves with the damage. The scatter cubes are fed into the exact analytical framework to produce the time domain signal. This analysis enables us to obtain the optimum design parameters for better detection of the cracks in a multiple-rivet-hole problem. The optimum parameters provide the guideline of the design of the sensor installation to obtain the most noticeable signals that represent the presence of cracks in the rivet hole.
Local Existence of Smooth Solutions to the FENE Dumbbell Model
Ge YANG
2012-01-01
The author proves the local existence of smooth solutions to the finite extensible nonlinear elasticity (FENE) dumbbell model of polymeric flows in some weighted spaces if the non-dimensional parameter b ＞ 2.
Impact Localization Using Lamb Wave and Spiral FSAT
Rimal, Nischal
Wear and tear exists in almost every physical infrastructure. Modern day science has something in its pocket to early detect such wear and tear known as Structural Health Monitoring (SHM). SHM features a key role in tracking a structural failure and could prevent loss of human lives and money. The size and prices of presently available defect detection devices make them not suitable for on-site SHM. The exploitation of directional transducers and Lamb wave propagation for SHM has been proposed. The basis of the project was to develop an accurate localization algorithm and implementation of Lamb waves to detect the crack present in the plate like structures. In regards, the use of Frequency Steerable Acoustic Transducer (FSAT) was studied. The theory governing the propagation of Lamb wave was reviewed. The derivation of the equations and dispersion curve of Lamb waves are included. FSAT was studied from both theoretical and application view of point. The experiments carried out give us better understanding of the FSAT excitation and Lamb wave generation and detection. The Lamb wave generation and crack localization algorithm was constructed and with the proposed algorithm, simulated impacts are detected.
Global existence and decay of solutions of a nonlinear system of wave equations
Said-Houari, Belkacem
2012-03-01
This work is concerned with a system of two wave equations with nonlinear damping and source terms acting in both equations. Under some restrictions on the nonlinearity of the damping and the source terms, we show that our problem has a unique local solution. Also, we prove that, for some restrictions on the initial data, the rate of decay of the total energy is exponential or polynomial depending on the exponents of the damping terms in both equations.
Nonlinear dynamics of DNA - Riccati generalized solitary wave solutions
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.
New travelling wave solutions for nonlinear stochastic evolution equations
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.
WAVE LOCALIZATION IN RANDOMLY DISORDERED PERIODIC PIEZOELECTRIC RODS
Li Fengming; Wang Yuesheng; Chen Ali
2006-01-01
The wave propagation in periodic and disordered periodic piezoelectric rods is studied in this paper. The transfer matrix between two consecutive unit cells is obtained according to the continuity conditions. The electromechanical coupling of piezoelectric materials is considered.According to the theory of matrix eigenvalues, the frequency bands in periodic structures are studied. Moreover, by introducing disorder in both the dimensionless length and elastic constants of the piezoelectric ceramics, the wave localization in disordered periodic structures is also studied by using the matrix eigenvalue method and Lyapunov exponent method. It is found that tuned periodic structures have the frequency passbands and stopbands and localization phenomenon can occur in mistuned periodic structures. Furthermore, owing to the effect of piezoelectricity, the frequency regions for waves that cannot propagate through the structures are slightly increased with the increase of the piezoelectric constant.
Slow waves in locally resonant metamaterials line defect waveguides
Kaina, Nadège; Bourlier, Yoan; Fink, Mathias; Berthelot, Thomas; Lerosey, Geoffroy
2016-01-01
The ability of electromagnetic waves to interact with matter governs many fascinating effects involved in fundamental and applied, quantum and classical physics. It is necessary to enhance these otherwise naturally weak effects by increasing the probability of wave/matter interactions, either through field confinement or slowing down of waves. This is commonly achieved with structured materials such as photonic crystal waveguides or coupled resonator optical waveguides. Yet their minimum structural scale is limited to the order of the wavelength which not only forbids ultra-small confinement but also severely limits their performance for slowing down waves. Here we show that line defect waveguides in locally resonant metamaterials can outperform these proposals due to their deep subwavelength scale. We experimentally demonstrate our approach in the microwave domain using 3D printed resonant wire metamaterials, achieving group indices ng as high as 227 over relatively wide frequency bands. Those results corres...
Mahillo-Isla, R; Gonźalez-Morales, M J; Dehesa-Martínez, C
2011-06-01
The slowly varying envelope approximation is applied to the radiation problems of the Helmholtz equation with a planar single-layer and dipolar sources. The analyses of such problems provide procedures to recover solutions of the Helmholtz equation based on the evaluation of solutions of the parabolic wave equation at a given plane. Furthermore, the conditions that must be fulfilled to apply each procedure are also discussed. The relations to previous work are given as well.
Existence and breaking property of real loop-solutions of two nonlinear wave equations
Ji-bin LI
2009-01-01
Dynamical analysis has revealed that,for some nonlinear wave equations,loop- and inverted loop-soliton solutions are actually visual artifacts. The so-called loop-soliton solution consists of three solutions,and is not a real solution. This paper answers the question as to whether or not nonlinear wave equations exist for which a "real" loop-solution exists,and if so,what are the precise parametric representations of these loop traveling wave solutions.
General expressions of peaked traveling wave solutions of CH-γ and CH equations
ZHANG Wenling
2004-01-01
We use qualitative analysis and numerical simulation to study peaked traveling wave solutions of CH-γ and CH equations. General expressions of peakon and periodic cusp wave solutions are obtained. Some previous results become our special cases.
The novel multi-solitary wave solution to the fifth-order KdV equation
Zhang Yi; Chen Deng-Yuan
2004-01-01
By using Hirota's method, the novel multi-solitary wave solutions to the fifth-order KdV equation are obtained.Furthermore, various new solitary wave solutions are also derived by a reconstructed bilinear Backlund transformation.
Exact time-localized solutions in Vacuum String Field Theory
Bonora, L; Santos, R J S; Tolla, D D
2004-01-01
We address the problem of finding star algebra projectors that exhibit localized time profiles. We use the double Wick rotation method, starting from an Euclidean (unconventional) lump solution, which is characterized by the Neumann matrix being the conventional one for the continuous spectrum, while the inverse of the conventional one for the discrete spectrum. This is still a solution of the projector equation and we show that, after inverse Wick-rotation, its time profile has the desired localized time dependence. We study it in detail in the low energy regime (field theory limit) and in the extreme high energy regime (tensionless limit) and show its similarities with the rolling tachyon solution.
Ultrasonic wave-based defect localization using probabilistic modeling
Todd, M. D.; Flynn, E. B.; Wilcox, P. D.; Drinkwater, B. W.; Croxford, A. J.; Kessler, S.
2012-05-01
This work presents a new approach rooted in maximum likelihood estimation for defect localization in sparse array guided wave ultrasonic interrogation applications. The approach constructs a minimally-informed statistical model of the guided wave process, where unknown or uncertain model parameters are assigned non-informative Bayesian prior distributions and integrated out of the a posteriori probability calculation. The premise of this localization approach is straightforward: the most likely defect location is the point on the structure with the maximum a posteriori probability of actually being the location of damage (i.e., the most probable location given a set of sensor measurements). The proposed approach is tested on a complex stiffened panel against other common localization approaches and found to have superior performance in all cases.
LOCAL DISCONTINUOUS GALERKIN METHODS FOR THREE CLASSES OF NONLINEAR WAVE EQUATIONS
Yan Xu; Chi-wang Shu
2004-01-01
In this paper, we further develop the local discontinuous Galerkin method to solve three classes of nonlinear wave equations formulated by the general KdV-Burgers type equations, the general fifth-order KdV type equations and the fully nonlinear K(n, n, n)equations, and prove their stability for these general classes of nonlinear equations. The schemes we present extend the previous work of Yan and Shu [30, 31] and of Levy, Shu and Yan [24] on local discontinuous Galerkin method solving partial differential equations with higher spatial derivatives. Numerical examples for nonlinear problems are shown to illustrate the accuracy and capability of the methods. The numerical experiments include stationary solitons, soliton interactions and oscillatory solitary wave solutions.The numerical experiments also include the compacton solutions of a generalized fifthorder KdV equation in which the highest order derivative term is nonlinear and the fully nonlinear K(n, n, n) equations.
Local absorbing boundary conditions for nonlinear wave equation on unbounded domain.
Li, Hongwei; Wu, Xiaonan; Zhang, Jiwei
2011-09-01
The numerical solution of the nonlinear wave equation on unbounded spatial domain is considered. The artificial boundary method is introduced to reduce the nonlinear problem on unbounded spatial domain to an initial boundary value problem on a bounded domain. Using the unified approach, which is based on the operator splitting method, we construct the efficient nonlinear local absorbing boundary conditions for the nonlinear wave equation, and give the stability analysis of the resulting boundary conditions. Finally, several numerical examples are given to demonstrate the effectiveness of our method.
A physical solution for plane SH waves in anelastic media
Ursin, Bjorn; Carcione, José M.; Gei, Davide
2017-05-01
In a lossy medium with complex frequency-dependent wave speed both rays and plane waves at an interface should satisfy the dispersion relation (that is, the wave equation), the radiation condition (the amplitude should go to zero at infinity) and the horizontal complex slowness should be continuous (Snell's law). It is known that this may lead to a transmitted wave which violates the radiation condition and which also causes problems with the phase of the reflection coefficient. In fact, ray-tracing algorithms and analytical evaluations of the reflection and transmission coefficients in anelastic media may lead to non-physical solutions related to the complex square roots of the vertical slowness and polarizations. The steepest-descent approximation with complex horizontal slowness involves non-physical complex horizontal distances, and in some cases also a non-physical vertical slowness that violates the radiation condition. Similarly, the reflection and transmission coefficients and ray-tracing codes obtained with this approach yields wrong results. In order to tackle this problem, we choose the stationary-phase approximation with real horizontal slowness. This gives real horizontal distances, the radiation condition is always satisfied and the reflection and transmission coefficients are correct. This is shown by comparison to full-wave space-time modelling results by computing the reflection and transmission coefficients and respective phase angles from synthetic seismograms. This numerical evaluation is based on a 2-D wavenumber-frequency Fourier transform. The results indicate that the stationary-phase method with a real horizontal slowness provides the correct physical solution.
Meshless RBF based pseudospectral solution of acoustic wave equation
Mishra, Pankaj K
2015-01-01
Chebyshev pseudospectral (PS) methods are reported to provide highly accurate solution using polynomial approximation. Use of polynomial basis functions in PS algorithms limits the formulation to univariate systems constraining it to tensor product grids for multi-dimensions. Recent studies have shown that replacing the polynomial by radial basis functions in pseudospectral method (RBF-PS) has the advantage of using irregular grids for multivariate systems. A RBF-PS algorithm has been presented here for the numerical solution of inhomogeneous Helmholtz's equation using Gaussian RBF for derivative approximation. Efficacy of RBF approximated derivatives has been checked through error analysis comparison with PS method. Comparative study of PS, RBF-PS and finite difference approach for the solution of a linear boundary value problem has been performed. Finally, a typical frequency domain acoustic wave propagation problem has been solved using Dirichlet boundary condition and a point source. The algorithm present...
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.
The periodic wave solutions for the generalized Nizhnik-Novikov-Veselov equation
张金良; 任东锋; 王明亮; 王跃明; 方宗德
2003-01-01
The periodic wave solutions expressed by Jacobi elliptic functions for the generalized Nizhnik-Novikov-Veselov equation are obtained using the F-expansion method proposed recently. In the limiting cases, the solitary wave solutions and other types of travelling wave solutions for the system are obtained.
Single-peak solitary wave solutions for the variant Boussinesq equations
Hong Li; Lilin Ma; Dahe Feng
2013-06-01
This paper presents all possible smooth, cusped solitary wave solutions for the variant Boussinesq equations under the inhomogeneous boundary condition. The parametric conditions for the existence of smooth, cusped solitary wave solutions are given using the phase portrait analytical technique. Asymptotic analysis and numerical simulations are provided for smooth, cusped solitary wave solutions of the variant Boussinesq equations.
Konopelchenko-Dubrovsky方程的周期解%Periodic Wave Solutions for Konopelchenko-Dubrovsky Equation
张金良; 张令元; 王明亮
2005-01-01
By using F-expansion method proposed recently, we derive the periodic wave solution expressed by Jacobi elliptic functions for Konopelchenko-Dubrovsky equation. In the limit case, the solitary wave solution and other type of the traveling wave solutions are derived.
Collins, Mike
2013-01-01
The notion of localism and decentralization in national policy has come increasingly to the fore in recent years. The national succession planning strategy for headteachers in England introduced by the National College for School Leadership promoted "local solutions for a national challenge". This article deals with some aspects of the…
Two-Mode Wave Solutions to the Degasperis-Procesi Equation
ZHANG Zheng-Di; BI Qin-Sheng
2008-01-01
@@ By introducing a new type of solutions, called the multiple-mode wave solutions which can be expressed in nonlinear superposition of single-mode waves with different speeds, we investigate the two-mode wave solutions in Degasperis-Procesi equation and two cases are derived.The explicit expressions for the two-mode waves as well as the existence conditions are presented.It is shown that the two-mode waves may be the nonlinear combinations of many types of single-mode waves, such as periodic waves, solitons, compactons, etc., and more complicated multiple-mode waves can be obtained if higher order or more single-mode waves are taken into consideration.It is pointed out that the two-mode wave solutions can be employed to display the typical mechanism of the interactions between different single-mode waves.
Solution of inverse localization problem associated to multistatic radar system
Boutkhil M.
2016-01-01
Full Text Available This work deals with the problem of inverse localization by a target with the aim to retrieve the position of the target, given the intensity and phase of the electromagnetic waves scattered by this object. Assuming the surface cross section to be known as well as the intensity and phase of the scattered waves, the target position was reconstructed through the echo signals scattered of each bistatic. We develop in the same time a multistatic ambiguity function trough bistatic ambiguity function to investigate several fundamental aspects that determine multistatic radar performance. We used a multistatic radar constructed of two bistatic radars, two transmitters and one receiver.
Sheppard, Colin J R; Saari, Peeter
2008-01-07
A criticism of the focus wave mode (FWM) solution for localized pulses is that it contains backward propagating components that are difficult to generate in many practical situations. We describe a form of FWM where the strength of the backward propagating components is identically zero and derive special cases where the field can be written in an analytic form. In particular, a free-space version of "backward light" pulse is considered, which moves in the opposite direction with respect to all its spectral constituents.
Reintjes, Moritz
2015-01-01
It is an open question whether solutions of the Einstein-Euler equations are smooth enough to admit locally inertial coordinates at points of shock wave interaction, or whether "regularity singularities" can exist at such points. The term regularity singularity was proposed by the authors as a point in spacetime where the gravitational metric tensor is Lipschitz continuous ($C^{0,1}$), but no smoother, in any coordinate system of the $C^{1,1}$ atlas. An existence theory for shock wave solutions in $C^{0,1}$ admitting arbitrary interactions has been proven for the Einstein-Euler equations in spherically symmetric spacetimes, but $C^{1,1}$ is the requisite smoothness required for space-time to be locally flat. Thus the open problem of regularity singularities is the problem as to whether locally inertial coordinate systems exist at shock waves, within the larger $C^{1,1}$ atlas. Our purpose here is to clarify and motivate the open problem of regularity singularities, and to prove that if locally inertial coordi...
A phase-plane analysis of localized frictional waves
Putelat, T.; Dawes, J. H. P.; Champneys, A. R.
2017-07-01
Sliding frictional interfaces at a range of length scales are observed to generate travelling waves; these are considered relevant, for example, to both earthquake ground surface movements and the performance of mechanical brakes and dampers. We propose an explanation of the origins of these waves through the study of an idealized mechanical model: a thin elastic plate subject to uniform shear stress held in frictional contact with a rigid flat surface. We construct a nonlinear wave equation for the deformation of the plate, and couple it to a spinodal rate-and-state friction law which leads to a mathematically well-posed problem that is capable of capturing many effects not accessible in a Coulomb friction model. Our model sustains a rich variety of solutions, including periodic stick-slip wave trains, isolated slip and stick pulses, and detachment and attachment fronts. Analytical and numerical bifurcation analysis is used to show how these states are organized in a two-parameter state diagram. We discuss briefly the possible physical interpretation of each of these states, and remark also that our spinodal friction law, though more complicated than other classical rate-and-state laws, is required in order to capture the full richness of wave types.
Effect of Local Temperature on the Detecting for Pulse Wave of Local Blood Volume
Tingting Yan
2013-07-01
Full Text Available [Objective] Temperature of a subject's external body parts is an interference condition in pulse wave of local blood volume measurement. It is necessary to rule it out. By changing the influence factors, an experiment to research the effect of temperature of subjected part in pulse wave of local blood volume measurement was carried out. [Methods] When the 32 experimenters' left middle finger temperature fall below to 20°C, pulse wave of local blood volume would be recorded detected in real-time until the temperature returned to the measured values before the experiment [Results] While the temperature of subjected part ranged from 26°C to 31°C, the parameters of K', K1', K2' and the amplitude of pulse wave remain basically unchanged. [Conclusion] As a result of the research data, it is stipulated that the pulse wave of local blood volume can be measured only if the finger temperature is in the range of 26-31°C.
The Travelling Wave Solutions for (2+1)-dimensional AKNS Equation
CHENG Zhi-long; HAO Xiao-hong
2015-01-01
Based on the travelling wave method, a (2+1)-dimensional AKNS equation is considered. Elliptic solution and soliton solution are presented and it is shown that the soliton solution can be reduced from the elliptic solution. It also proves that the result is consistent with the soliton solution of simplify Hirota bilinear method by Wazwaz and illustrate the solution are right travelling wave solution.
Xiang LI; Wei-guo ZHANG; Zheng-ming LI
2014-01-01
This paper aims at analyzing the shapes of the bounded traveling wave solu-tions for a class of nonlinear wave equation with a quintic term and obtaining its damped oscillatory solutions. The theory and method of planar dynamical systems are used to make a qualitative analysis to the planar dynamical system which the bounded traveling wave solutions of this equation correspond to. The shapes, existent number, and condi-tions are presented for all bounded traveling wave solutions. The bounded traveling wave solutions are obtained by the undetermined coefficients method according to their shapes, including exact expressions of bell and kink profile solitary wave solutions and approxi-mate expressions of damped oscillatory solutions. For the approximate damped oscillatory solution, using the homogenization principle, its error estimate is given by establishing the integral equation, which reflects the relation between the exact and approximate so-lutions. It can be seen that the error is infinitesimal decreasing in the exponential form.
Localization of angular momentum in optical waves propagating through turbulence.
Sanchez, Darryl J; Oesch, Denis W
2011-12-01
This is the first in a series of papers demonstrating that photons with orbital angular momentum can be created in optical waves propagating through distributed turbulence. The scope of this first paper is much narrower. Here, we demonstrate that atmospheric turbulence can impart non-trivial angular momentum to beams and that this non-trivial angular momentum is highly localized. Furthermore, creation of this angular momentum is a normal part of propagation through atmospheric turbulence.
Solution of wave-like equation based on Haar wavelet
Naresh Berwal
2012-11-01
Full Text Available Wavelet transform and wavelet analysis are powerful mathematical tools for many problems. Wavelet also can be applied in numerical analysis. In this paper, we apply Haar wavelet method to solve wave-like equation with initial and boundary conditions known. The fundamental idea of Haar wavelet method is to convert the differential equations into a group of algebraic equations, which involves a finite number or variables. The results and graph show that the proposed way is quite reasonable when compared to exact solution.
High-resolution seismic wave propagation using local time stepping
Peter, Daniel
2017-03-13
High-resolution seismic wave simulations often require local refinements in numerical meshes to accurately capture e.g. steep topography or complex fault geometry. Together with explicit time schemes, this dramatically reduces the global time step size for ground-motion simulations due to numerical stability conditions. To alleviate this problem, local time stepping (LTS) algorithms allow an explicit time stepping scheme to adapt the time step to the element size, allowing nearoptimal time steps everywhere in the mesh. This can potentially lead to significantly faster simulation runtimes.
Wave Localization and Density Bunching in Pair Ion Plasmas
Mahajan, Swadesh M
2008-01-01
By investigating the nonlinear propagation of high intensity electromagnetic (EM) waves in a pair ion plasma, whose symmetry is broken via contamination by a small fraction of high mass immobile ions, it is shown that this new and interesting state of (laboratory created) matter is capable of supporting structures that strongly localize and bunch the EM radiation with density excess in the region of localization. Testing of this prediction in controlled laboratory experiments can lend credence, inter alia, to conjectures on structure formation (via the same mechanism) in the MEV era of the early universe.
THE SMOOTH AND NONSMOOTH TRAVELLING WAVE SOLUTIONS IN A NONLINEAR WAVE EQUATION
李庶民
2001-01-01
The travelling wave solutions (7WS) in a class of P.D.E. is studied. The travelling wave equation of this P. D.E. is a planar cubic polynomial system in three-parameter space. The study for TWS became the topological classifications of bifurcations of phase portraits defined by the planar system. By using the theory of planar dynamical systems to do qualitative analysis, all topological classifications of the cubic polynomial system can be obtained. Returning the results of the phase plane analysis to TWS, u(ξ) , and considering discontinuity of the right side of the equation of TWS when ξ = x-ct is varied along a phase orbit and passing through a singular curve, all conditions of existence of smooth and nonsmooth travelling waves are given.
Exotic Localized Coherent Structures of the (2+1)-Dimensional Dispersive Long-Wave Equation
ZHANG JieFang
2002-01-01
This article is concerned with the extended homogeneous balance method for studying thc abundantlocalized solution structures in the (2-k1)-dimensional dispersive long-wave equations uty + xx + (u2)xy/2 = 0, ηt +(u + u + uxy)x = 0. Starting from the homogeneous balance method, we find that the richness of the localized coherentstructures of the model is caused by the entrance of two variable-separated arbitrary functions. For some special selectionsof the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, breathers,instantons and ring solitons.
Nonlinear wave dynamics near phase transition in PT-symmetric localized potentials
Nixon, Sean; Yang, Jianke
2016-09-01
Nonlinear wave propagation in parity-time symmetric localized potentials is investigated analytically near a phase-transition point where a pair of real eigenvalues of the potential coalesce and bifurcate into the complex plane. Necessary conditions for a phase transition to occur are derived based on a generalization of the Krein signature. Using the multi-scale perturbation analysis, a reduced nonlinear ordinary differential equation (ODE) is derived for the amplitude of localized solutions near phase transition. Above the phase transition, this ODE predicts a family of stable solitons not bifurcating from linear (infinitesimal) modes under a certain sign of nonlinearity. In addition, it predicts periodically-oscillating nonlinear modes away from solitons. Under the opposite sign of nonlinearity, it predicts unbounded growth of solutions. Below the phase transition, solution dynamics is predicted as well. All analytical results are compared to direct computations of the full system and good agreement is observed.
Nonlinear wave dynamics near phase transition in $\\mathcal{PT}$-symmetric localized potentials
Nixon, Sean
2015-01-01
Nonlinear wave propagation in parity-time ($\\mathcal{PT}$) symmetric localized potentials is investigated analytically near a phase-transition point where a pair of real eigenvalues of the potential coalesce and bifurcate into the complex plane. Necessary conditions for phase transition to occur are derived based on a generalization of the Krein signature. Using multi-scale perturbation analysis, a reduced nonlinear ODE model is derived for the amplitude of localized solutions near phase transition. Above phase transition, this ODE model predicts a family of stable solitons not bifurcating from linear (infinitesimal) modes under a certain sign of nonlinearity. In addition, it predicts periodically-oscillating nonlinear modes away from solitons. Under the opposite sign of nonlinearity, it predicts unbounded growth of solutions. Below phase transition, solution dynamics is predicted as well. All analytical results are compared to direct computations of the full system and good agreement is observed.
Existence Analysis of Traveling Wave Solutions for a Generalization of KdV Equation
Yao Long
2013-01-01
Full Text Available By using the bifurcation theory of dynamic system, a generalization of KdV equation was studied. According to the analysis of the phase portraits, the existence of solitary wave, cusp wave, periodic wave, periodic cusp wave, and compactons were discussed. In some parametric conditions, exact traveling wave solutions of this generalization of the KdV equation, which are different from those exact solutions in existing references, were given.
The classification of the single travelling wave solutions to the variant Boussinesq equations
YUE KAI
2016-10-01
The discrimination system for the polynomial method is applied to variant Boussinesq equations to classify single travelling wave solutions. In particular, we construct corresponding solutions to the concrete parameters to show that each solution in the classification can be realized.
Weiguo Rui
2014-01-01
Full Text Available By using the integral bifurcation method together with factoring technique, we study a water wave model, a high-order nonlinear wave equation of KdV type under some newly solvable conditions. Based on our previous research works, some exact traveling wave solutions such as broken-soliton solutions, periodic wave solutions of blow-up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. In particular, a series of smooth solitary wave solutions and nonsmooth peakon solutions are obtained. In order to show the properties of these exact solutions visually, we plot the graphs of some representative traveling wave solutions.
Sato, Masanori; Matsuura, Kazuo; Fujii, Toshitaka
2001-02-01
We show the experimental data of selective ethanol separation from ethanol-water solution, using ultrasonic atomization. Pure ethanol could be obtained directly from a solution with several mol% ethanol-water solution at 10 °C. This result can be explained in terms of parametric decay instability of capillary wave, in which high localization and accumulation of acoustic energy occur, leading to ultrasonic atomization. That is, parametric decay instability condenses the energy of longitudinal waves in a highly localized surface area of the capillary wave, and causes ultrasonic atomization.
On the exploitation of mode localization in surface acoustic wave MEMS
Hanley, T. H.; Gallacher, B. J.; Grigg, H. T. D.
2017-05-01
Mode localization sensing has been recently introduced as an alternative resonant sensing protocol. It has been shown to exhibit several advantages over other resonant methods, in particular a potential for higher sensitivity and rejection of common mode noise. This paper expounds the principles of utilising surface acoustic waves (SAW) to create a mode localization sensor. A generalised geometry consisting of a pair of coupled resonant cavities is introduced and an analytical solution found for the displacement fields within the cavities. The solution is achieved by coupling the internal cavity solutions using a ray tracing method. The results of the analytical solution are compared to a numerical solution found using commercial finite element method (FEM) software; exact agreement is found between the two solutions. The insight gained from the analytical model enables the determination of critical design parameters. A brief analysis is presented showing analogous operation to previous examples of mode localization sensors. The sensitivity of the device is shown to depend nonlinearly on the number of periods in the array coupling the two cavities.
Shen, Yanfeng; Cesnik, Carlos E. S.
2015-03-01
This paper presents a hybrid modeling technique for the efficient simulation of guided wave propagation and interaction with damage in composite structures. This hybrid approach uses a local finite element model (FEM) to compute the excitability of guided waves generated by piezoelectric transducers, while the global domain wave propagation, wave-damage interaction, and boundary reflections are modeled with the local interaction simulation approach (LISA). A small-size multi-physics FEM with non-reflective boundaries (NRB) was built to obtain the excitability information of guided waves generated by the transmitter. Frequency-domain harmonic analysis was carried out to obtain the solution for all the frequencies of interest. Fourier and inverse Fourier transform and frequency domain convolution techniques are used to obtain the time domain 3-D displacement field underneath the transmitter under an arbitrary excitation. This 3-D displacement field is then fed into the highly efficient time domain LISA simulation module to compute guided wave propagation, interaction with damage, and reflections at structural boundaries. The damping effect of composite materials was considered in the modified LISA formulation. The grids for complex structures were generated using commercial FEM preprocessors and converted to LISA connectivity format. Parallelization of the global LISA solution was achieved through Compute Unified Design Architecture (CUDA) running on Graphical Processing Unit (GPU). The multi-physics local FEM can reliably capture the detailed dimensions and local dynamics of the piezoelectric transducers. The global domain LISA can accurately solve the 3-D elastodynamic wave equations in a highly efficient manner. By combining the local FEM with global LISA, the efficient and accurate simulation of guided wave structural health monitoring procedure is achieved. Two numerical case studies are presented: (1) wave propagation in a unidirectional CFRP composite plate
Plane wave holonomies in quantum gravity. II. A sine wave solution
Neville, Donald E.
2015-08-01
This paper constructs an approximate sinusoidal wave packet solution to the equations of canonical gravity. The theory uses holonomy-flux variables with support on a lattice (LHF =lattice-holonomy flux ). There is an SU(2) holonomy on each edge of the LHF simplex, and the goal is to study the behavior of these holonomies under the influence of a passing gravitational wave. The equations are solved in a small sine approximation: holonomies are expanded in powers of sines and terms beyond sin2 are dropped; also, fields vary slowly from vertex to vertex. The wave is unidirectional and linearly polarized. The Hilbert space is spanned by a set of coherent states tailored to the symmetry of the plane wave case. Fixing the spatial diffeomorphisms is equivalent to fixing the spatial interval between vertices of the loop quantum gravity lattice. This spacing can be chosen such that the eigenvalues of the triad operators are large, as required in the small sine limit, even though the holonomies are not large. Appendices compute the energy of the wave, estimate the lifetime of the coherent state packet, discuss circular polarization and coarse-graining, and determine the behavior of the spinors used in the U(N) SHO realization of LQG.
Modulation of propagation-invariant Localized Waves for FSO communication systems
Salem, Mohamed
2012-01-01
The novel concept of spatio-Temporal modulation of Nyquist pulses is introduced, and the resulting wave-packets are termed Nyquist Localized Waves (LWs). Ideal Nyquist LWs belong to the generic family of LW solutions and can propagate indefinitely in unbounded media without attenuation or chromatic dispersion. The possibility of modulating Nyquist LWs for free-space optical (FSO) communication systems is demonstrated using two different modulation techniques. The first technique is on-off keying (OOK) with alternate mark inversion (AMI) coding for 1-bit per symbol transmission, and the second one is 16-Ary quadrature amplitude modulation (16-QAM) for 4-bits per symbol transmission. Aspects related to the performance, detection and generation of the spatio-Temporally coupled wave-packets are discussed and future research directions are outlined. © 2012 Optical Society of America.
The Local Stability of Solutions for a Nonlinear Equation
Haibo Yan
2014-01-01
Full Text Available The approach of Kruzkov’s device of doubling the variables is applied to establish the local stability of strong solutions for a nonlinear partial differential equation in the space L1(R by assuming that the initial value only lies in the space L1(R∩L∞(R.
Localized solutions for a nonlocal discrete NLS equation
Ben, Roberto I. [Instituto de Desarrollo Humano, Universidad Nacional de General Sarmiento, J.M. Gutiérrez 1150, 1613 Los Polvorines (Argentina); Cisneros Ake, Luís [Department of Mathematics, ESFM, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos Edificio 9, 07738 México D.F. (Mexico); Minzoni, A.A. [Depto. Matemáticas y Mecánica, I.I.M.A.S.-U.N.A.M., Apdo. Postal 20-726, 01000 México D.F. (Mexico); Panayotaros, Panayotis, E-mail: panos@mym.iimas.unam.mx [Depto. Matemáticas y Mecánica, I.I.M.A.S.-U.N.A.M., Apdo. Postal 20-726, 01000 México D.F. (Mexico)
2015-09-04
We study spatially localized time-periodic solutions of breather type for a cubic discrete NLS equation with a nonlocal nonlinearity that models light propagation in a liquid crystal waveguide array. We show the existence of breather solutions in the limit where both linear and nonlinear intersite couplings vanish, and in the limit where the linear coupling vanishes with arbitrary nonlinear intersite coupling. Breathers of this nonlocal regime exhibit some interesting features that depart from what is seen in the NLS breathers with power nonlinearity. One property we see theoretically is the presence of higher amplitude at interfaces between sites with zero and nonzero amplitude in the vanishing linear coupling limit. A numerical study also suggests the presence of internal modes of orbitally stable localized modes. - Highlights: • Show existence of spatially localized solutions in nonlocal discrete NLS model. • Study spatial properties of localized solutions for arbitrary nonlinear nonlocal coupling. • Present numerical evidence that nonlocality leads to internal modes around stable breathers. • Present theoretical and numerical evidence for amplitude maxima at interfaces.
New Travelling Wave Solutions to Compound KdV-Burgers Equation
YU Jun; KE Yun-Quan; ZHANG Wei-Jun
2004-01-01
The compound KdV-Burgers equation and combined KdV-mKdV equation are real physical models concerning many branches in physics.In this paper,applying the improved trigonometric function method to these equations,rich explicit and exact travelling wave solutions,which contain solitary-wave solutions,periodic solutions,and combined formal solitary-wave solutions,are obtained.
New Types of Travelling Wave Solutions From (2+1)-Dimensional Davey-Stewartson Equation
ZHAO Hong
2006-01-01
In this paper, based on new auxiliary nonlinear ordinary differential equation with a sixth-degree nonlinear term, we study the (2+1)-dimensional Davey-Stewartson equation and new types of travelling wave solutions are obtained, which include new bell and kink profile solitary wave solutions, triangular periodic wave solutions, and singular solutions. The method used here can be also extended to many other nonlinear partial differential equations.
Some Further Results on Traveling Wave Solutions for the ZK-BBM( Equations
Shaoyong Li
2013-01-01
Full Text Available We investigate the traveling wave solutions for the ZK-BBM( equations by using bifurcation method of dynamical systems. Firstly, for ZK-BBM(2, 2 equation, we obtain peakon wave, periodic peakon wave, and smooth periodic wave solutions and point out that the peakon wave is the limit form of the periodic peakon wave. Secondly, for ZK-BBM(3, 2 equation, we obtain some elliptic function solutions which include periodic blow-up and periodic wave. Furthermore, from the limit forms of the elliptic function solutions, we obtain some trigonometric and hyperbolic function solutions which include periodic blow-up, blow-up, and smooth solitary wave. We also show that our work extends some previous results.
Traveling Wave Solutions for Lotka-Volterra System Re-Visited
Leung, Anthony W; Feng, Wei
2009-01-01
Using a new method of monotone iteration of a pair of smooth lower- and upper-solutions, the traveling wave solutions of the classical Lotka-Volterra system are shown to exist for a family of wave speeds. Such constructed upper and lower solution pair enables us to derive the explicit value of the minimal (critical) wave speed as well as the asymptotic rates of the wave solutions at infinities. Furthermore, the traveling wave corresponding to each wave speed is unique modulo a translation of the origin. The stability of the traveling wave solutions with non-critical wave speed is also studied by spectral analysis of the linearized operator in exponentially weighted Banach spaces.
Unstable spiral waves and local Euclidean symmetry in a model of cardiac tissue
Marcotte, Christopher D.; Grigoriev, Roman O. [School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332 (United States)
2015-06-15
This paper investigates the properties of unstable single-spiral wave solutions arising in the Karma model of two-dimensional cardiac tissue. In particular, we discuss how such solutions can be computed numerically on domains of arbitrary shape and study how their stability, rotational frequency, and spatial drift depend on the size of the domain as well as the position of the spiral core with respect to the boundaries. We also discuss how the breaking of local Euclidean symmetry due to finite size effects as well as the spatial discretization of the model is reflected in the structure and dynamics of spiral waves. This analysis allows identification of a self-sustaining process responsible for maintaining the state of spiral chaos featuring multiple interacting spirals.
Abundant new travelling wave solutions for the (2 + 1)-dimensional Sine-Gordon equation
Li Zhu [College of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000 (China)], E-mail: lizhu1813@163.com; Dong Huanhe [College of Information Science and Engineering, Shandong University of Science and Technology, Qingdao 266510 (China)
2008-07-15
Abundant new travelling wave solutions of the (2 + 1)-dimensional Sine-Gordon equation are obtained by the generalized Jacobi elliptic function method. The solutions obtained include the kink-shaped solutions, bell-shaped solutions, singular solutions and periodic solutions.
Rogue waves: from nonlinear Schrödinger breather solutions to sea-keeping test.
Onorato, Miguel; Proment, Davide; Clauss, Günther; Klein, Marco
2013-01-01
Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship.
无
2012-01-01
In this paper,we consider the reaction diffusion equations with strong generic delay kernel and non-local effect,which models the microbial growth in a flow reactor.The existence of traveling waves is established for this model.More precisely,using the geometric singular perturbation theory,we show that traveling wave solutions exist provided that the delay is sufficiently small with the strong generic delay kernel.
Wang, Chuanjian; Dai, Zhengde; Liu, Changfu
2014-07-01
In this paper, two types of multi-parameter breather homoclinic wave solutions—including breather homoclinic wave and rational homoclinic wave solutions—are obtained by using the Hirota technique and ansätz with complexity of parameter for the coupled Schrödinger-Boussinesq equation. Rogue waves in the form of the rational homoclinic solution are derived when the periods of breather homoclinic wave go to infinite. Some novel features of homoclinic wave solutions are discussed and presented. In contrast to the normal bright rogue wave structure, a structure like a four-petaled flower in temporal-spatial distribution is exhibited. Further with the change of the wave number of the plane wave, the bright and dark rogue wave structures may change into each other. The bright rogue wave structure results from the full merger of two nearby peaks, and the dark rogue wave structure results from the full merger of two nearby holes. The dark rogue wave for the uncoupled Boussinesq equation is finally obtained. Its structural properties show that it never takes on bright rogue wave features with the change of parameter. It is hoped that these results might provide us with useful information on the dynamics of the relevant fields in physics.
Rapid and reliable sky localization of gravitational wave sources
Cornish, Neil J
2016-01-01
The first detection of gravitational waves by LIGO from the merger of two compact objects has sparked new interest in detecting electromagnetic counterparts to these violent events. For mergers involving neutron stars, it is thought that prompt high-energy emission in gamma rays and x-rays will be followed days to weeks later by an afterglow in visible light, infrared and radio. Rapid sky localization using the data from a network of gravitational wave detectors is essential to maximize the chances of making a joint detection. Here I describe a new technique that is able to produce accurate, fully Bayesian sky maps in seconds or less. The technique can be applied to spin-precessing compact binaries, and can take into account detector calibration and spectral estimation uncertainties.
Rogue waves and rational solutions of a (3+1)-dimensional nonlinear evolution equation
Zhaqilao,, E-mail: zhaqilao@imnu.edu.cn
2013-12-06
A simple symbolic computation approach for finding the rogue waves and rational solutions to the nonlinear evolution equation is proposed. It turns out that many rational solutions with real and complex forms of a (3+1)-dimensional nonlinear evolution equation are obtained. Some features of rogue waves and rational solutions are graphically discussed. -- Highlights: •A simple symbolic computation approach for finding the rational solutions to the NEE is proposed. •Some rogue waves and rational solutions with real and complex forms of a (3+1)-D NEE are obtained. •Some features of rogue waves are graphically discussed.
Detailed explicit solution of the electrodynamic wave equations
Iryna Yu. Dmitrieva
2015-10-01
Full Text Available Present results concern the general scientific tendency dealing with mathematical modeling and analytical study of electromagnetic field phenomena described by the systems of partial differential equations. Specific electrodynamic engineering process with expofunctional influences is simulated by the differential Maxwell system whose effective research is equivalent to the rigorous solution of the general wave partial differential equation regarding all scalar components of electromagnetic field vector intensities. The given equation is solved explicitly in detail using method of integral transforms and irrespectively to the concrete boundary conditions. Specific cases of unexcited vacuum and isotropic homogeneous medium were considered. Proposed approach can be applied to any finite dimensional system of partial differential equations with piece wise constant coefficients and its corresponding scalar equations representing mathematical models in modern electrodynamics. In comparison with the known results, current research is completely thorough and accurate that implies its direct practical application.
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.
Luchko, Yuri; Mainardi, Francesco
2013-06-01
In this paper, the one-dimensional time-fractional diffusion-wave equation with the Caputo fractional derivative of order α, 1 ≤ α ≤ 2 and with constant coefficients is revisited. It is known that the diffusion and the wave equations behave quite differently regarding their response to a localized disturbance. Whereas the diffusion equation describes a process where a disturbance spreads infinitely fast, the propagation speed of the disturbance is a constant for the wave equation. We show that the time-fractional diffusion-wave equation interpolates between these two different responses and investigate the behavior of its fundamental solution for the signalling problem in detail. In particular, the maximum location, the maximum value, and the propagation velocity of the maximum point of the fundamental solution for the signalling problem are described analytically and calculated numerically.
WEN Xiao-Yong
2009-01-01
With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the (2+1)-dimensional dispersive long wave equations are constructed by means of a function transformation, improved mapping approach, and variable separation approach, among which there are rational solitary wave solutions, periodic wave solutions and rational wave solutions.
Dynamical behaviours and exact travelling wave solutions of modified generalized Vakhnenko equation
JUNJUN XIAO; DAHE FENG; XIA MENG; YUANQUAN CHENG
2017-01-01
By using the bifurcation theory of planar dynamical systems and the qualitative theory of differential equations, we studied the dynamical behaviours and exact travelling wave solutions of the modified generalized Vakhnenko equation (mGVE). As a result, we obtained all possible bifurcation parametric sets and many explicit formulas of smooth and non-smooth travelling waves such as cusped solitons, loop solitons, periodic cusp waves, pseudopeakon solitons, smooth periodic waves and smooth solitons. Moreover, we provided some numerical simulations of these solutions.
Convection in Binary Fluid Mixtures; 2, Localized Traveling Waves
Barten, W; Kamps, M; Schmitz, R
1995-01-01
Nonlinear, spatially localized structures of traveling convection rolls are investigated in quantitative detail as a function of Rayleigh number for two different Soret coupling strengths (separation ratios) with Lewis and Prandtl numbers characterizing ethanol-water mixtures. A finite-difference method was used to solve the full hydrodynamic field equations numerically. Structure and dynamics of these localized traveling waves (LTW) are dominated by the concentration field. Like in the spatially extended convective states ( cf. accompanying paper), the Soret-induced concentration variations strongly influence, via density changes, the buoyancy forces that drive convection. The spatio-temporal properties of this feed-back mechanism, involving boundary layers and concentration plumes, show that LTW's are strongly nonlinear states. Light intensity distributions are determined that can be observed in side-view shadowgraphs. Detailed analyses of all fields are made using colour-coded isoplots, among others. In th...
Exciton localization in solution-processed organolead trihalide perovskites
He, Haiping; Yu, Qianqian; Li, Hui; Li, Jing; Si, Junjie; Jin, Yizheng; Wang, Nana; Wang, Jianpu; He, Jingwen; Wang, Xinke; Zhang, Yan; Ye, Zhizhen
2016-03-01
Organolead trihalide perovskites have attracted great attention due to the stunning advances in both photovoltaic and light-emitting devices. However, the photophysical properties, especially the recombination dynamics of photogenerated carriers, of this class of materials are controversial. Here we report that under an excitation level close to the working regime of solar cells, the recombination of photogenerated carriers in solution-processed methylammonium-lead-halide films is dominated by excitons weakly localized in band tail states. This scenario is evidenced by experiments of spectral-dependent luminescence decay, excitation density-dependent luminescence and frequency-dependent terahertz photoconductivity. The exciton localization effect is found to be general for several solution-processed hybrid perovskite films prepared by different methods. Our results provide insights into the charge transport and recombination mechanism in perovskite films and help to unravel their potential for high-performance optoelectronic devices.
Local numerical modelling of ultrasonic guided waves in linear and nonlinear media
Packo, Pawel; Radecki, Rafal; Kijanka, Piotr; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.
2017-04-01
Nonlinear ultrasonic techniques provide improved damage sensitivity compared to linear approaches. The combination of attractive properties of guided waves, such as Lamb waves, with unique features of higher harmonic generation provides great potential for characterization of incipient damage, particularly in plate-like structures. Nonlinear ultrasonic structural health monitoring techniques use interrogation signals at frequencies other than the excitation frequency to detect changes in structural integrity. Signal processing techniques used in non-destructive evaluation are frequently supported by modeling and numerical simulations in order to facilitate problem solution. This paper discusses known and newly-developed local computational strategies for simulating elastic waves, and attempts characterization of their numerical properties in the context of linear and nonlinear media. A hybrid numerical approach combining advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE) is proposed for unique treatment of arbitrary strain-stress relations. The iteration equations of the method are derived directly from physical principles employing stress and displacement continuity, leading to an accurate description of the propagation in arbitrarily complex media. Numerical analysis of guided wave propagation, based on the newly developed hybrid approach, is presented and discussed in the paper for linear and nonlinear media. Comparisons to Finite Elements (FE) are also discussed.
Ground state solutions for non-local fractional Schrodinger equations
Yang Pu
2015-08-01
Full Text Available In this article, we study a time-independent fractional Schrodinger equation with non-local (regional diffusion $$ (-\\Delta^{\\alpha}_{\\rho}u + V(xu = f(x,u \\quad \\text{in }\\mathbb{R}^{N}, $$ where $\\alpha \\in (0,1$, $N > 2\\alpha$. We establish the existence of a non-negative ground state solution by variational methods.
LOCAL ESTIMATES OF SINGULAR SOLUTION TO GAUSSIAN CURVATURE EQUATION
杨云雁
2003-01-01
In this paper, we derive the local estimates of a singular solution near its singular set Z of the Gaussian curvature equation △u(x) + K(x)eu(x) = 0 in Ω \\ Z,in the case that K(x) may be zero on Z, where Ω R2 is a bounded open domain, and Z is a set of finite points.
The (′/-Expansion Method for Abundant Traveling Wave Solutions of Caudrey-Dodd-Gibbon Equation
Hasibun Naher
2011-01-01
Full Text Available We construct the traveling wave solutions of the fifth-order Caudrey-Dodd-Gibbon (CDG equation by the (/-expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, the trigonometric, and the rational functions. It is shown that the (/-expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations.
Exact periodic wave solutions to the generalized Nizhnik-Novikov-Veselov equation
Yan-Ze Peng
2005-02-01
The extended mapping method with symbolic computation is developed to obtain exact periodic wave solutions to the generalized Nizhnik{Novikov{Veselov equation. Limit cases are studied and new solitary wave solutions and triangular periodic wave solutions are obtained. The method is applicable to a large variety of non-linear partial differential equations, as long as odd- and even-order derivative terms do not coexist in the equation under consideration.
J B ZHOU; J XU; J D WEI; X Q YANG
2017-04-01
This paper is concerned with the existence of travelling wave solutions to a singularly perturbed generalized Gardner equation with nonlinear terms of any order. By using geometric singular perturbation theory and based on the relation between solitary wave solution and homoclinic orbits of the associated ordinary differential equations, the persistence of solitary wave solutions of this equation is proved when the perturbation parameter is sufficiently small. The numerical simulations verify our theoretical analysis.
Rogue wave solutions of the nonlinear Schrödinger eqution with variable coefficients
Changfu Liu; Yan Yan Li; Meiping Gao; Zeping Wang; Zhengde Dai; Chuanjian Wang
2015-12-01
In this paper, a unified formula of a series of rogue wave solutions for the standard (1+1)-dimensional nonlinear Schrödinger equation is obtained through exp-function method. Further, by means of an appropriate transformation and previously obtained solutions, rogue wave solutions of the variable coefficient Schrödinger equation are also obtained. Two free functions of time and several arbitrary parameters are involved to generate a large number of wave structures.
无
2007-01-01
In this paper, we present an object reduction for nonlinear partial differential equations. As a concrete example of its applications in physical problems, this method is applied to the (2+1)-dimensional Boiti-Leon-Pempinelli system, which has the extensive physics background, and an abundance of exact solutions is derived from some reduction equations. Based on the derived solutions, the localized structures under the periodic wave background are obtained.
INTEGRATED DOCUMENT MANAGEMENT SOLUTION FOR THE LOCAL GOVERNMENT
Nistor Razvan
2013-07-01
Full Text Available In this paper we present system analysis and design elements for the integrated document management solution at local governing authorities in the rural areas. While specifically dealing with the actual management of the Agricultural Register, an important primary unitary evidence document, we also keep a general character of the discussion, in order to argue for the generality of the proposed solution. Hence, for the identified and described problem space we propose an administrative and software infrastructure solution. This work is an empirical research in which our aim is primarily to identify key problems within the local governing authorities from several perspectives concerning the management of the Agricultural Register then to address those problems with an integrated document management system. For the proposed solution we give and argue the general system architecture and describe the key-mechanisms that support quality requirements. The relevance of this research concern is given by the impact of the actual Agricultural Register management on important stakeholders. This can be measured as the satisfaction felt by taxpayers and the performance of the local governing authorities, the Financial Administration, the Agency of Payments and Intervention in Agriculture and the Ministry of Agriculture and Rural Development. This work is also intended as a start-point for a new, modern thinking of the governing authorities in their pursue to improve public services. For this, in our work we highlight the importance of complete system analysis at all administrative levels as a main priority concern for all public managers. Our aim is the improvement of the public service by rising the awareness of the decision makers on the necessity of using integrated document management solutions for the provided services. Also, our work aims at increasing the efficiency with which nowadays, governing authorities invest public funds in various IT projects
Numerical turbulence forced through localized random expansion waves
Mee, A J; Mee, Antony J.; Brandenburg, Axel
2006-01-01
In an attempt to determine the outer scale of turbulence driven by localized sources, such as supernova explosions in the interstellar medium, we consider a forcing function given by the gradient of gaussian profiles localized at random positions. Different coherence times of the forcing function are considered. In order to isolate the effects specific to the nature of the forcing function we consider the case of an isothermal equation of state and restrict ourselves to forcing amplitudes such that the flow remains subsonic. When the coherence time is short, the outer scale agrees with the scale of the gaussian. Longer coherence times can cause extra power at large scales, but this would not yield power law behavior at scales larger than that of the expansion waves. At scales smaller than the scale of the expansion waves the spectrum is close to power law with a spectral exponent of -2. The resulting flow is virtually free of vorticity. Viscous driving of vorticity turns out to be weak and self-amplification ...
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.
Explicit analytical wave solutions of unsteady 1D ideal gas flow with friction and heat transfer
无
2001-01-01
Several families of algebraically explicit analytical wavesolutions are derived for the unsteady 1D ideal gas flow with friction and heat-transfer, which include one family of travelling wave solutions, three families of standing wave solutions and one standing wave solution. \\{Among\\} them, the former four solution families contain arbitrary functions, so actually there are infinite analytical wave solutions having been derived. Besides their very important theoretical meaning, such analytical wave solutions can guide the development of some new equipment, and can be the benchmark solutions to promote the development of computational fluid dynamics. For example, we can use them to check the accuracy, convergence and effectiveness of various numerical computational methods and to improve the numerical computation skills such as differential schemes, grid generation ways and so on.
Explicit and exact travelling wave solutions for the generalized derivative Schroedinger equation
Huang Dingjiang [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)]. E-mail: hdj8116@163.com; Li Desheng [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China); Department of Mathematics, Shenyang Normal University, Shenyang 110034 (China); Zhang Hongqing [Department of Applied Mathematics, Dalian University of Technology, Dalian 116024 (China)
2007-02-15
In this paper, a new auxiliary equation expansion method and its algorithm is proposed by studying a first order nonlinear ordinary differential equation with a sixth-degree nonlinear term. Being concise and straightforward, the method is applied to the generalized derivative Schroedinger equation. As a result, some new exact travelling wave solutions are obtained which include bright and dark solitary wave solutions, triangular periodic wave solutions and singular solutions. This algorithm can also be applied to other nonlinear wave equations in mathematical physics.
El-Tantawy, S. A.; Aboelenen, Tarek
2017-05-01
Planar and nonplanar (cylindrical and spherical) ion-acoustic super rogue waves in an unmagnetized electronegative plasma are investigated, both analytically (for planar geometry) and numerically (for planar and nonplanar geometries). Using a reductive perturbation technique, the basic set of fluid equations is reduced to a nonplanar/modified nonlinear Schrödinger equation (NLSE), which describes a slow modulation of the nonlinear wave amplitude. The local modulational instability of the ion-acoustic structures governed by the planar and nonplanar NLSE is reported. Furthermore, the existence region of rogue waves is strictly defined. The parameters used in our calculations are from the lab observation data. The local discontinuous Galerkin (LDG) method is used to find rogue wave solutions of the planar and nonplanar NLSE and to prove L2 stability of this method. Also, it is found that the numerical simulations and the exact (analytical) solutions of the planar NLSE match remarkably well and numerical examples show that the convergence orders of the proposed LDG method are N + 1 when polynomials of degree N are used. Moreover, it is noted that the spherical rogue waves travel faster than their cylindrical counterpart. Also, the numerical solution showed that the spherical and cylindrical amplitudes of the localized pulses decrease with the increase in the time | τ |.
DECAY RATES TOWARD STATIONARY WAVES OF SOLUTIONS FOR DAMPED WAVE EQUATIONS
Fan Lili; Yin Hui; Zhao Huijiang
2008-01-01
This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the half space R+(utt-uxx+ut+f(u)x=0,t>0,z∈R+,(u(0,x)=u0(x)→u+, as x→+∞, (I)(ut(0,x)=u1(x),u(t,0)=ub.For the non-degenerate case,f'(u+)＜0,it is shown in[1]that the above initialboundary value problem admits a unique global solution u(t,x)which converges to the stationary wave φ(x)uniformly in x∈R+as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small.Moreover,by using the space-time weighted energy method initiated by Kawashima and Matsumura[2],the convergence rates(including the algebraic convergence rate and the exponential convergence rate)of u(t,x)toward φ(x)are also obtained in[1].We note,however,that the analysis in[1]relies heavily on the assumption that f'(ub)＜0.The main purpose of this paper is devoted to discussing the case of f'(ub)=0 and we show that similar results still hold for such a case.Our analysis is based on some delicate energy estimates.
Null Aether Theory: $pp$-Wave and AdS Wave Solutions
Gurses, Metin
2016-01-01
General quantum gravity arguments predict that Lorentz symmetry might not hold exactly in nature. This has motivated much interest in Lorentz breaking gravity theories recently. Among such models are vector-tensor theories with preferred direction established at every point of spacetime by a fixed-norm vector field. The dynamical vector field defined in this way is referred to as the aether. In this work, we study plane wave metrics in such a theory. For this purpose, we assume that the aether field is a null vector field satisfying certain conditions--we refer to the theory constructed in this way as Null Aether Theory (NAT). Assuming the Kerr-Schild form for such metrics we show that the theory admits exact plane wave solutions in any dimension $D\\geq3$. The field equations are reduced to two, in general coupled, differential equations when the background metric assumes the maximally symmetric form. Specifically, when the background metric is flat, i.e. for the $pp$-wave spacetimes, these equations decouple...
Sekerzh-Zen'kovich, S. Ya.
2015-10-01
The Cauchy problem for the wave equations of Boussinesq type is treated by considering the initial conditions taken from the solution of generalized Cauchy problem for the potential model of tsunami with some "simple" impulsive source under the assumption that the depth of the liquid is constant. The solutions of the problem under consideration are derived in the form of a single integral giving the wave height at every point of observation at any time moment after the pulsed action of the source. The results of comparing the time history of the the height of tsunami waves at different distances from the source for different values of its characteristic radius (these histories are calculated using two solutions, namely, the solution derived here and the solution known for the potential tsunami model) are described. Conclusions concerning the accuracy of the tested solutions are made.
On the local plane wave methods for in situ measurement of acoustic absorption
Wijnant, Y.H.
2015-01-01
In this paper we address a series of so-called local plane wave methods (LPW) to measure acoustic absorption. As opposed to other methods, these methods do not rely on assumptions of the global sound field, like e.g. a plane wave or diffuse field, but are based on a local plane wave assumption. Ther
Traveling Wave Solutions of ZK-BBM Equation Sine-Cosine Method
Sadaf Bibi
2014-03-01
Full Text Available Travelling wave solutions are obtained by using a relatively new technique which is called sine-cosine method for ZK-BBM equations. Solution procedure and obtained results re-confirm the efficiency of the proposed scheme.
New Exact Solutions of Ion-Acoustic Wave Equations by (G′/G-Expansion Method
Wafaa M. Taha
2013-01-01
Full Text Available The (G′/G-expansion method is used to study ion-acoustic waves equations in plasma physic for the first time. Many new exact traveling wave solutions of the Schamel equation, Schamel-KdV (S-KdV, and the two-dimensional modified KP (Kadomtsev-Petviashvili equation with square root nonlinearity are constructed. The traveling wave solutions obtained via this method are expressed by hyperbolic functions, the trigonometric functions, and the rational functions. In addition to solitary waves solutions, a variety of special solutions like kink shaped, antikink shaped, and bell type solitary solutions are obtained when the choice of parameters is taken at special values. Two- and three-dimensional plots are drawn to illustrate the nature of solutions. Moreover, the solution obtained via this method is in good agreement with previously obtained solutions of other researchers.
Levi, Paul
2015-01-01
Remarkable biological examples of molecular robots are the proteins kinesin-1 and dynein, which move and transport cargo down microtubule "highways," e.g., of the axon, to final nerve nodes or along dendrites. They convert the energy of ATP hydrolysis into mechanical forces and can thereby push them forwards or backwards step by step. Such mechano-chemical cycles that generate conformal changes are essential for transport on all different types of substrate lanes. The step length of an individual molecular robot is a matter of nanometers but the dynamics of each individual step cannot be predicted with certainty (as it is a random process). Hence, our proposal is to involve the methods of quantum field theory (QFT) to describe an overall reliable, multi-robot system that is composed of a huge set of unreliable, local elements. The methods of QFT deliver techniques that are also computationally demanding to synchronize the motion of these molecular robots on one substrate lane as well as across lanes. Three different challenging types of solutions are elaborated. The impact solution reflects the particle point of view; the two remaining solutions are wave based. The second solution outlines coherent robot motions on different lanes. The third solution describes running waves. Experimental investigations are needed to clarify under which biological conditions such different solutions occur. Moreover, such a nano-chemical system can be stimulated by external signals, and this opens a new, hybrid approach to analyze and control the combined system of robots and microtubules externally. Such a method offers the chance to detect mal-functions of the biological system.
Paul eLevi
2015-05-01
Full Text Available Remarkable biological examples of molecular robots are the proteins kinesin-1 and dynein, which move and transport cargo down microtubule highways, e.g. of the axon, to final nerve nodes or along dendrites. They convert the energy of ATP hydrolysis into mechanical forces and can thereby push them forwards or backwards step by step. Such mechano-chemical cycles that generate conformal changes are essential for transport on all different types of substrate lanes. The step length of an individual molecular robot is a matter of nanometers but the dynamics of each individual step cannot be predicted with certainty (as it is a random process. Hence, our proposal is to involve the methods of quantum field theory (QFT to describe an overall reliable, multi–robot system that is composed of a huge set of unreliable, local elements. The methods of QFT deliver techniques that are also computationally demanding to synchronize the motion of these molecular robots on one substrate lane as well as across lanes.Three different challenging types of solutions are elaborated. The impact solution reflects the particle point of view; the two remaining solutions are wave based. The second solution outlines coherent robot motions on different lanes. The third solution describes running waves. Experimental investigations are needed to clarify under which biological conditions such different solutions occur.Moreover, such a nano-chemical system can be stimulated by external signals, and this opens a new, hybrid approach to analyze and control the combined system of robots and microtubules externally. Such a method offers the chance to detect mal-functions of the biological system. In our framework, such defects can be characterized by the distortion of typical features of dynamic systems like attractive fixed points, limit cycles, etc. However, such additional details would overload this presentation and obscure the essentials that we wish to point out.
Four types of bounded wave solutions of CH-■ equation
2007-01-01
Recently, many authors have studied the following CH-γequation: ut + c0ux + 3uux -α2(wxxt + uuxxx + 2uxuxx) 4-γuxxx = 0,whereα2, c0 andγare paramters. Its bounded wave solutions have been investigated mainly for the caseα2 > 0. For the caseα2 < 0, the existence of three bounded waves (regular solitary waves, compactons, periodic peakons) was pointed out by Dullin et al. But the proof has not been given. In this paper, not only the existence of four types of bounded waves: periodic waves, compacton-like waves, kink-like waves, regular solitary waves, is shown, but also their explicit expressions or implicit expressions are given for the caseα2 < 0. Some planar graphs of the bounded wave solutions and their numerical simulations are given to show the correctness of our results.
Applications of F-expansion to Periodic Wave Solutions for Variant Boussinesq Equations
无
2005-01-01
We present an F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics, which can be thought of as a concentration of extended Jacobi elliptic function expansion method proposed recently. By using the F-expansion, without calculating Jacobi elliptic functions, we obtain simultaneously many periodic wave solutions expressed by various Jacobi elliptic functions for the variant Boussinesq equations. When the modulus m approaches 1 and 0, the hyperbolic function solutions (including the solitary wave solutions) and trigonometric solutions are also given respectively.
Feng, Lian-Li; Tian, Shou-Fu; Yan, Hui; Wang, Li; Zhang, Tian-Tian
2016-07-01
In this paper, a lucid and systematic approach is proposed to systematically study the periodic-wave solutions and asymptotic behaviors of a (2 + 1) -dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt (gKDKK) equation, which can be used to describe certain situations from the fluid mechanics, ocean dynamics and plasma physics. Based on Bell's polynomials, the bilinear formalism and N -soliton solution of the gKDKK equation are derived, respectively. Furthermore, based on multidimensional Riemann theta functions, the periodic-wave solutions of the equation are also constructed. Finally, an asymptotic relation between the periodic-wave solutions and soliton solutions are strictly established under a limited procedure.
Existence and stability of traveling wave solutions for multilayer cellular neural networks
Hsu, Cheng-Hsiung; Lin, Jian-Jhong; Yang, Tzi-Sheng
2015-08-01
The purpose of this article is to investigate the existence and stability of traveling wave solutions for one-dimensional multilayer cellular neural networks. We first establish the existence of traveling wave solutions using the truncated technique. Then we study the asymptotic behaviors of solutions for the Cauchy problem of the neural model. Applying two kinds of comparison principles and the weighed energy method, we show that all solutions of the Cauchy problem converge exponentially to the traveling wave solutions provided that the initial data belong to a suitable weighted space.
Propagation and localization of acoustic waves in Fibonacci phononic circuits
Aynaou, H [Laboratoire de Dynamique et d' Optique des Materiaux, Departement de Physique, Faculte des Sciences, Universite Mohamed Premier, 60000 Oujda (Morocco); Boudouti, E H El [Laboratoire de Dynamique et d' Optique des Materiaux, Departement de Physique, Faculte des Sciences, Universite Mohamed Premier, 60000 Oujda (Morocco); Djafari-Rouhani, B [Laboratoire de Dynamique et Structure des Materiaux Moleculaires, UMR CNRS 8024, UFR de Physique, Universite de Lille 1, F-59655 Villeneuve d' Ascq (France); Akjouj, A [Laboratoire de Dynamique et Structure des Materiaux Moleculaires, UMR CNRS 8024, UFR de Physique, Universite de Lille 1, F-59655 Villeneuve d' Ascq (France); Velasco, V R [Instituto de Ciencia de Materiales de Madrid, CSIC, Sor Juana Ines de la Cruz 3, 28049 Madrid (Spain)
2005-07-13
A theoretical investigation is made of acoustic wave propagation in one-dimensional phononic bandgap structures made of slender tube loops pasted together with slender tubes of finite length according to a Fibonacci sequence. The band structure and transmission spectrum is studied for two particular cases. (i) Symmetric loop structures, which are shown to be equivalent to diameter-modulated slender tubes. In this case, it is found that besides the existence of extended and forbidden modes, some narrow frequency bands appear in the transmission spectra inside the gaps as defect modes. The spatial localization of the modes lying in the middle of the bands and at their edges is examined by means of the local density of states. The dependence of the bandgap structure on the slender tube diameters is presented. An analysis of the transmission phase time enables us to derive the group velocity as well as the density of states in these structures. In particular, the stop bands (localized modes) may give rise to unusual (strong normal) dispersion in the gaps, yielding fast (slow) group velocities above (below) the speed of sound. (ii) Asymmetric tube loop structures, where the loops play the role of resonators that may introduce transmission zeros and hence new gaps unnoticed in the case of simple diameter-modulated slender tubes. The Fibonacci scaling property has been checked for both cases (i) and (ii), and it holds for a periodicity of three or six depending on the nature of the substrates surrounding the structure.
Propagation and localization of acoustic waves in Fibonacci phononic circuits
Aynaou, H.; El Boudouti, E. H.; Djafari-Rouhani, B.; Akjouj, A.; Velasco, V. R.
2005-07-01
A theoretical investigation is made of acoustic wave propagation in one-dimensional phononic bandgap structures made of slender tube loops pasted together with slender tubes of finite length according to a Fibonacci sequence. The band structure and transmission spectrum is studied for two particular cases. (i) Symmetric loop structures, which are shown to be equivalent to diameter-modulated slender tubes. In this case, it is found that besides the existence of extended and forbidden modes, some narrow frequency bands appear in the transmission spectra inside the gaps as defect modes. The spatial localization of the modes lying in the middle of the bands and at their edges is examined by means of the local density of states. The dependence of the bandgap structure on the slender tube diameters is presented. An analysis of the transmission phase time enables us to derive the group velocity as well as the density of states in these structures. In particular, the stop bands (localized modes) may give rise to unusual (strong normal) dispersion in the gaps, yielding fast (slow) group velocities above (below) the speed of sound. (ii) Asymmetric tube loop structures, where the loops play the role of resonators that may introduce transmission zeros and hence new gaps unnoticed in the case of simple diameter-modulated slender tubes. The Fibonacci scaling property has been checked for both cases (i) and (ii), and it holds for a periodicity of three or six depending on the nature of the substrates surrounding the structure.
EXISTENCE OF TIME PERIODIC SOLUTIONS FOR A DAMPED GENERALIZED COUPLED NONLINEAR WAVE EQUATIONS
房少梅; 郭柏灵
2003-01-01
The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time periodic solutions, a priori estimate and Laray-Schauder fixed point theorem to prove the convergence of the approximate solutions, the existence of time periodic solutions for a damped generalized coupled nonlinear wave equations can be obtained.
张卫国
2003-01-01
In this paper, we have obtained the bell-type and kink-type solitary wave solutions of the generalized symmetric regularized long-wave equations with high-order nonlinear terms by means of proper transformation and undetermined assumption method.
Methylparaben concentration in commercial Brazilian local anesthetics solutions
Gustavo Henrique Rodriguez da Silva
2012-08-01
Full Text Available OBJECTIVE: To detect the presence and concentration of methylparaben in cartridges of commercial Brazilian local anesthetics. MATERIAL AND METHODS: Twelve commercial brands (4 in glass and 8 in plastic cartridges of local anesthetic solutions for use in dentistry were purchased from the Brazilian market and analyzed. Different lots of the commercial brands were obtained in different Brazilian cities (Piracicaba, Campinas and São Paulo. Separation was performed using high performance liquid chromatography (HPLC with UV-Vis detector. The mobile phase used was acetonitrile:water (75:25 - v/v, pH 4.5, adjusted with acetic acid at a flow rate of 1.0 ml.min-1. RESULTS: When detected in the solutions, the methylparaben concentration ranged from 0.01% (m/v to 0.16% (m/v. One glass and all plastic cartridges presented methylparaben. CONCLUSION: 1. Methylparaben concentration varied among solutions from different manufacturers, and it was not indicated in the drug package inserts; 2. Since the presence of methylparaben in dental anesthetics is not regulated by the Brazilian National Health Surveillance Agency (ANVISA and this substance could cause allergic reactions, it is important to alert dentists about its possible presence.
Methylparaben concentration in commercial Brazilian local anesthetics solutions
da SILVA, Gustavo Henrique Rodriguez; BOTTOLI, Carla Beatriz Grespan; GROPPO, Francisco Carlos; VOLPATO, Maria Cristina; RANALI, José; RAMACCIATO, Juliana Cama; MOTTA, Rogério Heládio Lopes
2012-01-01
Objective To detect the presence and concentration of methylparaben in cartridges of commercial Brazilian local anesthetics. Material and methods Twelve commercial brands (4 in glass and 8 in plastic cartridges) of local anesthetic solutions for use in dentistry were purchased from the Brazilian market and analyzed. Different lots of the commercial brands were obtained in different Brazilian cities (Piracicaba, Campinas and São Paulo). Separation was performed using high performance liquid chromatography (HPLC) with UV-Vis detector. The mobile phase used was acetonitrile:water (75:25 - v/v), pH 4.5, adjusted with acetic acid at a flow rate of 1.0 ml.min-1. Results When detected in the solutions, the methylparaben concentration ranged from 0.01% (m/v) to 0.16% (m/v). One glass and all plastic cartridges presented methylparaben. Conclusion 1. Methylparaben concentration varied among solutions from different manufacturers, and it was not indicated in the drug package inserts; 2. Since the presence of methylparaben in dental anesthetics is not regulated by the Brazilian National Health Surveillance Agency (ANVISA) and this substance could cause allergic reactions, it is important to alert dentists about its possible presence. PMID:23032206
On analytic solutions of wave equations in regular coordinate systems on Schwarzschild background
Philipp, Dennis
2015-01-01
The propagation of (massless) scalar, electromagnetic and gravitational waves on fixed Schwarzschild background spacetime is described by the general time-dependent Regge-Wheeler equation. We transform this wave equation to usual Schwarzschild, Eddington-Finkelstein, Painleve-Gullstrand and Kruskal-Szekeres coordinates. In the first three cases, but not in the last one, it is possible to separate a harmonic time-dependence. Then the resulting radial equations belong to the class of confluent Heun equations, i.e., we can identify one irregular and two regular singularities. Using the generalized Riemann scheme we collect properties of all the singular points and construct analytic (local) solutions in terms of the standard confluent Heun function HeunC, Frobenius and asymptotic Thome series. We study the Eddington-Finkelstein case in detail and obtain a solution that is regular at the black hole horizon. This solution satisfies causal boundary conditions, i.e., it describes purely ingoing radiation at $r=2M$. ...
Weiguo ZHANG; Qiang LIU; Xiang LI; Boling GUO
2012-01-01
This paper deals with the problem of the bounded traveling wave solutions'shape and the solution to the generalized Whitham-Broer-Kaup equation with the dissipation terms which can be called WBK equation for short.The authors employ the theory and method of planar dynamical systems to make comprehensive qualitative analyses to the above equation satisfied by the horizontal velocity component u(ξ) in the traveling wave solution (u(ξ),H(ξ)),and then give its global phase portraits.The authors obtain the existent conditions and the number of the solutions by using the relations between the components u(ξ) and H(ξ) in the solutions.The authors study the dissipation effect on the solutions,find out a critical value r*,and prove that the traveling wave solution (u(ξ),H(ξ)) appears as a kink profile solitary wave if the dissipation effect is greater,i.e.,|r| ≥ r*,while it appears as a damped oscillatory wave if the dissipation effect is smaller,i.e.,|r| r*.Two solitary wave solutions to the WBK equation without dissipation effect is also obtained.Based on the above discussion and according to the evolution relations of orbits corresponding to the component u(ξ) in the global phase portraits,the authors obtain all approximate damped oscillatory solutions ((u)(ξ),(H)(ξ)) under various conditions by using the undetermined coefficients method. Finally,the error between the approximate damped oscillatory solution and the exact solution is an infinitesimal decreasing exponentially.
Gravitational Waves in Locally Rotationally Symmetric (LRS Class II Cosmologies
Michael Bradley
2017-10-01
Full Text Available In this work we consider perturbations of homogeneous and hypersurface orthogonal cosmological backgrounds with local rotational symmetry (LRS, using a method based on the 1 + 1 + 2 covariant split of spacetime. The backgrounds, of LRS class II, are characterised by that the vorticity, the twist of the 2-sheets, and the magnetic part of the Weyl tensor all vanish. They include the flat Friedmann universe as a special case. The matter contents of the perturbed spacetimes are given by vorticity-free perfect fluids, but otherwise the perturbations are arbitrary and describe gravitational, shear, and density waves. All the perturbation variables can be given in terms of the time evolution of a set of six harmonic coefficients. This set decouples into one set of four coefficients with the density perturbations acting as source terms, and another set of two coefficients describing damped source-free gravitational waves with odd parity. We also consider the flat Friedmann universe, which has been considered by several others using the 1 + 3 covariant split, as a check of the isotropic limit. In agreement with earlier results we find a second-order wavelike equation for the magnetic part of the Weyl tensor which decouples from the density gradient for the flat Friedmann universes. Assuming vanishing vector perturbations, including the density gradient, we find a similar equation for the electric part of the Weyl tensor, which was previously unnoticed.
Suppression of spiral waves using intermittent local electric shock
Ma Jun; Ying He-Ping; Li Yan-Long
2007-01-01
In this paper, an intermittent local electric shock scheme is proposed to suppress stable spiral waves in the Barkley model by a weak electric shock (about 0.4 to 0.7) imposed on a random selected n × n grids (n = 1-5, compared with the original 256×256 lattice) and monitored synchronically the evolutions of the activator on the grids as the sampled signal of the activator steps out a given threshold (i.e., the electric shock works on the n × n grids if the activator u (≤) 0.4 or u (≥) 0.8). The numerical simulations show that a breakup of spiral is observed in the media state evolution to finally obtain homogeneous states if the electric shock with appropriate intensity is imposed.
Lie symmetries and exact solutions for a short-wave model
Chen Ai-Yong; Zhang Li-Na; Wen Shuang-Quan
2013-01-01
In this paper,the Lie symmetry analysis and generalized symmetry method are performed for a short-wave model.The symmetries for this equation are given,and the phase portraits of the traveling wave systems are analyzed using the bifurcation theory of dynamical systems.The exact parametric representations of four types of traveling wave solutions are obtained.
周振功; 王彪
2001-01-01
The scattering of harmonic waves by two collinear symmetric cracks is studied using the non-local theory. A one-dimensional non-local kernel was used to replace a twodimensional one for the dynamic problem to obtain the stress occurring at the crack tips. The Fourier transform was applied and a mixed boundary value problem was formulated. Then a set of triple integral equations was solved by using Schmidt's method. This method is more exact and more reasonable than Eringen' s for solving this problem. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The non- local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the lattice parameter and the circular frequency of incident wave.
General solution of cumulative second harmonic by Lamb wave propagation in a solid plate
Deng Mingxi
2008-01-01
A straightforward approach has been developed for the general solution of cumulative second harmonic by Lamb wave propagation in a solid plate. The present analyses of second-harmonic generation by Lamb waves focus on the cases where the phase velocity of the fundamental Lamb wave is exactly or approximately equal to that of the double frequency Lamb wave (DFLW). Based on the general solution obtained, the numerical analyses show that the cumulative second-harmonic fields are associated with the position of excitation source and the difference between the phase velocity of the fundamental Lamb wave and that of the dominant DFLW component.
Travelling wave solutions for the Painleve-integrable coupled KdV equations
Xiao-Biao Lin
2008-06-01
Full Text Available We study the travelling wave solutions for a system of coupled KdV equations derived by Lou et al [11]. In that paper, they found 5 types of Painleve integrable systems for the coupled KdV system. We show that each of them can be reduced to a partially or completely uncoupled system, through which the dynamical behavior of travelling wave solutions can be determined. In some parameter regions, exact formulas for periodic and solitary waves can be obtained while in other cases, bounded travelling wave solution are discussed.
Regularity for solutions of non local parabolic equations
Lara, Héctor A Chang
2011-01-01
We study the regularity of solutions of parabolic fully nonlinear nonlocal equations. We proof $C^\\a$ regularity in space and time and for translation invariant equations and under different assumptions on the kernels $C^{1,\\a}$ in space and time regularity. The proofs rely on a weak parabolic ABP inspired in recent work done by L. Silvestre and the classic ideas of K. Tso and L. Wang. Our results remain uniform as $\\s\\to2$ allowing us to understand the non local theory as an extension to the classical one.
New Exact Travelling Wave and Periodic Solutions of Discrete Nonlinear Schr(o)dinger Equation
YANG Qin; DAI Chao-Qing; ZHANG Jie-Fang
2005-01-01
Some new exact travelling wave and period solutions of discrete nonlinear Schrodinger equation are found by using a hyperbolic tangent function approach, which was usually presented to find exact travelling wave solutions of certain nonlinear partial differential models. Now we can further extend the new algorithm to other nonlinear differentialdifferent models.
Peakons and new exact solitary wave solutions of extended quantum Zakharov-Kuznetsov equation
Zhang, Ben-gong; Li, Weibo; Li, Xiangpeng
2017-06-01
In this paper, the three dimensional extended quantum Zakharov-Kuznetsov equation, which arises in the dimensionless hydrodynamic equations describing the nonlinear propagation of the quantum ion-acoustic waves, is investigated by an auxiliary equation method. As a result, peakons and a series of new exact traveling wave solutions, including bell-shaped, kink-type solitary wave, shock wave, periodic wave, and Jacobi elliptic solutions, are obtained. We also analyze the three kinds of nonlinear structures of our results, i.e., blowup, peakons, and shock wave. These new exact solutions will enrich the previous results and help us to further understand the physical structures and analyze the nonlinear propagation of the quantum ion-acoustic waves.
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.
Cuesta, C. M.; Achleitner, F.
2017-01-01
We add a theorem to F. Achleitner, C.M. Cuesta and S. Hittmeir (2014) [1]. In that paper we studied travelling wave solutions of a Korteweg-de Vries-Burgers type equation with a non-local diffusion term. In particular, the proof of existence and uniqueness of these waves relies on the assumption that the exponentially decaying functions are the only bounded solutions of the linearised equation. In this addendum we prove this assumption and thus close the existence and uniqueness proof of travelling wave solutions.
Localized Pulsating Solutions of the Generalized Complex Cubic-Quintic Ginzburg-Landau Equation
Ivan M. Uzunov
2014-01-01
Full Text Available We study the dynamics of the localized pulsating solutions of generalized complex cubic-quintic Ginzburg-Landau equation (CCQGLE in the presence of intrapulse Raman scattering (IRS. We present an approach for identification of periodic attractors of the generalized CCQGLE. Using ansatz of the travelling wave and fixing some relations between the material parameters, we derive the strongly nonlinear Lienard-Van der Pol equation for the amplitude of the nonlinear wave. Next, we apply the Melnikov method to this equation to analyze the possibility of existence of limit cycles. For a set of fixed parameters we show the existence of limit cycle that arises around a closed phase trajectory of the unperturbed system and prove its stability. We apply the Melnikov method also to the equation of Duffing-Van der Pol oscillator used for the investigation of the influence of the IRS on the bandwidth limited amplification. We prove the existence and stability of a limit cycle that arises in a neighborhood of a homoclinic trajectory of the corresponding unperturbed system. The condition of existence of the limit cycle derived here coincides with the relation between the critical value of velocity and the amplitude of the solitary wave solution (Uzunov, 2011.
On the nonlinear dynamics of the traveling-wave solutions of the Serre equations
Mitsotakis, Dimitrios; Carter, John D
2014-01-01
In this paper, we study numerically nonlinear phenomena related to the dynamics of the traveling wave solutions of the Serre equations including their stability, their persistence, resolution into solitary waves, and wave breaking. Other forms of solutions such as DSWs, are also considered. Some differences between the solutions of the Serre equations and the full Euler equations are also studied. Euler solitary waves propagate without large variations in shape when they are used as initial conditions in the Serre equations. The nonlinearities seem to play a crucial role in the generation of small-amplitude waves and appear to cause a recurrence phenomenon in linearly unstable solutions. The numerical method used in the paper utilizes a high order FEM with smooth, periodic splines in space and explicit Runge-Kutta methods in time. The solutions of the Serre system are compared with the corresponding ones of the asymptotically-related Euler system whenever is possible.
Global smooth solutions in R3 to short wave-long wave interactions in magnetohydrodynamics
Frid, Hermano; Jia, Junxiong; Pan, Ronghua
2017-04-01
We consider a Benney-type system modeling short wave-long wave interactions in compressible viscous fluids under the influence of a magnetic field. Accordingly, this large system now consists of the compressible MHD equations coupled with a nonlinear Schrödinger equation along particle paths. We study the global existence of smooth solutions to the Cauchy problem in R3 when the initial data are small smooth perturbations of an equilibrium state. An important point here is that, instead of the simpler case having zero as the equilibrium state for the magnetic field, we consider an arbitrary non-zero equilibrium state B bar for the magnetic field. This is motivated by applications, e.g., Earth's magnetic field, and the lack of invariance of the MHD system with respect to either translations or rotations of the magnetic field. The usual time decay investigation through spectral analysis in this non-zero equilibrium case meets serious difficulties, for the eigenvalues in the frequency space are no longer spherically symmetric. Instead, we employ a recently developed technique of energy estimates involving evolution in negative Besov spaces, and combine it with the particular interplay here between Eulerian and Lagrangian coordinates.
Construction of a series of travelling wave solutions to nonlinear equations
Zhao Hong [School of Physics Science and Information Engineering, Liaocheng University, Shandong 252059 (China)], E-mail: ldzhaohong@hotmail.com
2008-06-15
In this paper, based on new auxiliary ordinary differential equation with a sixth-degree nonlinear term, we study the (1 + 1)-dimensional combined KdV-MKdV equation, Hirota equation and (2 + 1)-dimensional Davey-Stewartson equation. Then, a series of new types of travelling wave solutions are obtained which include new bell and kink profile solitary wave solutions, triangular periodic wave solutions and singular solutions. The method used here can be also extended to many other nonlinear partial differential equations.
Quantum stability of nonlinear wave type solutions with intrinsic mass parameter in QCD
Kim, Youngman; Lee, Bum-Hoon; Pak, D. G.; Park, Chanyong; Tsukioka, Takuya
2017-09-01
The problem of the existence of a stable vacuum field in pure QCD is revised. Our approach is based on using classical stationary nonlinear wave type solutions with an intrinsic mass scale parameter. Such solutions can be treated as quantum-mechanical wave functions describing massive spinless states in quantum theory. We verify whether nonlinear wave type solutions can form a stable vacuum field background within the framework of the effective action formalism. We demonstrate that there is a special class of stationary generalized Wu-Yang monopole solutions that are stable against quantum gluon fluctuations.
Travelling wave solutions for some two-component shallow water models
Dutykh, Denys; Ionescu-Kruse, Delia
2016-07-01
In the present study we perform a unified analysis of travelling wave solutions to three different two-component systems which appear in shallow water theory. Namely, we analyze the celebrated Green-Naghdi equations, the integrable two-component Camassa-Holm equations and a new two-component system of Green-Naghdi type. In particular, we are interested in solitary and cnoidal-type solutions, as two most important classes of travelling waves that we encounter in applications. We provide a complete phase-plane analysis of all possible travelling wave solutions which may arise in these models. In particular, we show the existence of new type of solutions.
Extended F-Expansion Method and Periodic Wave Solutions for Klein-Gordon-Schr(o)dinger Equations
LI Xiao-Yan; LI Xiang-Zheng; WANG Ming-Liang
2006-01-01
We present an extended F-expansion method for finding periodic wave solutions of nonlinear evolution equations in mathematical physics. By using extended F-expansion method, many periodic wave solutions expressed by various Jacobi elliptic functions for the Klein-Gordon-Schrodinger equations are obtained. In the limit cases, the solitary wave solutions and trigonometric function solutions for the equations are also obtained.
Jianping Shi; Jibin Li; Shumin Li
2013-11-01
By using dynamical system method, this paper considers the (2+1)-dimensional Davey–Stewartson-type equations. The analytical parametric representations of solitary wave solutions, periodic wave solutions as well as unbounded wave solutions are obtained under different parameter conditions. A few diagrams corresponding to certain solutions illustrate some dynamical properties of the equations.
Elimination of Anti-spiral Waves by Local Inhomogeneity in Oscillatory Systems
Fu-cheng Liu; Xiao-fei Wang
2008-01-01
Anti-spiral waves are controlled in an oscillatory system by using a local inhomogeneity. The inhomogeneity acts as a wave source, and gives rise to the propagating plane waves. It is found that there is a critical pacemaking domain size below which no wave will be created at all. Two types of ordered waves (target waves and traveling waves) are created depending on the geometry of the local inhomogeneity. The competition between the anti-spiral waves and the ordered waves is discussed. Two different competition mechanisma were observed, which are related to the ordered waves obtained from different local inhomogeneities. It is found that traveling waves with either lower frequency or higher frequency can both eliminate the anti-spiral waves, while only the target waves with lower absolute value of frequency can eliminate the anti-spiral waves. This method also applies to outwardly rotating spiral waves.The control mechanism is intuitively explained and the control method is easily operative.
High-order finite difference solution for 3D nonlinear wave-structure interaction
Ducrozet, Guillaume; Bingham, Harry B.; Engsig-Karup, Allan Peter;
2010-01-01
This contribution presents our recent progress on developing an efficient fully-nonlinear potential flow model for simulating 3D wave-wave and wave-structure interaction over arbitrary depths (i.e. in coastal and offshore environment). The model is based on a high-order finite difference scheme...... OceanWave3D presented in [1, 2]. A nonlinear decomposition of the solution into incident and scattered fields is used to increase the efficiency of the wave-structure interaction problem resolution. Application of the method to the diffraction of nonlinear waves around a fixed, bottom mounted circular...
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.
Numerical study of wave effects on groundwater flow and solute transport in a laboratory beach
Geng, Xiaolong; Boufadel, Michel C.; Xia, Yuqiang; Li, Hailong; Zhao, Lin; Jackson, Nancy L.; Miller, Richard S.
2014-09-01
A numerical study was undertaken to investigate the effects of waves on groundwater flow and associated inland-released solute transport based on tracer experiments in a laboratory beach. The MARUN model was used to simulate the density-dependent groundwater flow and subsurface solute transport in the saturated and unsaturated regions of the beach subjected to waves. The Computational Fluid Dynamics (CFD) software, Fluent, was used to simulate waves, which were the seaward boundary condition for MARUN. A no-wave case was also simulated for comparison. Simulation results matched the observed water table and concentration at numerous locations. The results revealed that waves generated seawater-groundwater circulations in the swash and surf zones of the beach, which induced a large seawater-groundwater exchange across the beach face. In comparison to the no-wave case, waves significantly increased the residence time and spreading of inland-applied solutes in the beach. Waves also altered solute pathways and shifted the solute discharge zone further seaward. Residence Time Maps (RTM) revealed that the wave-induced residence time of the inland-applied solutes was largest near the solute exit zone to the sea. Sensitivity analyses suggested that the change in the permeability in the beach altered solute transport properties in a nonlinear way. Due to the slow movement of solutes in the unsaturated zone, the mass of the solute in the unsaturated zone, which reached up to 10% of the total mass in some cases, constituted a continuous slow release of solutes to the saturated zone of the beach. This means of control was not addressed in prior studies.
Distorted Waves with Exact Non-Local Exchange a Canonical Function Approach
Fakhreddine, K; Vien, G N; Tannous, C; Langlois, J M; Robaux, O
2002-01-01
It is shown how the Canonical Function approach can be used to obtain accurate solutions for the distorted wave problem taking account of direct static and polarisation potentials and exact non-local exchange. Calculations are made for electrons in the field of atomic hydrogen and the phaseshifts are compared with those obtained using a modified form of the DWPO code of McDowell and collaborators: for small wavenumbers our approach avoids numerical instabilities otherwise present. Comparison is also made with phaseshifts calculated using local equivalent-exchange potentials and it is found that these are inaccurate at small wavenumbers. Extension of our method to the case of atoms having other than s-type outer shells is dicussed.
Dynamic aspects of apparent attenuation and wave localization in layered media
Haney, M.M.; Van Wijk, K.
2008-01-01
We present a theory for multiply-scattered waves in layered media which takes into account wave interference. The inclusion of interference in the theory leads to a new description of the phenomenon of wave localization and its impact on the apparent attenuation of seismic waves. We use the theory to estimate the localization length at a CO2 sequestration site in New Mexico at sonic frequencies (2 kHz) by performing numerical simulations with a model taken from well logs. Near this frequency, we find a localization length of roughly 180 m, leading to a localization-induced quality factor Q of 360.
Qualitative Analysis and Travelling Wave Solutions for the Chaffee-Infante Equation
Qiang, Liu; Yun, Zhu; Yuanzheng, Wang
2013-04-01
This paper employs the theory of planar dynamical systems and undetermined coefficient method to study travelling wave solutions to the Chaffee-Infante equation. By qualitative analysis, global phase portraits of the dynamic system corresponding to the equation are obtained for different parameter conditions. Furthermore, the relations between the properties of travelling wave solutions and the diffusion coefficient λ of the equation are investigated. In addition, all possible kink profile solitary wave solutions and approximate damped oscillatory solutions to the equation are obtained by using undetermined coefficient method. Error estimates indicate that the approximate solutions are meaningful. Based on these studies, the main contribution in this paper is to reveal the diffusion effect on travelling wave solutions to the Chaffee-Infante equation.
TRAVELING WAVE SPEED AND SOLUTION IN REACTION-DIFFUSION EQUATION IN ONE DIMENSION
周天寿; 张锁春
2001-01-01
By Painlevé analysis, traveling wave speed and solution of reaction-diffusion equations for the concentration of one species in one spatial dimension are in detail investigated. When the exponent of the creation term is larger than the one of the annihilation term, two typical cases are studied, one with the exact traveling wave solutions, yielding the values of speeds, the other with the series expansion solution, also yielding the value of speed. Conversely, when the exponent of creation term is smaller than the one of the annihilation term, two typical cases are also studied, but only for one of them, there is a series development solution, yielding the value of speed, and for the other, traveling wave solution cannot exist. Besides, the formula of calculating speeds and solutions of planar wave within the thin boundary layer are given for a class of typical excitable media.
Xianbin Wu
2013-01-01
Full Text Available We study a generalized KdV equation of neglecting the highest order infinitesimal term, which is an important water wave model. Some exact traveling wave solutions such as singular solitary wave solutions, semiloop soliton solutions, dark soliton solutions, dark peakon solutions, dark loop-soliton solutions, broken loop-soliton solutions, broken wave solutions of U-form and C-form, periodic wave solutions of singular type, and broken wave solution of semiparabola form are obtained. By using mathematical software Maple, we show their profiles and discuss their dynamic properties. Investigating these properties, we find that the waveforms of some traveling wave solutions vary with changes of certain parameters.
NEW EXPLICIT AND EXACT TRAVELLING WAVE SOLUTIONS FOR A COMPOUND KdV-BURGERS EQUATION
XIA TIE-CHENG; ZHANG HONG-QING; YAN ZHEN-YA
2001-01-01
In this paper, new explicit and exact travelling wave solutions for a compound KdV-Burgers equation are obtained by using the hyperbola function method and the Wu elimination method, which include new solitary wave solutions and periodic solutions. Particularly important cases of the equation, such as the compound KdV, mKdV-Burgers and mKdV equations can be solved by this method. The method can also solve other nonlinear partial differential equations.
A unified approach in seeking the solitary wave solutions to sine-Gordon type equations
Xie Yuan-Xi; Tang Jia-Shi
2005-01-01
By utilizing the solutions of an auxiliary ordinary differential equation introduced in this paper, we present a simple and direct method to uniformly construct the exact solitary wave solutions for sine-Gordon type equations.As illustrative examples, the exact solitary wave solutions of some physically significant sine-Gordon type equations,including the sine-Gordon equation, double sine-Gordon equation and mKdV-sine-Gordon equation, are investigated by means of this method.
Analytical solitary wave solutions of the nonlinear Kronig-Penney model in photonic structures.
Kominis, Y
2006-06-01
A phase space method is employed for the construction of analytical solitary wave solutions of the nonlinear Kronig-Penney model in a photonic structure. This class of solutions is obtained under quite generic conditions, while the method is applicable to a large variety of systems. The location of the solutions on the spectral band gap structure as well as on the low dimensional space of system's conserved quantities is studied, and robust solitary wave propagation is shown.
Exotic Localized Coherent Structures of the （2＋1）—Dimensional Dispersive Long—Wave Equation
ZHANGJie－Fang
2002-01-01
This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structures in the (2+1)-dimensional dispersive long-wave equations uty+ηxx+(u2)xy/2=0,ηt+(uη+u+uxy)x=0.Starting from the homogeneous balance method,we find that the richness of the localized coberent structures of the model is caused by the entrance of two variable-separated arbitrary functions.for some special selections of the arbitrary functions,it is shown that the localized structures of the model may be dromions,lumps,breathers,instantons and ring solitons.
Analytical solution of Boussinesq equations as a model of wave generation
Wiryanto, L. H.; Mungkasi, S.
2016-02-01
When a uniform stream on an open channel is disturbed by existing of a bump at the bottom of the channel, the surface boundary forms waves growing splitting and propagating. The model of the wave generation can be a forced Korteweg de Vries (fKdV) equation or Boussinesq-type equations. In case the governing equations are approximated from steady problem, the fKdV equation is obtained. The model gives two solutions representing solitary-like wave, with different amplitude. However, phyically there is only one profile generated from that process. Which solution is occured, we confirm from unsteady model. The Boussinesq equations are proposed to determine the stabil solution of the fKdV equation. From the linear and steady model, its solution is developed to determine the analytical solution of the unsteady equations, so that it can explain the physical phenomena, i.e. the process of the wave generation, wave splitting and wave propagation. The solution can also determine the amplitude and wave speed of the waves.
Generalized pp-wave solutions on product of Ricci-flat spaces
Ivashchuk, V D
2003-01-01
A multidimensional gravitational model with several scalar fields and fields of forms is considered. A wide class of generalized pp-wave solutions defined on a product of n+1 Ricci-flat spaces is obtained. Certain examples of solutions (e.g. in supergravitational theories) are singled out. For special cone-type internal factor spaces the solutions are written in Brinkmann form. An example of pp-wave solution is obtained using Penrose limit of a solution defined on product of two Einstein spaces.
Existence of traveling wave solutions for a nonlinear dissipative-dispersive equation
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.
Analytic solution of Hubbell's model of local community dynamics
McKane, A; Sole, R; Kane, Alan Mc; Alonso, David; Sole, Ricard
2003-01-01
Recent theoretical approaches to community structure and dynamics reveal that many large-scale features of community structure (such as species-rank distributions and species-area relations) can be explained by a so-called neutral model. Using this approach, species are taken to be equivalent and trophic relations are not taken into account explicitly. Here we provide a general analytic solution to the local community model of Hubbell's neutral theory of biodiversity by recasting it as an urn model i.e.a Markovian description of states and their transitions. Both stationary and time-dependent distributions are analysed. The stationary distribution -- also called the zero-sum multinomial -- is given in closed form. An approximate form for the time-dependence is obtained by using an expansion of the master equation. The temporal evolution of the approximate distribution is shown to be a good representation for the true temporal evolution for a large range of parameter values.
Multiple solutions for perturbed non-local fractional Laplacian equations
Massimiliano Ferrara
2013-11-01
Full Text Available In article we consider problems modeled by the non-local fractional Laplacian equation $$\\displaylines{ (-\\Delta^s u=\\lambda f(x,u+\\mu g(x,u \\quad\\text{in } \\Omega\\cr u=0 \\quad\\text{in } \\mathbb{R}^n\\setminus \\Omega, }$$ where $s\\in (0,1$ is fixed, $(-\\Delta ^s$ is the fractional Laplace operator, $\\lambda,\\mu$ are real parameters, $\\Omega$ is an open bounded subset of $\\mathbb{R}^n$ ($n>2s$ with Lipschitz boundary $\\partial \\Omega$ and $f,g:\\Omega\\times\\mathbb{R}\\to\\mathbb{R}$ are two suitable Caratheodory functions. By using variational methods in an appropriate abstract framework developed by Servadei and Valdinoci [17] we prove the existence of at least three weak solutions for certain values of the parameters.
Nonextensive local composition models in theories of solutions
Borges, Ernesto P
2012-01-01
Thermodynamic models present binary interaction parameters, based on the Boltzmann weight. Discrepancies from experimental data lead to empirically consider temperature dependence of the parameters, but these modifications keep unchanged the exponential nature of the equations. We replace the Boltzmann weight by the nonextensive Tsallis weight, and generalize three models for nonelectrolyte solutions that use the local composition hypothesis, namely Wilson's, NRTL, and UNIQUAC models. The proposed generalizations present a nonexponential dependence on the temperature, and relies on a theoretical basis of nonextensive statistical mechanics. The $q$-models present one extra binary parameter $q_{ij}$, that recover the original cases in the limit $q_{ij} \\to 1$. Comparison with experimental data is illustrated with two examples of the activity coefficient of ethanol, infinitely diluted in toluene, and in decane.
Travelling waves and fold localization in hovercraft seals
Wiggins, Andrew; Zalek, Steve; Perlin, Marc; Ceccio, Steve
2013-11-01
The seal system on hovercraft consists of a series of open-ended fabric cylinders that contact the free surface and, when inflated, form a compliant pressure barrier. Due to a shortening constraint imposed by neighboring seals, bow seals operate in a post-buckled state. We present results from large-scale experiments on these structures. These experiment show the hydroelastic response of seals to be characterized by striking stable and unstable post-buckling behavior. Using detailed 3-d measurements of the deformed seal shape, dominant response regimes are identified. These indicate that mode number decreases with wetted length, and that the form of the buckling packet becomes localized with increased velocity and decreased bending stiffness. Eventually, at a critical pressure, travelling waves emerge. To interpret the wide range of observed behavior, a 2-d nonlinear post-buckling model is developed and compared with the experimental studies. The model shows the importance of seal shortening and the buckling length, which is driven by the balance of hydrodynamic and bending energies. Preliminary scaling laws for the fold amplitude and mode number are presented. The experiments may ultimately provide insight into the bedeviling problem of seal wear. Sponsored by the Office of Naval Research under grant N00014-10-1-0302, Ms. Kelly B. Cooper, program manager.
Analytical solution for wave-induced response of isotropic poro-elastic seabed
无
2010-01-01
By use of separation of variables,the governing equations describing the Biot consolidation model is firstly transformed into a complex coefficient linear homogeneous ordinary differential equation,and the general solution of the horizontal displacement of seabed is constructed by employing a complex wave number,thus,all the explicit analytical solutions of the Biot consolidation model are determined. By comparing with the experimental results and analytical solution of Yamamoto etc. and the analytical solution of Hsu and Jeng,the validity and superiority of the suggested solution are verified. After investigating the influence of seabed depth on the wave-induced response of isotropic poro-elastic seabed based on the present theory,it can be concluded that the influence depth of wave-induced hydrodynamic pressure in the seabed is equal to the wave length.
F-string Solution in AdS4 X CP3 PP-wave Background
Banerjee, Gourav
2016-01-01
We present supergravity solution for F-string in pp wave background obtained from AdS4 X CP3 with zero flat directions.The classical solution is shown to break all space-time supersymmetries. We explicitly write down the standard as well as supernumerary Killing spinors both for the background and F-string solution.
Masson, Yder; Romanowicz, Barbara
2016-11-01
We derive a fast discrete solution to the scattering problem. This solution allows us to compute accurate synthetic seismograms or waveforms for arbitrary locations of sources and receivers within a medium containing localized perturbations. The key to efficiency is that wave propagation modeling does not need to be carried out in the entire volume that encompasses the sources and the receivers but only within the sub-volume containing the perturbations or scatterers. The proposed solution has important applications, for example, it permits the imaging of remote targets located in regions where no sources or receivers are present. Our solution relies on domain decomposition: within a small volume that contains the scatterers, wave propagation is modeled numerically, while in the surrounding volume, where the medium isn't perturbed, the response is obtained through wavefield extrapolation. The originality of this work is the derivation of discrete formulas for representation theorems and Kirchhoff-Helmholtz integrals that naturally adapt to the numerical scheme employed for modeling wave propagation. Our solution applies, for example, to finite difference methods or finite/spectral elements methods. The synthetic seismograms obtained with our solution can be considered "exact" as the total numerical error is comparable to that of the method employed for modeling wave propagation. We detail a basic implementation of our solution in the acoustic case using the finite difference method and present numerical examples that demonstrate the accuracy of the method. We show that ignoring some terms accounting for higher order scattering effects in our solution has a limited effect on the computed seismograms and significantly reduces the computational effort. Finally, we show that our solution can be used to compute localised sensitivity kernels and we discuss applications to target oriented imaging. Extension to the elastic case is straightforward and summarised in a
On the integrability and quasi-periodic wave solutions of the Boussinesq equation in shallow water
Ma, Pan-Li; Tian, Shou-Fu; Tu, Jian-Min; Xu, Mei-Juan
2015-05-01
In this paper, the complete integrability of the Boussinesq equation in shallow water is systematically investigated. By using generalized Bell's polynomials, its bilinear formalism, bilinear Bäcklund transformations, Lax pairs of the Boussinesq equation are constructed, respectively. By virtue of its Lax equations, we find its infinite conservation laws. All conserved densities and fluxes are obtained by lucid recursion formulas. Furthermore, based on multidimensional Riemann theta functions, we construct periodic wave solutions of the Boussinesq equation. Finally, the relations between the periodic wave solutions and soliton solutions are strictly constructed. The asymptotic behaviors of the periodic waves are also analyzed by a limiting procedure.
Traveling Wave Solutions for Epidemic Cholera Model with Disease-Related Death
Tianran Zhang; Qingming Gou
2014-01-01
Based on Codeço's cholera model (2001), an epidemic cholera model that incorporates the pathogen diffusion and disease-related death is proposed. The formula for minimal wave speed c ∗ is given. To prove the existence of traveling wave solutions, an invariant cone is constructed by upper and lower solutions and Schauder's fixed point theorem is applied. The nonexistence of traveling wave solutions is proved by two-sided Laplace transform. However, to apply two-sided Laplace transform, the pri...
Stability of Travelling Wave Solutions of the Derivative Ginzburg—Landau Equations
BolingGuo; BainianLU; 等
1997-01-01
The existence of travelling wave solution of the quinitic Ginzburg-Landau equation with derivatives is proved by the geometric singular perturbation theory.The stability of the wave solution is presented by topological methods which are proposed in Alexander,Gardner and Jones[6].The Chern number of the unstable augmented bundle is used to count the number of the linearizing operator L.For derivative Ginzburg-Landau equations,the Chern number of the unstable augmented bundle is equal to zero.I.e.c1（ε）=0,then the wave solution is stable.
Spherical Wave Propagation in a Poroelastic Medium with Infinite Permeability: Time Domain Solution
Mehmet Ozyazicioglu
2014-01-01
Full Text Available Exact time domain solutions for displacement and porepressure are derived for waves emanating from a pressurized spherical cavity, in an infinitely permeable poroelastic medium with a permeable boundary. Cases for blast and exponentially decaying step pulse loadings are considered; letter case, in the limit as decay constant goes to zero, also covers the step (uniform pressure. Solutions clearly show the propagation of the second (slow p-wave. Furthermore, Biot modulus Q is shown to have a pronounced influence on wave propagation characteristics in poroelastic media. Results are compared with solutions in classical elasticity theory.
Mvogo, Alain; Tambue, Antoine; Ben-Bolie, Germain H.; Kofané, Timoléon C.
2016-10-01
We investigate localized wave solutions in a network of Hindmarsh-Rose neural model taking into account the long-range diffusive couplings. We show by a specific analytical technique that the model equations in the infrared limit (wave number k → 0) can be governed by the complex fractional Ginzburg-Landau (CFGL) equation. According to the stiffness of the system, we propose both the semi and the linearly implicit Riesz fractional finite-difference schemes to solve efficiently the CFGL equation. The obtained fractional numerical solutions for the nerve impulse reveal localized short impulse properties. We also show the equivalence between the continuous CFGL and the discrete Hindmarsh-Rose models for relatively large network.
Multiple-resonance local wave functions for accurate excited states in quantum Monte Carlo
Zulfikri, Habiburrahman; Amovilli, Claudio; Filippi, Claudia
2016-01-01
We introduce a novel class of local multideterminant Jastrow–Slater wave functions for the efficient and accurate treatment of excited states in quantum Monte Carlo. The wave function is expanded as a linear combination of excitations built from multiple sets of localized orbitals that correspond to
Application of local wave time-frequency method in reciprocating mechanical fault diagnosis
Wang Lei; Wang Fengtao; Ma Xiaojiang
2006-01-01
To diagnose the reciprocating mechanical fault. We utilized local wave time-frequency approach. Firstly,we gave the principle. Secondly, the application of local wave time-frequency was given. Finally, we discussed its virtue in reciprocating mechanical fault diagnosis.
Similarity solution of the shock wave propagation in water
Muller M.
2007-11-01
Full Text Available This paper presents the possibility of calculation of propagation of a shock wave generated during the bubble collapse in water including the dissipation effect. The used semi-empirical model is based on an assumption of similarity between the shock pressure time profiles in different shock wave positions. This assumption leads to a system of two ordinary differential equations for pressure jump and energy at the shock front. The NIST data are used for the compilation of the equation of state, which is applied to the calculation of the shock wave energy dissipation. The initial conditions for the system of equations are obtained from the modified method of characteristics in the combination with the differential equations of cavitation bubble dynamics, which considers viscous compressible liquid with the influence of surface tension. The initial energy of the shock wave is estimated from the energy between the energies of the bubble growth to the first and second maximum bubble radii.
Exact solution of earth-flattening transformation for P-SV waves: Taking surface wave as an example
HUANG Hui; CHEN Xiao-fei
2008-01-01
Taking surface wave as an example this paper proposes an exact solution of earth-flattening transformation for P-SV waves and discusses the applicability of the approximate methods. The results show that the transform parameter m has little influence on the final results, and on the condition of short wave approximation, approximate earth-flattening transformation is suitable. Moreover, the efficiency of approximate transformation is twice of that of exact transformation. For low frequency problems exact earth-flattening transformation should be used.
Barucq, H.; Bendali, A.; Fares, M.; Mattesi, V.; Tordeux, S.
2017-02-01
A general symmetric Trefftz Discontinuous Galerkin method is built for solving the Helmholtz equation with piecewise constant coefficients. The construction of the corresponding local solutions to the Helmholtz equation is based on a boundary element method. A series of numerical experiments displays an excellent stability of the method relatively to the penalty parameters, and more importantly its outstanding ability to reduce the instabilities known as the "pollution effect" in the literature on numerical simulations of long-range wave propagation.
Symbolic computation and abundant travelling wave solutions to KdV–mKdV equation
SYED TAHIR RAZA RIZVI; KASHIF ALI; ALI SARDAR; MUHAMMAD YOUNIS; AHMET BEKIR
2017-01-01
In this article, the novel $(G'/G)$-expansion method is successfully applied to construct the abundant travelling wave solutions to the KdV–mKdV equation with the aid of symbolic computation. This equation is one of the most popular equation in soliton physics and appear in many practical scenarios like thermal pulse, wave propagation of bound particle, etc. The method is reliable and useful, and gives more general exact travelling wave solutions than the existing methods. The solutions obtained are in the form of hyperbolic, trigonometricand rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and engineering. Many of these solutions are new and some have already been constructed. Additionally, the constraint conditions, for the existence of the solutions are also listed.
Symbolic computation and abundant travelling wave solutions to KdV-mKdV equation
Raza Rizvi, Syed Tahir; Ali, Kashif; Sardar, Ali; Younis, Muhammad; Bekir, Ahmet
2017-01-01
In this article, the novel ( G '/ G)-expansion method is successfully applied to construct the abundant travelling wave solutions to the KdV-mKdV equation with the aid of symbolic computation. This equation is one of the most popular equation in soliton physics and appear in many practical scenarios like thermal pulse, wave propagation of bound particle, etc. The method is reliable and useful, and gives more general exact travelling wave solutions than the existing methods. The solutions obtained are in the form of hyperbolic, trigonometric and rational functions including solitary, singular and periodic solutions which have many potential applications in physical science and engineering. Many of these solutions are new and some have already been constructed. Additionally, the constraint conditions, for the existence of the solutions are also listed.
WANG Qi; CHEN Yong; LI Biao; ZHANG Hong-Qing
2005-01-01
Taking the (2+1)-dimensional Broer-Kaup-Kupershmidt system as a simple example, some families of rational form solitary wave solutions, triangular periodic wave solutions, and rational wave solutions are constructed by using the Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.
L2-stability of traveling wave solutions to nonlocal evolution equations
Lang, Eva; Stannat, Wilhelm
2016-10-01
Stability of the traveling wave solution to a general class of one-dimensional nonlocal evolution equations is studied in L2-spaces, thereby providing an alternative approach to the usual spectral analysis with respect to the supremum norm. We prove that the linearization around the traveling wave solution satisfies a Lyapunov-type stability condition in a weighted space L2 (ρ) for a naturally associated density ρ. The result can be applied to obtain stability of the traveling wave solution under stochastic perturbations of additive or multiplicative type. For small wave speeds, we also prove an alternative Lyapunov-type stability condition in L2 (m), where m is the symmetrizing density for the traveling wave operator, which allows to derive a long-term stochastic stability result.
Second-Order Solutions for Random Interfacial Waves Under Steady Uniform Currents
SONG Jin-bao
2005-01-01
In the present research, the study of Song (2004) for random interfacial waves in two-layer fluid is extended to the case of fluids moving at different steady uniform speeds. The equations describing the random displacements of the density interface and the associated velocity potentials in two-layer fluid are solved to the second order, and the wave-wave interactions of the wave components and the interactions between the waves and currents are described. As expected, the extended solutions include those obtained by Song (2004) as one special case where the steady uniform currents of the two fluids are taken as zero, and the solutions reduce to those derived by Sharma and Dean (1979) for random surface waves if the density of the upper fluid and the current of the lower fluid are both taken as zero.
Traveling Wave Solutions for Epidemic Cholera Model with Disease-Related Death
Tianran Zhang
2014-01-01
Full Text Available Based on Codeço’s cholera model (2001, an epidemic cholera model that incorporates the pathogen diffusion and disease-related death is proposed. The formula for minimal wave speed c∗ is given. To prove the existence of traveling wave solutions, an invariant cone is constructed by upper and lower solutions and Schauder’s fixed point theorem is applied. The nonexistence of traveling wave solutions is proved by two-sided Laplace transform. However, to apply two-sided Laplace transform, the prior estimate of exponential decrease of traveling wave solutions is needed. For this aim, a new method is proposed, which can be applied to reaction-diffusion systems consisting of more than three equations.
Lunin, Andrei; Grudiev, Alexej
2011-01-01
Analytical solutions are derived for transient and steady state gradient distributions in the travelling wave accelerating structures with arbitrary variation of parameters over the structure length. The results of both the unloaded and beam loaded cases are presented.
Traveling wave solutions for epidemic cholera model with disease-related death.
Zhang, Tianran; Gou, Qingming
2014-01-01
Based on Codeço's cholera model (2001), an epidemic cholera model that incorporates the pathogen diffusion and disease-related death is proposed. The formula for minimal wave speed c (∗) is given. To prove the existence of traveling wave solutions, an invariant cone is constructed by upper and lower solutions and Schauder's fixed point theorem is applied. The nonexistence of traveling wave solutions is proved by two-sided Laplace transform. However, to apply two-sided Laplace transform, the prior estimate of exponential decrease of traveling wave solutions is needed. For this aim, a new method is proposed, which can be applied to reaction-diffusion systems consisting of more than three equations.
Periodic Wave Solutions of Generalized Derivative Nonlinear Schr(o)dinger Equation
ZHA Qi-Lao; LI Zhi-Bin
2008-01-01
A Darboux transformation of the generalized derivative nonlinear Schr(o)dinger equation is derived. As an application, some new periodic wave solutions of the generalized derivative nonlinear Schr(o)dinger equation are explicitly given.
Single and multi-solitary wave solutions to a class of nonlinear evolution equations
Wang, Deng-Shan; Li, Hongbo
2008-07-01
In this paper, an effective discrimination algorithm is presented to deal with equations arising from physical problems. The aim of the algorithm is to discriminate and derive the single traveling wave solutions of a large class of nonlinear evolution equations. Many examples are given to illustrate the algorithm. At the same time, some factorization technique are presented to construct the traveling wave solutions of nonlinear evolution equations, such as Camassa-Holm equation, Kolmogorov-Petrovskii-Piskunov equation, and so on. Then a direct constructive method called multi-auxiliary equations expansion method is described to derive the multi-solitary wave solutions of nonlinear evolution equations. Finally, a class of novel multi-solitary wave solutions of the (2+1)-dimensional asymmetric version of the Nizhnik-Novikov-Veselov equation are given by three direct methods. The algorithm proposed in this paper can be steadily applied to some other nonlinear problems.
Exact Traveling Wave Solutions for a Kind of Generalized Ginzburg-Landau Equation
LIU Cheng-Shi
2005-01-01
Using a complete discrimination system for polynomials, new exact traveling wave solutions for generalized Ginzburg-Landau equation are obtained. The method has general meaning for many similar problems.
XIATie-cheng; ZHANGHong-qing; LIPei-chun
2003-01-01
In this paper,many new explicit and exact travelling wave solutions for Burgers-Kolmogorov-Prtrovskii-Piscounov(Burgers-KPP) equations are obtained by using hyperbola function method and Wu-elimination method,which include new singular solitary wave solutions and periodic solutions,Particular important cases of the equation.such as the generalized Burgers-Fisher equation.Burgers-Chaffee-infante equation and KPP equation,the corresponding solutions can be obtained also,The method can also solve other nonliear partial differential equations.
Liu Cheng-Shi
2007-01-01
Under the travelling wave transformation, the Camassa-Holm equation with dispersion is reduced to an integrable ordinary differential equation (ODE), whose general solution can be obtained using the trick of one-parameter group.Furthermore, by using a complete discrimination system for polynomial, the classification of all single travelling wave solutions to the Camassa-Holm equation with dispersion is obtained. In particular, an affine subspace structure in the set of the solutions of the reduced ODE is obtained. More generally, an implicit linear structure in the Camassa-Holm equation with dispersion is found. According to the linear structure, we obtain the superposition of multi-solutions to Camassa-Holm equation with dispersion.
Exact Traveling Wave Solutions for Wick-Type Stochastic Schamel KdV Equation
Hossam A. Ghany
2014-01-01
Full Text Available F-expansion method is proposed to seek exact solutions of nonlinear partial differential equations. By means of Hermite transform, inverse Hermite transform, and white noise analysis, the variable coefficients and Wick-type stochastic Schamel KdV equations are completely described. Abundant exact traveling wave solutions for variable coefficients Schamel KdV equations are given. These solutions include exact stochastic Jacobi elliptic functions, trigonometric functions, and hyperbolic functions solutions.
New Complexiton Solutions of (1+1)-Dimensional Dispersive Long Wave Equation
无
2006-01-01
By means of two different Riccati equations with different parameters as subequation in the components of finite rational expansion method, new complexiton solutions for the (1+1 )-dimensional dispersive long wave equation are successfully constructed, which include various combination of trigonometric periodic and hyperbolic function solutions, various combination of trigonometric periodic and rational function solutions, and various combination of hyperbolic and rational function solutions.
Travelling wave solutions for some time-delayed equations through factorizations
Fahmy, E.S. [King Saud University, Women Students Medical Studies and Sciences Sections, Mathematics Department, P.O. Box 22452, Riyadh 11495 (Saudi Arabia)], E-mail: esfahmy@operamail.com
2008-11-15
In this work, we use factorization method to find explicit particular travelling wave solutions for the following important nonlinear second-order partial differential equations: The generalized time-delayed Burgers-Huxley, time-delayed convective Fishers, and the generalized time-delayed Burgers-Fisher. Using the particular solutions for these equations we find the general solutions, two-parameter solution, as special cases.
Travelling wave solutions for a singularly perturbed Burgers–KdV equation
M B A Mansour
2009-11-01
This paper concerns with the existence problem of travelling wave solutions to a singularly perturbed Burgers–KdV equation. For this, we use the dynamical systems approach, specifically, the geometric singular perturbation theory and centre manifold theory. We also numerically show approximations, in particular, for kink-type waves.
LI Zheng-yuan; LIU Ying-dong; YE Qi-xiao
2001-01-01
In this paper we study the strong and weak property of travelling wave front solutions for a class of degenerate parabolic equations. How the strong and weak property changes under the effects of wave speed and reaction-diffusion terms are showed.
Travelling Wave Solutions in Delayed Reaction Diffusion Systems with Partial Monotonicity
Jian-hua Huang; Xing-fu Zou
2006-01-01
This paper deals with the existence of travelling wave fronts of delayed reaction diffusion systems with partial quasi-monotonicity. We propose a concept of "desirable pair of upper-lower solutions", through which a subset can be constructed. We then apply the Schauder's fixed point theorem to some appropriate operator in this subset to obtain the existence of the travelling wave fronts.
Bifurcation analysis and the travelling wave solutions of the Klein–Gordon–Zakharov equations
Zaiyun Zhang; Fnag-Li Xia; Xin-Ping Li
2013-01-01
In this paper, we investigate the bifurcations and dynamic behaviour of travelling wave solutions of the Klein–Gordon–Zakharov equations given in Shang et al, Comput. Math. Appl. 56, 1441 (2008). Under different parameter conditions, we obtain some exact explicit parametric representations of travelling wave solutions by using the bifurcation method (Feng et al, Appl. Math. Comput. 189, 271 (2007); Li et al, Appl. Math. Comput. 175, 61 (2006)).
Nonlocal Symmetries, Explicit Solutions, and Wave Structures for the Korteweg-de Vries Equation
Ma, Zheng-Yi; Fei, Jin-Xi
2016-08-01
From the known Lax pair of the Korteweg-de Vries (KdV) equation, the Lie symmetry group method is successfully applied to find exact invariant solutions for the KdV equation with nonlocal symmetries by introducing two suitable auxiliary variables. Meanwhile, based on the prolonged system, the explicit analytic interaction solutions related to the hyperbolic and Jacobi elliptic functions are derived. Figures show the physical interaction between the cnoidal waves and a solitary wave.
The superposition method in seeking the solitary wave solutions to the KdV-Burgers equation
Yuanxi Xie; Jilashi Tang
2006-03-01
In this paper, starting from the careful analysis on the characteristics of the Burgers equation and the KdV equation as well as the KdV-Burgers equation, the superposition method is put forward for constructing the solitary wave solutions of the KdV-Burgers equation from those of the Burgers equation and the KdV equation. The solitary wave solutions for the KdV-Burgers equation are presented successfully by means of this method.
Chang Jing; Gao Yi-xian; Cai Hua
2014-01-01
In this paper, the generalized extended tanh-function method is used for constructing the traveling wave solutions of nonlinear evolution equations. We choose Fisher’s equation, the nonlinear schr¨odinger equation to illustrate the validity and ad-vantages of the method. Many new and more general traveling wave solutions are obtained. Furthermore, this method can also be applied to other nonlinear equations in physics.
Lamb wave band gaps in locally resonant phononic crystal strip waveguides
Yao, Yuanwei, E-mail: yaoyw@scut.edu.cn [Department of Physics, Guangdong University of Technology, Guangzhou 510006 (China); Wu, Fugen [Experiment and Educational Center, Guangdong University of Technology, Guangzhou 510006 (China); Zhang, Xin [Department of Physics, Guangdong University of Technology, Guangzhou 510006 (China); Hou, Zhilin [Department of Physics, South China University of Technology, Guangzhou 510640 (China)
2012-01-09
Using finite element method, we have made a theoretically study of the band structure of Lamb wave in a locally resonant phononic crystal strip waveguide with periodic soft rubber attached on the two sides of epoxy main plate. The numerical results show that the Lamb wave band gap based on local resonant mechanism can be opened up in the stub strip waveguides, and the width of the local resonant band gap is narrower than that based on the Bragg scattering mechanism. The results also show that the stub shape and width have influence on the frequency and width of the Lamb wave band gap. -- Highlights: ► The local resonant Lamb wave band gap can be opened up in a stub strip waveguides. ► The width of the local resonant band gap is narrower than that Bragg scattering band gap. ► The shape and width of the stub have strongly influence on the local resonant band gap.
Ai-Min Yang
2014-03-01
Full Text Available The fractal heat flow within local fractional derivative is investigated. The nonhomogeneous heat equations arising in fractal heat flow are discussed. The local fractional Fourier series solutions for one-dimensional nonhomogeneous heat equations are obtained. The nondifferentiable series solutions are given to show the efficiency and implementation of the present method.
Ammonia nitrogen removal from aqueous solution by local agricultural wastes
Azreen, I.; Lija, Y.; Zahrim, A. Y.
2017-06-01
Excess ammonia nitrogen in the waterways causes serious distortion to environment such as eutrophication and toxicity to aquatic organisms. Ammonia nitrogen removal from synthetic solution was investigated by using 40 local agricultural wastes as potential low cost adsorbent. Some of the adsorbent were able to remove ammonia nitrogen with adsorption capacity ranging from 0.58 mg/g to 3.58 mg/g. The highest adsorption capacity was recorded by Langsat peels with 3.58 mg/g followed by Jackfruit seeds and Moringa peels with 3.37 mg/g and 2.64 mg/g respectively. This experimental results show that the agricultural wastes can be utilized as biosorbent for ammonia nitrogen removal. The effect of initial ammonia nitrogen concentration, pH and stirring rate on the adsorption process were studied in batch experiment. The adsorption capacity reached maximum value at pH 7 with initial concentration of 500 mg/L and the removal rate decreased as stirring rate was applied.
Local Existence of Solutions of Self Gravitating Relativistic Perfect Fluids
Brauer, Uwe; Karp, Lavi
2014-01-01
This paper deals with the evolution of the Einstein gravitational fields which are coupled to a perfect fluid. We consider the Einstein-Euler system in asymptotically flat spacestimes and therefore use the condition that the energy density might vanish or tend to zero at infinity, and that the pressure is a fractional power of the energy density. In this setting we prove local in time existence, uniqueness and well-posedness of classical solutions. The zero order term of our system contains an expression which might not be a C ∞ function and therefore causes an additional technical difficulty. In order to achieve our goals we use a certain type of weighted Sobolev space of fractional order. In Brauer and Karp (J Diff Eqs 251:1428-1446, 2011) we constructed an initial data set for these of systems in the same type of weighted Sobolev spaces. We obtain the same lower bound for the regularity as Hughes et al. (Arch Ratl Mech Anal 63(3):273-294, 1977) got for the vacuum Einstein equations. However, due to the presence of an equation of state with fractional power, the regularity is bounded from above.
Local Existence of Solutions of Self Gravitating Relativistic Perfect Fluids
Brauer, Uwe
2011-01-01
This paper deals with the evolution of the Einstein gravitational fields which are coupled to a perfect fluid. We consider the Einstein--Euler system in asymptotically flat spacestimes and therefore use the condition that the energy density might vanish or tend to zero at infinity, and that the pressure is a fractional power of the energy density. In this setting we prove a local in time existence, uniqueness and well-posedness of classical solutions. The zero order term of our system contains an expression which might not be a $C^\\infty$ function and therefore causes an additional technical difficulty. In order to achieve our goals we use a certain type of weighted Sobolev space of fractional order. Previously the authors constructed an initial data set for these of systems in the same type of weighted Sobolev spaces. We obtain the same lower bound for the regularity as the one of the classical result of Hughes, Kato and Marsden for the vacuum Einstein equations. However, due to the presence of an equation o...
Solutions of Maxwell equations for hollow curved wave conductor
Bashkov, V I
1995-01-01
In the present paper the idea is proposed to solve Maxwell equations for a curved hollow wave conductor by means of effective Riemannian space, in which the lines of motion of fotons are isotropic geodesies for a 4-dimensional space-time. The algorithm of constructing such a metric and curvature tensor components are written down explicitly. The result is in accordance with experiment.
PROGRESSING WAVE SOLUTIONS TO QUASI-LINEAR SYSTEMS MIXED PROBLEMS
WANGWEIKE
1994-01-01
The author studies the technique of paradifferential operator defined on a space of conormal distribution with three indeces,and then use this technique to prove that a progressing wave which hits the boundary is reflected according to the usual law.
Bednarik, Michal; Konicek, Petr
2002-07-01
This paper deals with using the generalized Burgers equation for description of nonlinear waves in circular ducts. Two new approximate solutions of the generalized Burgers equation (GBE) are presented. These solutions take into account the boundary layer effects. The first solution is valid for the preshock region and gives more precise results than the Fubini solution, whereas the second one is valid for the postshock (sawtooth) region and provides better results than the Fay solution. The approximate solutions are compared with numerical results of the GBE. Furthermore, the limits of validity of the used model equation are discussed with respect to boundary conditions and radius of a circular duct.
Very weak solutions of wave equation for Landau Hamiltonian with irregular electromagnetic field
Ruzhansky, Michael; Tokmagambetov, Niyaz
2017-04-01
In this paper, we study the Cauchy problem for the Landau Hamiltonian wave equation, with time-dependent irregular (distributional) electromagnetic field and similarly irregular velocity. For such equations, we describe the notion of a `very weak solution' adapted to the type of solutions that exist for regular coefficients. The construction is based on considering Friedrichs-type mollifier of the coefficients and corresponding classical solutions, and their quantitative behaviour in the regularising parameter. We show that even for distributional coefficients, the Cauchy problem does have a very weak solution, and that this notion leads to classical or distributional-type solutions under conditions when such solutions also exist.
A time-localized response of wave growth process under turbulent winds
Z. Ge
2007-06-01
Full Text Available Very short time series (with lengths of approximately 40 s or 5~7 wave periods of wind velocity fluctuations and wave elevation were recorded simultaneously and investigated using the wavelet bispectral analysis. Rapid changes in the wave and wind spectra were detected, which were found to be intimately related to significant energy transfers through transient quadratic wind-wave and wave-wave interactions. A possible pattern of energy exchange between the wind and wave fields was further deduced. In particular, the generation and variation of the strong wave-induced perturbation velocity in the wind can be explained by the strengthening and diminishing of the associated quadratic interactions, which cannot be unveiled by linear theories. On small time scales, the wave-wave quadratic interactions were as active and effective in transferring energy as the wind-wave interactions. The results also showed that the wind turbulence was occasionally effective in transferring energy between the wind and the wave fields, so that the background turbulence in the wind cannot be completely neglected. Although these effects are all possibly significant over short times, the time-localized growth of the wave spectrum may not considerably affect the long-term process of wave development.
Dierckx, Hans; Bernus, Olivier; Verschelde, Henri
2011-09-02
The dependency of wave velocity in reaction-diffusion (RD) systems on the local front curvature determines not only the stability of wave propagation, but also the fundamental properties of other spatial configurations such as vortices. This Letter gives the first derivation of a covariant eikonal-curvature relation applicable to general RD systems with spatially varying anisotropic diffusion properties, such as cardiac tissue. The theoretical prediction that waves which seem planar can nevertheless possess a nonvanishing geometrical curvature induced by local anisotropy is confirmed by numerical simulations, which reveal deviations up to 20% from the nominal plane wave speed.
Dynamical System Approach to a Coupled Dispersionless System: Localized and Periodic Traveling Waves
Gambo Betchewe; Kuetche Kamgang Victor; Bouetou Bouetou Thomas; Timoleon Crepin Kofane
2009-01-01
We investigate the dynamical behavior of a coupled dispersionlees system describing a current-conducting string with infinite length within a magnetic field.Thus,following a dynamical system approach,we unwrap typical miscellaneous traveling waves including localized and periodic ones.Studying the relative stabilities of such structures through their energy densities,we find that under some boundary conditions,localized waves moving in positive directions are more stable than periodic waves which in contrast stand for the most stable traveling waves in another boundary condition situation.
Van Gorder, Robert A., E-mail: Robert.VanGorder@maths.ox.ac.uk [Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford OX2 6GG (United Kingdom)
2015-09-15
In a recent paper, we give a study of the purely rotational motion of general stationary states in the two-dimensional local induction approximation (2D-LIA) governing superfluid turbulence in the low-temperature limit [B. Svistunov, “Superfluid turbulence in the low-temperature limit,” Phys. Rev. B 52, 3647 (1995)]. Such results demonstrated that variety of stationary configurations are possible from vortex filaments exhibiting purely rotational motion in addition to commonly discussed configurations such as helical or planar states. However, the filaments (or, more properly, waves along these filaments) can also exhibit translational motion along the axis of orientation. In contrast to the study on vortex configurations for purely rotational stationary states, the present paper considers non-stationary states which exhibit a combination of rotation and translational motions. These solutions can essentially be described as waves or disturbances which ride along straight vortex filament lines. As expected from our previous work, there are a number of types of structures that can be obtained under the 2D-LIA. We focus on non-stationary states, as stationary states exhibiting translation will essentially take the form of solutions studied in [R. A. Van Gorder, “General rotating quantum vortex filaments in the low-temperature Svistunov model of the local induction approximation,” Phys. Fluids 26, 065105 (2014)], with the difference being translation along the reference axis, so that qualitative appearance of the solution geometry will be the same (even if there are quantitative differences). We discuss a wide variety of general properties of these non-stationary solutions and derive cases in which they reduce to known stationary states. We obtain various routes to Kelvin waves along vortex filaments and demonstrate that if the phase and amplitude of a disturbance both propagate with the same wave speed, then Kelvin waves will result. We also consider the self
Singular boundary method using time-dependent fundamental solution for scalar wave equations
Chen, Wen; Li, Junpu; Fu, Zhuojia
2016-11-01
This study makes the first attempt to extend the meshless boundary-discretization singular boundary method (SBM) with time-dependent fundamental solution to two-dimensional and three-dimensional scalar wave equation upon Dirichlet boundary condition. The two empirical formulas are also proposed to determine the source intensity factors. In 2D problems, the fundamental solution integrating along with time is applied. In 3D problems, a time-successive evaluation approach without complicated mathematical transform is proposed. Numerical investigations show that the present SBM methodology produces the accurate results for 2D and 3D time-dependent wave problems with varied velocities c and wave numbers k.
Rational solutions to the KPI equation and multi rogue waves
Gaillard, Pierre
2016-04-01
We construct here rational solutions to the Kadomtsev-Petviashvili equation (KPI) as a quotient of two polynomials in x, y and t depending on several real parameters. This method provides an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2 N(N + 1) in x, y and t depending on 2 N - 2 real parameters for each positive integer N. We give explicit expressions of the solutions in the simplest cases N = 1 and N = 2 and we study the patterns of their modulus in the (x , y) plane for different values of time t and parameters.
Experimental signatures of localization in Langmuir wave turbulence
Rose, H.A.; DuBois, D.F.; Russell, D.; Bezzerides, B.
1988-01-01
Features in certain laser-plasma and ionospheric experiments are identified with the basic properties of Langmuir wave turbulence. Also, a model of caviton nucleation is presented which leads to certain novel scaling predictions. 12 refs., 19 figs.
Extreme localization of light with femtosecond subwavelength rogue waves
Liu, Changxu
2015-01-01
By using theory and experiments, we investigate a new mechanism based on spontaneous synchronization of random waves which generates ultrafast subwavelength rare events in integrated photonic chips. © 2014 Optical Society of America.
Two-state model based on the block-localized wave function method
Mo, Yirong
2007-06-01
The block-localized wave function (BLW) method is a variant of ab initio valence bond method but retains the efficiency of molecular orbital methods. It can derive the wave function for a diabatic (resonance) state self-consistently and is available at the Hartree-Fock (HF) and density functional theory (DFT) levels. In this work we present a two-state model based on the BLW method. Although numerous empirical and semiempirical two-state models, such as the Marcus-Hush two-state model, have been proposed to describe a chemical reaction process, the advantage of this BLW-based two-state model is that no empirical parameter is required. Important quantities such as the electronic coupling energy, structural weights of two diabatic states, and excitation energy can be uniquely derived from the energies of two diabatic states and the adiabatic state at the same HF or DFT level. Two simple examples of formamide and thioformamide in the gas phase and aqueous solution were presented and discussed. The solvation of formamide and thioformamide was studied with the combined ab initio quantum mechanical and molecular mechanical Monte Carlo simulations, together with the BLW-DFT calculations and analyses. Due to the favorable solute-solvent electrostatic interaction, the contribution of the ionic resonance structure to the ground state of formamide and thioformamide significantly increases, and for thioformamide the ionic form is even more stable than the covalent form. Thus, thioformamide in aqueous solution is essentially ionic rather than covalent. Although our two-state model in general underestimates the electronic excitation energies, it can predict relative solvatochromic shifts well. For instance, the intense π →π* transition for formamide upon solvation undergoes a redshift of 0.3eV, compared with the experimental data (0.40-0.5eV).
Hybrid localized waves supported by resonant anisotropic metasurfaces
Bogdanov, A. A.; Yermakov, O. Y.; Ovcharenko, A. I.
2016-01-01
We study both theoretically and experimentally a new class of surface electromagnetic waves supported by resonant anisotropic metasurface. At certain frequency this type of metasurface demonstrates the topological transition from elliptical to hyperbolic regime.......We study both theoretically and experimentally a new class of surface electromagnetic waves supported by resonant anisotropic metasurface. At certain frequency this type of metasurface demonstrates the topological transition from elliptical to hyperbolic regime....
A Parabolic Equation Approach to Modeling Acousto-Gravity Waves for Local Helioseismology
Del Bene, Kevin; Lingevitch, Joseph; Doschek, George
2016-08-01
A wide-angle parabolic-wave-equation algorithm is developed and validated for local-helioseismic wave propagation. The parabolic equation is derived from a factorization of the linearized acousto-gravity wave equation. We apply the parabolic-wave equation to modeling acoustic propagation in a plane-parallel waveguide with physical properties derived from helioseismic data. The wavenumber power spectrum and wave-packet arrival-time structure for receivers in the photosphere with separation up to 30° is computed, and good agreement is demonstrated with measured values and a reference spectral model.
SOLUTION TO BSDE WITH NONHOMOGENEOUS JUMPS UNDER LOCALLY LIPSCHITZIAN CONDITION
无
2008-01-01
In this paper, we investigate the existence and uniqueness of the solution to a quasilinear backward stochastic differential equation with Poisson jumps. By introducing a series of approximate equations, we can show that BSDE has a unique adapted solution.
Nonlinear wave structures as exact solutions of Vlasov-Maxwell equations.
Dasgupta, B.; Tsurutani, B. T.; Janaki, M. S.; Sharma, A. S.
2001-12-01
Many recent observations by POLAR and Geotail spacecraft of the low-latitudes magnetopause boundary layer (LLBL) and the polar cap boundary layer (PCBL) have detected nonlinear wave structures [Tsurutani et al, Geophys. Res. Lett., 25, 4117, 1998]. These nonlinear waves have electromagnetic signatures that are identified with Alfven and Whistler modes. Also solitary waves with mono- and bi-polar features were observed. In general such electromagnetic structures are described by the full Vlasov-Maxwell equations for waves propagating at an angle to the ambient magnetic field, but it has been a diffficult task obtaining the solutions because of the inherent nonlinearity. We have obtained an exact nonlinear solution of the full Vlasov-Maxwell equations in the presence of an electromagnetic wave propagating at an arbitrary direction with an ambient magnetic field. This is accomplished by finding the constants of motion of the charged particles in the electromagnetic field of the wave and then constructing a realistic distribution function as a function of these constants of motion. The corresponding trapping conditions for such waves are obtained, yielding the self-consistent description for the particles in the presence of the nonlinear waves. The interpretation of the observed nonlinear structures in terms of these general solutions will be presented.
A method for finding the optimal predictor indices for local wave climate conditions
Camus, Paula; Méndez, Fernando J.; Losada, Inigo J.; Menéndez, Melisa; Espejo, Antonio; Pérez, Jorge; Rueda, Ana; Guanche, Yanira
2014-07-01
In this study, a method to obtain local wave predictor indices that take into account the wave generation process is described and applied to several locations. The method is based on a statistical model that relates significant wave height with an atmospheric predictor, defined by sea level pressure fields. The predictor is composed of a local and a regional part, representing the sea and the swell wave components, respectively. The spatial domain of the predictor is determined using the Evaluation of Source and Travel-time of wave Energy reaching a Local Area (ESTELA) method. The regional component of the predictor includes the recent historical atmospheric conditions responsible for the swell wave component at the target point. The regional predictor component has a historical temporal coverage ( n-days) different to the local predictor component (daily coverage). Principal component analysis is applied to the daily predictor in order to detect the dominant variability patterns and their temporal coefficients. Multivariate regression model, fitted at daily scale for different n-days of the regional predictor, determines the optimum historical coverage. The monthly wave predictor indices are selected applying a regression model using the monthly values of the principal components of the daily predictor, with the optimum temporal coverage for the regional predictor. The daily predictor can be used in wave climate projections, while the monthly predictor can help to understand wave climate variability or long-term coastal morphodynamic anomalies.
General Solution of EM Wave Propagation in Anisotropic Media
Lee, Jinyoung
2010-01-01
When anisotropy is involved, the wave equation becomes simultaneous partial differential equations that are not easily solved. Moreover, when the anisotropy occurs due to both permittivity and permeability, these equations are insolvable without a numerical or an approximate method. The problem is essentially due to the fact neither $\\e$ nor $\\m$ can be extracted from the curl term, when they are in it. The terms $\
The homotopic mapping solution for the solitary wave for a generalized nonlinear evolution equation
Mo Jia-Qi; Lin Su-Rong
2009-01-01
This paper studies a generalized nonlinear evolution equation. Using the homotopic mapping method,it constructs a corresponding homotopic mapping transform. Selecting a suitable initial approximation and using homotopic mapping,it obtains an approximate solution with an arbitrary degree of accuracy for the solitary wave. From the approximate solution obtained by using the homotopic mapping method,it possesses a good accuracy.
Travelling wave solutions to nonlinear physical models by means of the ﬁrst integral method
İsmail Aslan Aslan
2011-04-01
This paper presents the ﬁrst integral method to carry out the integration of nonlinear partial differential equations in terms of travelling wave solutions. For illustration, three important equations of mathematical physics are analytically investigated. Through the established ﬁrst integrals, exact solutions are successfully constructed for the equations considered.
ON THE NUMERICAL SOLUTION OF QUASILINEAR WAVE EQUATION WITH STRONG DISSIPATIVE TERM
Aytekin Gülle
2004-01-01
The numerical solution for a type of quasilinear wave equation is studied. The three-level difference scheme for quasi-linear waver equation with strong dissipative term is constructed and the convergence is proved. The error of the difference solution is estimated.The theoretical results are controlled on a numerical example.
Xiaohong Tian
2014-01-01
Full Text Available A delayed SIRS infectious disease model with nonlocal diffusion and nonlinear incidence is investigated. By constructing a pair of upper-lower solutions and using Schauder's fixed point theorem, we derive the existence of a traveling wave solution connecting the disease-free steady state and the endemic steady state.
Exact periodic wave and soliton solutions in two-component Bose-Einstein condensates
Li Hua-Mei
2007-01-01
We present several families of exact solutions to a system of coupled nonlinear Schr(o)dinger equations. The model describes a binary mixture of two Bose-Einstein condensates in a magnetic trap potential. Using a mapping deformation method, we find exact periodic wave and soliton solutions, including bright and dark soliton pairs.
Classical implicit travelling wave solutions for a quasilinear convection-diffusion equation
Hearns, Jessica; Van Gorder, Robert A.
2012-11-01
We discuss classical implicit solutions to the partial differential equation ut=(H(u))xx+(G(u))x, a general convection-diffusion PDE with particular subcases appearing in many areas of fluids and astrophysics. As an illustrative example, and to compare our results with those present in the literature, we frequently consider travelling wave solutions for the quasilinear PDE ut=(um)xx+(un)x, which has been used to describe the flow of viscous fluids on an inclined bed and as a model of convection-diffusion processes. When n ⩾ m > 1, this equation can be used to model the flow of a fluid under gravity through a homogeneous and isotropic porous medium. The travelling wave ODE for both the general and more specific cases have a first integral which is used to obtain an implicit solution for the travelling wave profiles. We should mention that, for some values of m, the implicit relation can be solved in closed form for explicit exact solutions. In the case of n = 2m - 1, solving the implicit relation gives a general way of obtaining the solutions found in Vanaja [Vanaja, V., 2009. Physica Scripta 80, p. 045402] where the travelling wave solutions for the cases (m, n) = (2, 3) and (m, n) = (3, 5) were explicitly constructed using a more complicated ansatz method. For other more complicated cases where inversion cannot be performed, we apply the method of series reversion to construct series solutions from the implicit relations. Furthermore, we deduce the dependence of travelling wave solutions on the wave speed, even in cases where the explicit exact solution cannot be found.
Diffraction of localized shear wave at the edge of semi-infinite crack in compound elastic space
Grigoryan E.Kh.
2014-12-01
Full Text Available The diffraction of localized shear plane Love`s wave, falling from infinity in a piecewise-homogeneous elastic space weakened by a semi-infinite crack parallel to the line of heterogeneity is considered. With the help of Fourier transform, mixed boundary value problem of diffraction of elastic waves is reduced to the problem of Riemann type theory of analytic functions on the real axis with the right part of the generalized Dirac function . Obtaining in generalized functions solution of functional equations allowed us to obtain the distribution of wave field in each subregion of elastic space, as well as asymptotic formulas defining the characteristics of the diffraction field in remote areas.
Traveling wave solutions of nonlinear evolution equations via the enhanced (G′/G-expansion method
Kamruzzaman Khan
2014-07-01
Full Text Available In this article, an enhanced (G′/G-expansion method is suggested to find the traveling wave solutions for the modified Korteweg de-Vries (mKDV equation. Abundant traveling wave solutions are derived, which are expressed by the hyperbolic and trigonometric functions involving several parameters. The efficiency of this method for finding these exact solutions has been demonstrated. It is shown that the proposed method is effective and can be used for many other nonlinear evolution equations (NLEEs in mathematical physics.
Lijun Zhang
2014-01-01
Full Text Available An integral-differential model equation arising from neuronal networks with very general kernel functions is considered in this paper. The kernel functions we study here include pure excitations, lateral inhibition, lateral excitations, and more general synaptic couplings (e.g., oscillating kernel functions. The main goal of this paper is to prove the existence and uniqueness of the traveling wave front solutions. The main idea we apply here is to reduce the nonlinear integral-differential equation into a solvable differential equation and test whether the solution we get is really a wave front solution of the model equation.
Solitary Wave Solutions of KP equation, Cylindrical KP Equation and Spherical KP Equation
Li, Xiang-Zheng; Zhang, Jin-Liang; Wang, Ming-Liang
2017-02-01
Three (2+1)-dimensional equations-KP equation, cylindrical KP equation and spherical KP equation, have been reduced to the same KdV equation by different transformation of variables respectively. Since the single solitary wave solution and 2-solitary wave solution of the KdV equation have been known already, substituting the solutions of the KdV equation into the corresponding transformation of variables respectively, the single and 2-solitary wave solutions of the three (2+1)-dimensional equations can be obtained successfully. Supported by the National Natural Science Foundation of China under Grant No. 11301153 and the Doctoral Foundation of Henan University of Science and Technology under Grant No. 09001562, and the Science and Technology Innovation Platform of Henan University of Science and Technology under Grant No. 2015XPT001
Existence of traveling wave solutions for diffusive predator-prey type systems
Hsu, Cheng-Hsiung; Yang, Chi-Ru; Yang, Ting-Hui; Yang, Tzi-Sheng
In this work we investigate the existence of traveling wave solutions for a class of diffusive predator-prey type systems whose each nonlinear term can be separated as a product of suitable smooth functions satisfying some monotonic conditions. The profile equations for the above system can be reduced as a four-dimensional ODE system, and the traveling wave solutions which connect two different equilibria or the small amplitude traveling wave train solutions are equivalent to the heteroclinic orbits or small amplitude periodic solutions of the reduced system. Applying the methods of Wazewski Theorem, LaSalle's Invariance Principle and Hopf bifurcation theory, we obtain the existence results. Our results can apply to various kinds of ecological models.
Solitary waves and their stability in colloidal media: semi-analytical solutions
Marchant, T R
2012-01-01
Spatial solitary waves in colloidal suspensions of spherical dielectric nanoparticles are considered. The interaction of the nanoparticles is modelled as a hard-sphere gas, with the Carnahan-Starling formula used for the gas compressibility. Semi-analytical solutions, for both one and two spatial dimensions, are derived using an averaged Lagrangian and suitable trial functions for the solitary waves. Power versus propagation constant curves and neutral stability curves are obtained for both cases, which illustrate that multiple solution branches occur for both the one and two dimensional geometries. For the one-dimensional case it is found that three solution branches (with a bistable regime) occur, while for the two-dimensional case two solution branches (with a single stable branch) occur in the limit of low background packing fractions. For high background packing fractions the power versus propagation constant curves are monotonic and the solitary waves stable for all parameter values. Comparisons are mad...
El-Wakil, S A; Abd-El-Hamid, H M; Abulwafa, E M
2010-01-01
A rigorous theoretical investigation has been made on electron acoustic wave propagating in unmagnetized collisionless plasma consisting of a cold electron fluid, non-thermal hot electrons and stationary ions. Based on the pseudo-potential approach, large amplitude potential structures and the existence of solitary waves are discussed. The reductive perturbation method has been employed to derive the Korteweg-de Vries (KdV) equation for small but finite amplitude electrostatic waves. An algebraic method with computerized symbolic computation, which greatly exceeds the applicability of the existing tanh, extended tanh methods in obtaining a series of exact solutions of the KdV equation. Numerical studies have been made using plasma parameters close to those values corresponding to the dayside auroral zone reveals different solutions i.e., bell-shaped solitary pulses, rational pulses and solutions with singularity at a finite points which called blowup solutions in addition to the propagation of an explosive pu...
Nonlinear Whitham-Broer-Kaup Wave Equation in an Analytical Solution
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.
Water Wave Solutions of the Coupled System Zakharov-Kuznetsov and Generalized Coupled KdV Equations
A. R. Seadawy
2014-01-01
Full Text Available An analytic study was conducted on coupled partial differential equations. We formally derived new solitary wave solutions of generalized coupled system of Zakharov-Kuznetsov (ZK and KdV equations by using modified extended tanh method. The traveling wave solutions for each generalized coupled system of ZK and KdV equations are shown in form of periodic, dark, and bright solitary wave solutions. The structures of the obtained solutions are distinct and stable.
Water wave solutions of the coupled system Zakharov-Kuznetsov and generalized coupled KdV equations.
Seadawy, A R; El-Rashidy, K
2014-01-01
An analytic study was conducted on coupled partial differential equations. We formally derived new solitary wave solutions of generalized coupled system of Zakharov-Kuznetsov (ZK) and KdV equations by using modified extended tanh method. The traveling wave solutions for each generalized coupled system of ZK and KdV equations are shown in form of periodic, dark, and bright solitary wave solutions. The structures of the obtained solutions are distinct and stable.
Zhu Jia-Min; Zheng Chun-Long; Ma Zheng-Yi
2004-01-01
A general mapping deformation method is applied to a generalized variable coefficient KdV equation. Many new types of exact solutions, including solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions and other exact excitations are obtained by the use of a simple algebraic transformation relation between the generalized variable coefficient KdV equation and a generalized cubic nonlinear Klein-Gordon equation.
Gorobets, Y. I.; Gorobets, Y.; Kulish, V. V.
2017-01-01
In the paper, spin waves in a uniaxial two-sublattice antiferromagnet are investigated. A new class of self-similar solutions of the Landau-Lifshitz equation is obtained and, therefore, a new type of spin waves is described. Examples of solutions of the found class are presented. New type of solution admits both linear and non-linear spin waves, including solitons. Space transformations used in the solution are mathematically analogous to the relativistic transformations.
TREASURY EXECUTION OF LOCAL SPENDING BUDGETS: PROBLEMS AND SOLUTIONS
Dema, Dmitry; Feshchenko, Natalya
2014-01-01
The theoretical and practical aspects of using a treasury management system for servicing of local budgets are considered; the role of treasury bodies in routine management of local finances is defined. Current problems of treasury-based execution of local spending budgets are investigated and main deregulating factors affecting the procedure of cash execution of budgets are arranged in a system.Ways to improve budget funds management at the local level are proposed including: improvement of ...
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.
Wavelet-based integral representation for solutions of the wave equation
Perel, Maria V; Sidorenko, Mikhail S [Department of Mathematical Physics, Physics Faculty, St Petersburg University, Ulyanovskaya 1-1, Petrodvorets, St Petersburg 198904 (Russian Federation)], E-mail: perel@mph.phys.spbu.ru, E-mail: M-Sidorenko@yandex.ru
2009-09-18
An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on mathematical techniques of continuous wavelet analysis. The formulae obtained are justified from the point of view of distribution theory. A comparison of the results with those by G Kaiser is carried out. Methods of obtaining physical wavelets are discussed.
Letlhogonolo Daddy Moleleki
2014-01-01
Full Text Available We analyze the (3+1-dimensional Boussinesq equation, which has applications in fluid mechanics. We find exact solutions of the (3+1-dimensional Boussinesq equation by utilizing the Lie symmetry method along with the simplest equation method. The solutions obtained are traveling wave solutions. Moreover, we construct the conservation laws of the (3+1-dimensional Boussinesq equation using the new conservation theorem, which is due to Ibragimov.
Self-similar wave produced by local perturbation of the Kelvin-Helmholtz shear-layer instability.
Hoepffner, Jérôme; Blumenthal, Ralf; Zaleski, Stéphane
2011-03-11
We show that the Kelvin-Helmholtz instability excited by a localized perturbation yields a self-similar wave. The instability of the mixing layer was first conceived by Helmholtz as the inevitable growth of any localized irregularity into a spiral, but the search and uncovering of the resulting self-similar evolution was hindered by the technical success of Kelvin's wavelike perturbation theory. The identification of a self-similar solution is useful since its specific structure is witness of a subtle nonlinear equilibrium among the forces involved. By simulating numerically the Navier-Stokes equations, we analyze the properties of the wave: growth rate, propagation speed and the dependency of its shape upon the density ratio of the two phases of the mixing layer.
Carvalho, Tiago; Llibre, Jaume
2017-06-01
Lorenz studied the coupled Rosby waves and gravity waves using the differential system U˙ = -VW + bVZ,V˙ = UW - bUZ,Ẇ = -UV,Ẋ = -Z,Ż = bUV + X. This system has the two first integrals H1 = U2 + V2,H 2 = V2 + W2 + X2 + Z2. Our main result shows that in each invariant set {H1 = h1 > 0}∩{H2 = h2 > 0} there are at least four (resp., 2) periodic solutions of the differential system with b≠0 and h2 > h1 (resp., h2 < h1).
Complexiton solutions of the (2+1)-dimensional dispersive long wave equation
Chen Yong; Fan En-Gui
2007-01-01
In this pager a pure algebraic method implemented in a computer algebraic system, named multiple Riccati equations rational expansion method, is presented to construct a novel class of complexiton solutions to integrable equations and nonintegrable equations. By solving the (2+1)-dimensional dispersive long wave equation, it obtains many new types of complexiton solutions such as various combination of trigonometric periodic and hyperbolic function solutions,various combination of trigonometric periodic and rational function solutions, various combination of hyperbolic and rational function solutions, etc.
Noundjeu, P
2003-01-01
Using the iterative Scheme we prove the local existence and uniqueness of solutions of the spherically symmetric Einstein-Vlasov-Maxwell system with small initial data. We prove a continuation criterion to global in-time solutions.
无
2008-01-01
The authors prove the local existence and uniqueness of weak solution of a hyperbolic-parabolic system and establish the global existence of the weak solution for this system for the spatial dimension n = 1.
Initial Assessment of Mooring Solutions for Floating Wave Energy Converters
Thomsen, Jonas Bjerg; Kofoed, Jens Peter; Delaney, Martin
2016-01-01
The present study investigates three different types of mooring systems in order to establish potential cost reductions and applicability to wave energy converters (WECs). Proposed mooring systems for three existing WECs create the basis for this study, and the study highlights areas of interest ...... type system can provide a paramount cost reduction compared to a traditional CALM type system with chain lines. Similarly, use of nylon ropes similarly appears to provide low cost.......The present study investigates three different types of mooring systems in order to establish potential cost reductions and applicability to wave energy converters (WECs). Proposed mooring systems for three existing WECs create the basis for this study, and the study highlights areas of interest...... using a preliminary cost estimation and discussion of buildability issues. Using synthetic rope and variations in the mooring configuration has the potential of influencing the cost significantly. In order to quantify this potential, a simple quasi-static analysis is performed, which shows that a SALM...
Electromagnetic Waves with Frequencies Near the Local Proton Gryofrequency: ISEF-3 1 AU Observations
Tsurutani, B.
1993-01-01
Low Frequency electromagnetic waves with periods near the local proton gyrofrequency have been detected near 1 AU by the magnetometer onboard ISEE-3. For these 1 AU waves two physical processes are possible: solar wind pickup of nuetral (interstellar?) particles and generation by relativistic electron beams propagating from the Sun.
Electromagnetic Waves with Frequencies Near the Local Proton Gryofrequency: ISEF-3 1 AU Observations
Tsurutani, B.
1993-01-01
Low Frequency electromagnetic waves with periods near the local proton gyrofrequency have been detected near 1 AU by the magnetometer onboard ISEE-3. For these 1 AU waves two physical processes are possible: solar wind pickup of nuetral (interstellar?) particles and generation by relativistic electron beams propagating from the Sun.
Erofeev, V. I.; Leontieva, A. V.; Malkhanov, A. O.
2017-06-01
Within the framework of self consistent dynamic problems, the impact of dislocations and point defects on the spatial localization of nonlinear acoustic waves propagating in materials has been studied.
Integrated submm wave receiver with superconductive local oscillator
Koshelets, VP; Shitov, SV; Filippenko, LV; Ermakov, AB; Luinge, W; Gao, [No Value; Lehikoinen, P; Rogalla, H; Blank, DHA
1997-01-01
A fully superconductive integrated receiver is very promising for submm space astronomy where low weight, low power consumption, and limited volume are required. The new versions of the integrated quasioptical submm wave receiver have been designed, fabricated and tested in the frequency range of 45
Lamb Wave Polarization Techniques for Structural Damage Localization and Quantification
2011-11-01
technological applications based on wave propagation, such as optics, seismology , telecommunications, and radar science. As opposed to other fields...Sorrento, Naples, Italy , 2010. 12. Sundaresan, M. J.; Pai, P. F.; Ghoshal, A.; Schulz, M.; Ferguson, F.; Chung, J. F. Methods of Distributed Sensing
Generation of localized magnetic moments in the charge-density-wave state
Akzyanov, R. S.; Rozhkov, A. V.
2014-01-01
We propose a mechanism explaining the generation of localized magnetic moments in charge-density-wave compounds. Our model Hamiltonian describes an Anderson impurity placed in a host material exhibiting the charge-density wave. There is a region of the model's parameter space, where even weak Coulomb repulsion on the impurity site is able to localize the magnetic moment on the impurity. The phase diagram of a single impurity at T=0 is mapped. To establish the connection with experiment thermo...
Torsion Wave Solutions in Yang-Mielke Theory of Gravity
Pasic, Vedad
2015-01-01
The approach of metric-affine gravity initially distinguishes it from Einstein's general relativity. Using an independent affine connection produces a theory with 10+64 unknowns. We write down the Yang-Mills action for the affine connection and produce the Yang-Mills equation and the so called complementary Yang-Mills equation by independently varying with respect to the connection and the metric respectively. We call this theory the Yang-Mielke theory of gravity. We construct explicit spacetimes with pp-metric and purely axial torsion and show that they represent a solution of Yang-Mills theory. Finally we compare these spacetimes to existing solutions of metric-affine gravity and present future research possibilities.
Exact Spherical Wave Solutions to Maxwell's Equations with Applications
Silvestri, Guy G.
Electromagnetic radiation from bounded sources represent an important class of physical problems that can be solved for exactly. However, available texts on this subject almost always resort to approximate solution techniques that not only obscure the essential features of the problem but also restrict application to limited ranges of observation. This dissertation presents exact solutions for this important class of problems and demonstrates how these solutions can be applied to situations of genuine physical interest, in particular, the design of device structures with prespecified emission characteristics. The strategy employed is to solve Maxwell's equations in the spherical coordinate system. In this system, fundamental parameters such as electric and magnetic multipole moments fall out quite naturally. Expressions for radiated power, force, and torque assume especially illuminating and simple forms when expressed in terms of these multipole moments. All solutions are derived ab initio using first-principles arguments exclusively. Two operator-equations that receive particularly detailed treatment are the vector Helmholtz equation for the time-independent potential vec a and the "covariant divergence" equation for the energy-momentum-stress tensor T^{mu nu}. An application of classical formulas, as modified by the requirements of statistical mechanics, to the case of heated blackbodies leads to inquiries into the foundations of quantum mechanics and their relation to classical field theory. An application of formulas to various emission structures (spherically-shaped antennas, surface diffraction gratings, collimated beams) provides a basis upon which to characterize these structures in an exact sense, and, ultimately, to elicit clues as to their optimum design.
Van Gorder, Robert A.
2016-05-01
Very recent experimental work has demonstrated the existence of Kelvin waves along quantized vortex filaments in superfluid helium. The possible configurations and motions of such filaments is of great physical interest, and Svistunov previously obtained a Hamiltonian formulation for the dynamics of quantum vortex filaments in the low-temperature limit under the assumption that the vortex filament is essentially aligned along one axis, resulting in a two-dimensional (2D) problem. It is standard to approximate the dynamics of thin filaments by employing the local induction approximation (LIA), and we show that by putting the two-dimensional LIA into correspondence with the first equation in the integrable Wadati-Konno-Ichikawa-Schimizu (WKIS) hierarchy, we immediately obtain solutions to the two-dimensional LIA, such as helix, planar, and self-similar solutions. These solutions are obtained in a rather direct manner from the WKIS equation and then mapped into the 2D-LIA framework. Furthermore, the approach can be coupled to existing inverse scattering transform results from the literature in order to obtain solitary wave solutions including the analog of the Hasimoto one-soliton for the 2D-LIA. One large benefit of the approach is that the correspondence between the 2D-LIA and the WKIS allows us to systematically obtain vortex filament solutions directly in the Cartesian coordinate frame without the need to solve back from curvature and torsion. Implications of the results for the physics of experimentally studied solitary waves, Kelvin waves, and postvortex reconnection events are mentioned.
Makarov, V A; Petnikova, V M; Potravkin, N N; Shuvalov, V V [International Laser Center, M. V. Lomonosov Moscow State University, Moscow (Russian Federation)
2014-02-28
Using the linearization method, we obtain approximate solutions to a one-dimensional nonintegrable problem of propagation of elliptically polarised light waves in an isotropic gyrotropic medium with local and nonlocal components of the Kerr nonlinearity and group-velocity dispersion. The consistent evolution of two orthogonal circularly polarised components of the field is described analytically in the case when their phases vary linearly during propagation. The conditions are determined for the excitation of waves with a regular and 'chaotic' change in the polarisation state. The character of the corresponding nonlinear solutions, i.e., periodic analogues of multisoliton complexes, is analysed. (nonlinear optical phenomena)
Graphene edges; localized edge state and electron wave interference
Enoki Toshiaki
2012-03-01
Full Text Available The electronic structure of massless Dirac fermion in the graphene hexagonal bipartite is seriously modified by the presence of edges depending on the edge chirality. In the zigzag edge, strongly spin polarized nonbonding edge state is created as a consequence of broken symmetry of pseudo-spin. In the scattering at armchair edges, the K-K’ intervalley transition gives rise to electron wave interference. The presence of edge state in zigzag edges is observed in ultra-high vacuum STM/STS observations. The electron wave interference phenomenon in the armchair edge is observed in the Raman G-band and the honeycomb superlattice pattern with its fine structure in STM images.
JianlanHU; X.FENG; ZhiLi
2000-01-01
New exact traveling wave solutions are derived for the fifth order KdV type equations by using a delicate way of rank analysis two-step ansatz method. Solitary shallowwater waves described by the above equation are discussed.
Numerical study of Anderson localization of terahertz waves in disordered waveguides
Lapointe, C P; Enderli, F; Feurer, T; Skipetrov, S E; Scheffold, F
2014-01-01
We present a numerical study of electromagnetic wave transport in disordered quasi-one-dimensional waveguides at terahertz frequencies. Finite element method calculations of terahertz wave propagation within LiNbO$_{3}$ waveguides with randomly arranged air-filled circular scatterers exhibit an onset of Anderson localization at experimentally accessible length scales. Results for the average transmission as a function of waveguide length and scatterer density demonstrate a clear crossover from diffusive to localized transport regime. In addition, we find that transmission fluctuations grow dramatically when crossing into the localized regime. Our numerical results are in good quantitative agreement with theory over a wide range of experimentally accessible parameters both in the diffusive and localized regime opening the path towards experimental observation of terahertz wave localization.
Said-Houari, Belkacem
2012-03-01
In this paper, we consider a viscoelastic wave equation with an absorbing term and space-time dependent damping term. Based on the weighted energy method, and by assuming that the kernel decaying exponentially, we obtain the L2 decay rates of the solutions. More precisely, we show that the decay rates are the same as those obtained in Lin et al. (2010) [15] for the semilinear wave equation with absorption term. © 2011 Elsevier Inc.
Group Classification and Exact Solutions of a Class of Variable Coefficient Nonlinear Wave Equations
HUANG Ding-Jiang; MEI Jian-Qin; ZHANG Hong-Qing
2009-01-01
Complete group classification of a class of variable coefficient (1 + 1)-dimensional wave equations is performed.The possible additional equivalence transformations between equations from the class under consideration and the conditional equivalence groups are also investigated. These allow simplification of the results of the classification and further applications of them. The derived Lie symmetries are used to construct exact solutions of special forms of these equations via the classical Lie method. Nonclassical symmetries of the wave equations are discussed.
Classification of All Single Travelling Wave Solutions to Calogero-Degasperis-Focas Equation
无
2007-01-01
Under the travelling wave transformation, Calogero-Degasperis-Focas equation is reduced to an ordinary differential equation. Using a symmetry group of one parameter, this ODE is reduced to a second-order linear inho-mogeneous ODE. Furthermore, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classification of all single travelling wave solutions to Calogero-Degasperis-Focas equation.
Nonlinear Alignment and Its Local Linear Iterative Solution
Sumin Zhang
2016-01-01
Full Text Available In manifold learning, the aim of alignment is to derive the global coordinate of manifold from the local coordinates of manifold’s patches. At present, most of manifold learning algorithms assume that the relation between the global and local coordinates is locally linear and based on this linear relation align the local coordinates of manifold’s patches into the global coordinate of manifold. There are two contributions in this paper. First, the nonlinear relation between the manifold’s global and local coordinates is deduced by making use of the differentiation of local pullback functions defined on the differential manifold. Second, the method of local linear iterative alignment is used to align the manifold’s local coordinates into the manifold’s global coordinate. The experimental results presented in this paper show that the errors of noniterative alignment are considerably large and can be reduced to almost zero within the first two iterations. The large errors of noniterative/linear alignment verify the nonlinear nature of alignment and justify the necessity of iterative alignment.
High order local absorbing boundary conditions for acoustic waves in terms of farfield expansions
Villamizar, Vianey; Acosta, Sebastian; Dastrup, Blake
2017-03-01
We devise a new high order local absorbing boundary condition (ABC) for radiating problems and scattering of time-harmonic acoustic waves from obstacles of arbitrary shape. By introducing an artificial boundary S enclosing the scatterer, the original unbounded domain Ω is decomposed into a bounded computational domain Ω- and an exterior unbounded domain Ω+. Then, we define interface conditions at the artificial boundary S, from truncated versions of the well-known Wilcox and Karp farfield expansion representations of the exact solution in the exterior region Ω+. As a result, we obtain a new local absorbing boundary condition (ABC) for a bounded problem on Ω-, which effectively accounts for the outgoing behavior of the scattered field. Contrary to the low order absorbing conditions previously defined, the error at the artificial boundary induced by this novel ABC can be easily reduced to reach any accuracy within the limits of the computational resources. We accomplish this by simply adding as many terms as needed to the truncated farfield expansions of Wilcox or Karp. The convergence of these expansions guarantees that the order of approximation of the new ABC can be increased arbitrarily without having to enlarge the radius of the artificial boundary. We include numerical results in two and three dimensions which demonstrate the improved accuracy and simplicity of this new formulation when compared to other absorbing boundary conditions.
ZHOU Yu-Bin; LI Chao
2009-01-01
A modified G'/G-expansion method is presented to derive traveling wave solutions for a class of nonlinear partial differential equations called Whitham-Broer-Kaup-Like equations.As a result, the hyperbolic function solutions, trigonometric function solutions, and rational solutions with parameters to the equations are obtained.When the parameters are taken as special values the solitary wave solutions can be obtained.
Localized Electromagnetic Waves: Interactions with Surfaces and Nanostructures
Anderson, Nicholas R.
The interaction of electromagnetic waves with nanostructures is an important area of research for signal processing devices, magnetic data storage, biosensors and a variety of other applications. In this work, we present analytic and numerical calculations for oscillating electric and magnetic fields coupling with excitations in magnetic materials as well as metallic and dielectric materials, near their resonance frequencies. One of the problems with the miniaturization of signal processing components is that there is a cutoff frequency associated with the transverse electric (TE) mode in waveguides. However, it is usually the TE mode which is used to achieve nonreciprocity for devices such as isolators. As a first step to circumvent this problem we looked at the absorption of electromagnetic waves in an antiferromagnet and a ferrite when the incident wave is at an arbitrary angle with respect to the magnetization direction. We calculated reflectivity and attenuated total reflectivity and found absorption and nonreciprocity, asymmetric behavior for waves traveling in opposite directions, for a broad range of propagation angles. Subsequently we also performed calculations for a transverse magnetic mode in a waveguide. The wave was allowed to propagate at an arbitrary angle with respect to the magnetization direction of the ferrite in the waveguide. We again found nonreciprocity for a wide range of angles. Our results show that this system could be used as an on-chip isolator with isolation values over 75 dB/cm in the 50 GHz range. We explored another signal processing device operating in the GHz range: a nonlinear phase shifter. Using Fe as the magnetic material allows the phase shifter to operate over a wide frequency and power range. We found a differential phase shift of greater than 50° over 3 cm for this device. The theoretical results compared well with experimental measurements. Finally, we study surface plasmon polaritons propagating along a metallic
Essick, Reed; Katsavounidis, Erik; Vedovato, Gabriele; Klimenko, Sergey
2014-01-01
The Laser Interferometer Gravitational wave Observatory (LIGO) and Virgo, advanced ground-based gravitational-wave detectors, will begin collecting science data in 2015. With first detections expected to follow, it is important to quantify how well generic gravitational-wave transients can be localized on the sky. This is crucial for correctly identifying electromagnetic counterparts as well as understanding gravitational-wave physics and source populations. We present a study of sky localization capabilities for two search and parameter estimation algorithms: coherent WaveBurst, a maximum likelihood algorithm operating in close to real-time, and LALInferenceBurst, a Markov chain Monte Carlo parameter estimation algorithm developed to recover generic transient signals with latency of a few hours. Furthermore, we focus on the first few years of the advanced detector era, when we expect to only have two (2015) and later three (2016) operational detectors, all below design sensitivity. These detector configurati...
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.
Millimetre-Wave Backhaul for 5G Networks: Challenges and Solutions.
Feng, Wei; Li, Yong; Jin, Depeng; Su, Li; Chen, Sheng
2016-06-16
The trend for dense deployment in future 5G mobile communication networks makes current wired backhaul infeasible owing to the high cost. Millimetre-wave (mm-wave) communication, a promising technique with the capability of providing a multi-gigabit transmission rate, offers a flexible and cost-effective candidate for 5G backhauling. By exploiting highly directional antennas, it becomes practical to cope with explosive traffic demands and to deal with interference problems. Several advancements in physical layer technology, such as hybrid beamforming and full duplexing, bring new challenges and opportunities for mm-wave backhaul. This article introduces a design framework for 5G mm-wave backhaul, including routing, spatial reuse scheduling and physical layer techniques. The associated optimization model, open problems and potential solutions are discussed to fully exploit the throughput gain of the backhaul network. Extensive simulations are conducted to verify the potential benefits of the proposed method for the 5G mm-wave backhaul design.
Localized waves supported by the rotating waveguide array
Zhang, Xiao; Ye, Fangwei; Kartashov, Yaroslav V.; Vysloukh, Victor A.; Chen, Xianfeng
2016-09-01
We show that truncated rotating square waveguide arrays support new types of localized modes that exist even in the linear case, in complete contrast to localized excitations in nonrotating arrays requiring nonlinearity for their existence and forming above the energy flow threshold. These new modes appear either around array center, since rotation leads to the emergence of the effective attractive potential with a minimum at the rotation axis, or in the array corners, in which case localization occurs due to competition between centrifugal force (in terms of quasi-particle analogy) and total internal reflection at the interface of the truncated array. The degree of localization of the central and corner modes mediated by rotation increases with rotation frequency. Stable rotating soliton families bifurcating from linear modes are analyzed in both focusing and defocusing media.
Localized waves supported by the rotating waveguide array
Zhang, Xiao; Kartashov, Yaroslav V; Vysloukh, Victor A; Chen, Xianfeng
2016-01-01
We show that truncated rotating square waveguide arrays support new types of localized modes that exist even in the linear case, in complete contrast to localized excitations in nonrotating arrays requiring nonlinearity for their existence and forming above the energy flow threshold. These new modes appear either around array center, since rotation leads to the emergence of the effective attractive potential with a minimum at the rotation axis, or in the array corners, in which case localization occurs due to competition between centrifugal force (in terms of quasi-particle analogy) and total internal reflection at the interface of the truncated array. The degree of localization of the central and corner modes mediated by rotation increases with rotation frequency. Stable rotating soliton families bifurcating from linear modes are analyzed in both focusing and defocusing media.
Pollitz, F.F.; Snoke, J. Arthur
2010-01-01
We utilize two-and-three-quarter years of vertical-component recordings made by the Transportable Array (TA) component of Earthscope to constrain three-dimensional (3-D) seismic shear wave velocity structure in the upper 200 km of the western United States. Single-taper spectral estimation is used to compile measurements of complex spectral amplitudes from 44 317 seismograms generated by 123 teleseismic events. In the ﬁrst step employed to determine the Rayleigh-wave phase-velocity structure, we implement a new tomographic method, which is simpler and more robust than scattering-based methods (e.g. multi-plane surface wave tomography). The TA is effectively implemented as a large number of local arrays by deﬁning a horizontal Gaussian smoothing distance that weights observations near a given target point. The complex spectral-amplitude measurements are interpreted with the spherical Helmholtz equation using local observations about a succession of target points, resulting in Rayleigh-wave phase-velocity maps at periods over the range of 18–125 s. The derived maps depend on the form of local ﬁts to the Helmholtz equation, which generally involve the nonplane-wave solutions of Friederich et al. In a second step, the phase-velocity maps are used to derive 3-D shear velocity structure. The 3-D velocity images conﬁrm details witnessed in prior body-wave and surface-wave studies and reveal new structures, including a deep (>100 km deep) high-velocity lineament, of width ∼200 km, stretching from the southern Great Valley to northern Utah that may be a relic of plate subduction or, alternatively, either a remnant of the Mojave Precambrian Province or a mantle downwelling. Mantle seismic velocity is highly correlated with heat ﬂow, Holocene volcanism, elastic plate thickness and seismicity. This suggests that shallow mantle structure provides the heat source for associated magmatism, as well as thinning of the thermal lithosphere, leading to relatively high
Analytical Solution for Wave-Induced Response of Seabed with Variable Shear Modulus
无
2007-01-01
A plane strain analysis based on the generalized Biot's equation is utilized to investigate the wave-induced response of a poro-elastic seabed with variable shear modulus. By employing integral transform and Frobenius methods, the transient and steady solutions for the wave-induced pore water pressure, effective stresses and displacements are analytically derived in detail. Verification is available through the reduction to the simple case of homogeneous seabed. The numerical results indicate that the inclusion of variable shear modulus significantly affects the wave-induced seabed response.
Wu, Jian; Xiang, Dao; Gordon, Reuven
2016-06-13
We demonstrate continuous-wave four-wave mixing to probe the acoustic vibrations of gold nanorods in aqueous solution. The nonlinear optical response of gold nanorods, resonantly enhanced by electrostriction coupling to the acoustic vibration modes, shows an extensional vibration which combines an expansion along the long axis with a contraction along the short axis. We also observed the extensional vibration of gold nanospheres as byproducts of the gold nanorod synthesis. Theoretical calculation of the nanoparticle size and distribution based on the vibrational frequency agrees well with the experimental results obtained from the scanning electron microscopic examination, indicating the four-wave mixing technique can provide in situ nanoparticle characterization.
Tang, Liguo; Wu, Zhaojun; Liu, Shengxing; Yang, Wuyi
2012-08-01
The objective of this study is to investigate the three-dimensional (3-D) analytical solution for transient guided wave propagation in liquid-filled pipe systems using the eigenfunction expansion method (EEM). The eigenfunctions corresponding to finite liquid-filled pipe systems with a traction-free lateral boundary and rigid smooth end boundaries are obtained. Additionally, the orthogonality of the eigenfunctions is proved in detail. Subsequently, the exact 3-D analytical transient response of finite liquid-filled pipe systems to external body forces is constructed using the EEM, based on which, the approximate 3-D analytical transient response of the systems to external surface forces is derived. Furthermore, the analytical solution for transient guided wave propagation in finite liquid-filled pipe systems is extended explicitly and concisely to infinite liquid-filled pipe systems. Several numerical examples are given to illustrate the analysis of the spatial and frequency distributions of the radial and axial displacement amplitudes of various guided wave modes; the numerical examples also simulate the transient displacement of the pipe wall and the transient pressure of the internal liquid from the present solution. The present solution can provide some theoretical guidelines for the guided wave nondestructive evaluation of liquid-filled pipes and the guided wave technique for downhole data transfer.
Mao Jie-Jian; Yang Jian-Rong
2006-01-01
Using the solution of general Korteweg-de Vries (KdV) equation, the solutions of the generalized wriable coefficient Kadomtsev-Petviashvili (KP) equation are constructed, and then its new solitary wave-like solution and Jacobi clliptic function solution are obtained.
MA Song-Hua; JIANG Yong-Qing; FANG Jian-Ping
2008-01-01
With the help of the conditional similarity reduction method, some new exact solutions of the (2+1)-dimensional modified dispersive water-wave system (MDWW) are obtained. Based on the derived solution, we investigate the evolution of solitons in the background waves.
Simulation study of localization of electromagnetic waves in two-dimensional random dipolar systems.
Wang, Ken Kang-Hsin; Ye, Zhen
2003-12-01
We study the propagation and scattering of electromagnetic waves by random arrays of dipolar cylinders in a uniform medium. A set of self-consistent equations, incorporating all orders of multiple scattering of the electromagnetic waves, is derived from first principles and then solved numerically for electromagnetic fields. For certain ranges of frequencies, spatially localized electromagnetic waves appear in such a simple but realistic disordered system. Dependence of localization on the frequency, radiation damping, and filling factor is shown. The spatial behavior of the total, coherent, and diffusive waves is explored in detail, and found to comply with a physical intuitive picture. A phase diagram characterizing localization is presented, in agreement with previous investigations on other systems.
Xue, Daokai [School of Atmospheric Sciences, Nanjing University, Nanjing China; Lu, Jian [Atmospheric Sciences and Global Change Division, Pacific Northwest National Laboratory, Richland Washington USA; Sun, Lantao [CIRES, University of Colorado Boulder, Boulder Colorado USA; PSD, ESRL, NOAA, Boulder Colorado USA; Chen, Gang [Department of Earth and Atmospheric Sciences, UCLA, Los Angeles California USA; Zhang, Yaocun [School of Atmospheric Sciences, Nanjing University, Nanjing China
2017-04-10
In an attempt to resolve the controversy as to whether Arctic sea ice loss leads to more mid-latitude extremes, a metric of finite-amplitude wave activity is adopted to quantify the midlatitude wave activity and its change during the observed period of the drastic Arctic sea ice decline in both ERA Interim reanalysis data and a set of AMIP-type of atmospheric model experiments. Neither the experiment with the trend in the SST or that with the declining trend of Arctic sea ice can simulate the sizable midlatitude-wide reduction in the total wave activity (Ae) observed in the reanalysis, leaving its explanation to the atmospheric internal variability. On the other hand, both the diagnostics of the flux of the local wave activity and the model experiments lend evidence to a possible linkage between the sea ice loss near the Barents and Kara seas and the increasing trend of anticyclonic local wave activity over the northern part of the central Eurasia and the associated impacts on the frequency of temperature extremes.
柳银萍; 李志斌
2003-01-01
Based on a 0 of elliptic equation, a new algebraic method to construct a series of exact solutions for nonlinear evolution equations is proposed, meanwhile, its complete implementation TRWS in Maple is presented. The TRWS can output a series of travelling wave solutions entirely automatically, which include polynomial solutions, exponential function solutions, triangular function solutions, hyperbolic function solutions, rational function solutions, Jacobi elliptic function solutions, and Weierstrass elliptic function solutions. The effectiveness of the package is illustrated by applying it to a variety of equations. Not only are previously known solutions recovered but also new solutions and more general form of solutions are obtained.
A new variable coefficient algebraic method and non-traveling wave solutions of nonlinear equations
Lu Bin; Zhang Hong-Qing
2008-01-01
In this paper,a new auxiliary equation method is presented of constructing more new non-travelling wave solutions of nonlinear differential equations in mathematical physics,which is direct and more powerful than projective Riccati equation method.In order to illustrate the validity and the advantages of the method,(2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation is employed and many new double periodic non-travelling wave solutions are obtained.This algorithm can also be applied to other nonlinear differential equations.
One-dimensional wave propagation in rods of variable cross section: A WKBJ solution
Ochi, Simeon C. U.; Williams, James H., Jr.
1987-01-01
As an important step in the characterization of a particular dynamic surface displacement transducer (IQI Model 501), a one-dimensional wave propagation in isotropic nonpiezoelectric and piezoelectric rods of variable cross section are presented. With the use of the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximate solution technique, an approximate formula, which relates the ratio of the amplitudes of a propagating wave observed at any two locations along the rod to the ratio of the cross sectional radii at these respective locations, is derived. The domains of frequency for which the approximate solution is valid are discussed for piezoelectric and nonpiezoelectric materials.
无
2005-01-01
In this paper, an extended method is proposed for constructing new forms ofexact travelling wave solutions to nonlinear partial differential equations by making a more general transformation. For illustration, we apply the method to the asymmetric Nizhnik-Novikov-Vesselov equation and the coupled Drinfel'd-Sokolov-Wilson equation and successfully cover the previously known travelling wave solutions found by Chen's method [Y. Chen, et al. Chaos, Solitons and Fractals 22 (2004) 675; Y. Chen, et al. Int. J. Mod. Phys. C 4 (2004) 595].
TRAVELLING WAVE SOLUTIONS OF NONLINEAR EVOLUTION EQUATIONS BY USING SYMBOLIC COMPUTATION
FanEngui
2001-01-01
Abstract. A Riccati equation involving a parameter and symbolic computation are used to uni-formly construct the different forms of travelling wave solutions for nonlinear evolution equa-tions. It is shown that the sign of the parameter can be applied in judging the existence of vari-ous forms of travelling wave solutions. An efficiency of this method is demonstrated on some e-quations,which include Burgers-Huxley equation,Caudrey-Dodd-Gibbon-Kawada equation,gen-eralized Benjamin-Bona-Mahony equation and generalized Fisher equation.
Xiao-jing LIU; Ji-zeng WANG; Xiao-min WANG; You-he ZHOU
2014-01-01
General exact solutions in terms of wavelet expansion are obtained for multi-term time-fractional diffusion-wave equations with Robin type boundary conditions. By proposing a new method of integral transform for solving boundary value problems, such fractional partial differential equations are converted into time-fractional ordinary differ-ential equations, which are further reduced to algebraic equations by using the Laplace transform. Then, with a wavelet-based exact formula of Laplace inversion, the resulting exact solutions in the Laplace transform domain are reversed to the time-space domain. Three examples of wave-diffusion problems are given to validate the proposed analytical method.
A class of solutions to the Einstein equations with AVTD behavior in generalized wave gauges
Ames, Ellery; Isenberg, James; LeFloch, Philippe G
2016-01-01
We establish the existence of smooth vacuum Gowdy solutions, which are asymptotically velocity term dominated (AVTD) and have T3-spatial topology, in an infinite dimensional family of generalized wave gauges. These results show that the AVTD property, which is known to hold for solutions in areal coordinates, is stable to perturbations with respect to the gauge source functions. Our proof is based on an analysis of the singular initial value problem for the Einstein vacuum equations in the generalized wave gauge formalism, and provides a framework which we anticipate to be useful for more general spacetimes.
A practical localization solution for wireless sensor networks deployed in linear topography
Zhang, Kui; Guo, Peng; Meratnia, Nirvana; Havinga, Paul J.M.
2010-01-01
In this paper, we propose a practical range-free localization solution for wireless sensor networks (WSNs). Different from existing localization approaches, the proposed solution is specially designed for an ultra sparse mobile WSNs deployed in coal mine tunnels with linear topography. To obtain mor
Solitary Wave Solutions of the Boussinesq Equation and Its Improved Form
Reza Abazari
2013-01-01
Full Text Available This paper presents the general case study of previous works on generalized Boussinesq equations, (Abazari, 2011 and (Kılıcman and Abazari, 2012, that focuses on the application of G′/G-expansion method with the aid of Maple to construct more general exact solutions for the coupled Boussinesq equations. In this work, the mentioned method is applied to construct more general exact solutions of Boussinesq equation and improved Boussinesq equation, which the French scientist Joseph Valentin Boussinesq (1842–1929 described in the 1870s model equations for the propagation of long waves on the surface of water with small amplitude. Our work is motivated by the fact that the G′/G-expansion method provides not only more general forms of solutions but also periodic, solitary waves and rational solutions. The method appears to be easier and faster by means of a symbolic computation.
Self-similar solutions for the Hasselmann equation and experimental scaling of wind-wave spectra
Badulin, S. I.; Pushkarev, A. N.; Resio, D.; Zakharov, V. E.
2003-04-01
The solutions for the Hasselmann equation (kinetic equation for wind-driven waves) are studied numerically for the case of duration-limited growth and different conventional parameterizations of wave sources and sinks (Snyderet al. 1981; Plant 1982; Hsiao &Shemdin 1983; Komen, Hasselmann & Hasselmann 1984; Donelan, Pierson 1987). The strong self-similar behavior of the numerical solutions is found for all the parameterizations in a wide range of wind speeds and wave ages. Moreover, the resulting self-similar solutions are found to be surprisingly close to experimentally established approximations in magnitudes and shapes of frequency spectra. The comparison with JONSWAP modified spectra (Donelan et al. 1985) is detailed. It is found that this approximation being obtained for the case of fetch-limited growth fits quite well the corresponding spectra for the numerical duration limited solutions in a wide range of wave ages (C_p/U10 ≈ 0.4div 1.4 ). Theoretical overview of self-similar solutions for the kinetic equation is given in its relation to the experimentally observed dependencies of mean parameters (i.e. mean energy, frequency) of wind-driven waves both in cases of fetch-limited and duration limited growth. Universality features of the dependencies are treated as a result of dominating nonlinear transfer in wind-wave field. The research was conducted under the U.S. Army Corps of Engineers, RDT&E program, grant DACA 42-00-C0044, ONR grant N00014-98-1-0070 and NSF grant NDMS0072803, INTAS grant 01-234 and Russian Foundation for Basic Research 01-05-64603, 01-05-64464, 02-05-65140. This support is gratefully acknowledged.
Yoon, Young Dae; Bellan, Paul M.
2016-10-01
A full three-dimensional computer code was developed in order to simulate a 3D-localized magnetic reconnection. We assume an incompressible two-fluid regime where the ions are stationary, and electron inertia and Hall effects are present. We solve a single dimensionless differential equation for perturbed magnetic fields with arbitrary background fields. The code has successfully reproduced both experimental and analytic solutions to resonance and Gendrin mode whistler waves in a uniform background field. The code was then modified to model 3D-localized magnetic reconnection as a 3D-localized perturbation on a hyperbolic-tangent background field. Three-dimensional properties that are asymmetric in the out-of-plane direction have been observed. These properties pertained to magnetic field lines, electron currents and their convection. Helicity and energy have also been examined, as well as the addition of a guide field.
WANG Jun-Mao; ZHANG Miao; ZHANG Wen-Liang; ZHANG Rui; HAN Jia-Hua
2008-01-01
We present a new method to find the exact travelling wave solutions of nonlinear evolution equations, with the aid of the symbolic computation. Based on this method, we successfully solve the modified Benjamin-Bona-Mahoney equation, and obtain some new solutions which can be expressed by trigonometric functions and hyperbolic functions. It is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations in mathematical physics.
ZHANGJin-Liang; WANGMing-Liang
2004-01-01
The complex tanh-function expansion method was presented recently, and it can be applied to derive exact solutions to the Schroedinger-type nonlinear evolution equations directly without transformation. In this paper,the complex tanh-function expansion method is applied to derive the exact solutions to the general coupled nonlinear evolution equations. Zakharov system and a long-short-wave interaction system are considered as examples, and the new applications of the complex tanh-function expansion method are shown.
Singular solitons and other solutions to a couple of nonlinear wave equations
Mustafa Inc; Esma Uluta(s); Anjan Biswas
2013-01-01
This paper addresses the extended (G′/G)-expansion method and applies it to a couple of nonlinear wave equations.These equations are modified the Benjamin-Bona-Mahoney equation and the Boussinesq equation.This extended method reveals several solutions to these equations.Additionally,the singular soliton solutions are revealed,for these two equations,with the aid of the ansatz method.
Ibragimov, Nail H
2011-01-01
The paper is devoted to the group analysis of equations of motion of two-dimensional uniformly stratified rotating fluids used as a basic model in geophysical fluid dynamics. It is shown that the nonlinear equations in question have a remarkable property to be self-adjoint. This property is crucial for constructing conservation laws provided in the present paper. Invariant solutions are constructed using certain symmetries. The invariant solutions are used for defining internal wave beams.
SPHERICAL NONLINEAR PULSES FOR THE SOLUTIONS OF NONLINEAR WAVE EQUATIONS Ⅱ, NONLINEAR CAUSTIC
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.
ZHANG Jin-Liang; WANG Ming-Liang
2004-01-01
The complex tanh-function expansion method was presented recently, and it can be applied to derive exact solutions to the Schrodinger-type nonlinear evolution equations directly without transformation. In this paper,the complex tanh-function expansion method is applied to derive the exact solutions to the general coupled nonlinear evolution equations. Zakharov system and a long-short-wave interaction system are considered as examples, and the new applications of the complex tanh-function expansion method are shown.
Explicit Soliton and Periodic Solutions to Three-Wave System with Quadratic and Cubic Nonlinearities
LIN Ji; ZHAO Li-Na; LI Hua-Mei
2011-01-01
Lie group theoretical method and the equation of the Jacobi elliptic function are used to study the three wave system that couples two fundamental frequency (FF) and a single second harmonic (SH) one by competing x(2)(quadratic) and x(3) (cubic) nonlinearities and birefringence.This system shares some of the nice properties of soliton system.On the phase-locked condition, we obtain large families of analytical solutions as the soliton, kink and periodic solutions of this system.
The Exact Traveling Wave Solutions to Two Integrable KdV6 Equations
Jibin LI; Yi ZHANG
2012-01-01
The exact explicit traveling solutions to the two completely integrable sixthorder nonlinear equations KdV6 are given by using the method of dynamical systems and Cosgrove's work.It is proved that these traveling wave solutions correspond to some orbits in the 4-dimensional phase space of two 4-dimensional dynamical systems.These orbits lie in the intersection of two level sets defined by two first integrals.
Exact traveling wave solution of nonlinear variants of the RLW and the PHI-four equations
Soliman, A.A. [Department of Mathematics, Faculty of Education (AL-Arish), Suez Canal University, AL-Arish 45111 (Egypt); Department of Mathematics, Teacher' s College, Bisha, P.O. Box 551 (Saudi Arabia)], E-mail: asoliman_99@yahoo.com
2007-08-27
By means of the modified extended tanh-function (METF) method the multiple traveling wave solutions of some different kinds of nonlinear partial differential equations are presented and implemented in a computer algebraic system. The solutions for the nonlinear equations such as variants of the RLW and variant of the PHI-four equations are exactly obtained and so the efficiency of the method can be demonstrated.
Chen Xiao-Gang; Guo Zhi-Ping; Song Jin-Bao
2008-01-01
In the present paper,the random interfacial waves in N-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique,and the second-order asymptotic solutions of the random displacements of the density interfaces and the associated velocity potentials in N-layer fluid are presented based on the small amplitude wave theory.The obtained results indicate that the wave-wave second-order nonlinear interactions of the wave components and the second-order nonlinear interactions between the waves and currents are described.As expected,the solutions include those derived by Chen(2006)as a special case where the steady uniform currents of the N-layer fluids are taken as zero,and the solutions also reduce to those obtained by Song(2005)for second-order solutions for random interracial waves with steady uniform currents if N=2.
The APOSTLE simulations: solutions to the Local Group's cosmic puzzles
Sawala, Till; Fattahi, Azadeh; Navarro, Julio F; Bower, Richard G; Crain, Robert A; Vecchia, Claudio Dalla; Furlong, Michelle; Helly, John C; Jenkins, Adrian; Oman, Kyle A; Schaller, Matthieu; Schaye, Joop; Theuns, Tom; Trayford, James; White, Simon D M
2015-01-01
The Local Group of galaxies offer some of the most discriminating tests of models of cosmic structure formation. For example, observations of the Milky Way (MW) and Andromeda satellite populations appear to be in disagreement with N-body simulations of the "Lambda Cold Dark Matter" ({\\Lambda}CDM) model: there are far fewer satellite galaxies than substructures in cold dark matter halos (the "missing satellites" problem); dwarf galaxies seem to avoid the most massive substructures (the "too-big-to-fail" problem); and the brightest satellites appear to orbit their host galaxies on a thin plane (the "planes of satellites" problem). Here we present results from APOSTLE (A Project Of Simulating The Local Environment), a suite of cosmological hydrodynamic simulations of twelve volumes selected to match the kinematics of the Local Group (LG) members. Applying the Eagle code to the LG environment, we find that our simulations match the observed abundance of LG galaxies, including the satellite galaxies of the MW and ...
Analytical Solution of the Blast Wave Problem in a Non-Ideal Gas
L. P. Singh; S. D. Ram; D. B. Singh
2011-01-01
An analytical approach is used to construct the exact solution of the blast wave problem with generalized geometries in a non-ideal medium. It is assumed that the density ahead of the shock front varies according to a power of distance from the source of the blast wave. Also, an analytical expression for the total energy in a non-ideal medium is derived.%An analytical approach is used to construct the exact solution of the blast wave problem with generalized geometries in a non-ideal medium.It is assumed that the density ahead of the shock front varies according to a power of distance from the source of the blast wave.Also,an analytical expression for the total energy in a non-ideal medium is derived.Blast waves are common occurrences in the Earth's atmosphere.They result from a sudden release of a relatively large amount of energy.Typical examples are lightening and chemical or nuclear explosions.Assume that we have an explosion,following which there may exist a very small region filled with hot matter at high pressure in a duration,which starts to expand outwards with its front headed by a strong shock.The process generally takes place in a very short time after which a forward-moving shock wave develops,which continuously assimilates the ambient air into the blast wave.Although some of the explosive material may still remain near the center,the amount of the air absorbed increases with time,and the later behavior of the blast wave may well be represented by the model of the shock wave at the front and a purely gasdynamic treatment for the motion of the air inside,which may be assumed to have ideal and non-viscous adiabatic heat exponent.
The Seeking Solutions Approach: Solving Challenging Business Problems with Local Open Innovation
Christophe Deutsch
2013-03-01
Full Text Available How can small and medium-sized enterprises try open innovation and increase their level of collaboration with local partners? This article describes a possible solution: the Seeking Solutions approach. The Seeking Solutions process consists of four steps: a call for problems, problem selection, problem broadcast, and a collaborative event. This approach has been successfully used for the Quebec Seeks Solutions events in 2010 and 2012 with concrete results and real impacts. By mixing open innovation and collaboration, the Seeking Solutions approach has introduced a new concept: local open innovation.
A Local Composition Model for Paraffinic Solid Solutions
Coutinho, A.P. João; Knudsen, Kim; Andersen, Simon Ivar
1996-01-01
The description of the solid-phase non-ideality remains the main obstacle in modelling the solid-liquid equilibrium of hydrocarbons. A theoretical model, based on the local composition concept, is developed for the orthorhombic phase of n-alkanes and tested against experimental data for binary sy...... systems. It is shown that it can adequately predict the experimental phase behaviour of paraffinic mixtures. This work extends the applicability of local composition models to the solid phase. Copyright (C) 1996 Elsevier Science Ltd....
Lost in localization: A solution with neuroinformatics 2.0?
Nielsen, Finn Årup
2009-01-01
The commentary by Derrfuss and Mar (Derrfuss, J., Mar, R.A., 2009. Lost in localization: The need for a universal coordinate database. NeuroImage, doi:10.1016/j.neuroimage.2009.01.053.) discusses some of the limitations of the present databases and calls for a universal coordinate database. Here I...
Regional acidosis locally inhibits but remotely stimulates Ca2+ waves in ventricular myocytes.
Ford, Kerrie L; Moorhouse, Emma L; Bortolozzi, Mario; Richards, Mark A; Swietach, Pawel; Vaughan-Jones, Richard D
2017-07-01
Spontaneous Ca2+ waves in cardiomyocytes are potentially arrhythmogenic. A powerful controller of Ca2+ waves is the cytoplasmic H+ concentration ([H+]i), which fluctuates spatially and temporally in conditions such as myocardial ischaemia/reperfusion. H+-control of Ca2+ waves is poorly understood. We have therefore investigated how [H+]i co-ordinates their initiation and frequency. Spontaneous Ca2+ waves were imaged (fluo-3) in rat isolated ventricular myocytes, subjected to modest Ca2+-overload. Whole-cell intracellular acidosis (induced by acetate-superfusion) stimulated wave frequency. Pharmacologically blocking sarcolemmal Na+/H+ exchange (NHE1) prevented this stimulation, unveiling inhibition by H+. Acidosis also increased Ca2+ wave velocity. Restricting acidosis to one end of a myocyte, using a microfluidic device, inhibited Ca2+ waves in the acidic zone (consistent with ryanodine receptor inhibition), but stimulated wave emergence elsewhere in the cell. This remote stimulation was absent when NHE1 was selectively inhibited in the acidic zone. Remote stimulation depended on a locally evoked, NHE1-driven rise of [Na+]i that spread rapidly downstream. Acidosis influences Ca2+ waves via inhibitory Hi+ and stimulatory Nai+ signals (the latter facilitating intracellular Ca2+-loading through modulation of sarcolemmal Na+/Ca2+ exchange activity). During spatial [H+]i-heterogeneity, Hi+-inhibition dominates in acidic regions, while rapid Nai+ diffusion stimulates waves in downstream, non-acidic regions. Local acidosis thus simultaneously inhibits and stimulates arrhythmogenic Ca2+-signalling in the same myocyte. If the principle of remote H+-stimulation of Ca2+ waves also applies in multicellular myocardium, it raises the possibility of electrical disturbances being driven remotely by adjacent ischaemic areas, which are known to be intensely acidic.
Guo, Bang-Xing; Gao, Zhan-Jie; Lin, Ji
2016-12-01
The consistent tanh expansion (CTE) method is applied to the (2+1)-dimensional Boussinesq equation which describes the propagation of ultrashort pulse in quadratic nonlinear medium. The interaction solutions are explicitly given, such as the bright soliton-periodic wave interaction solution, variational amplitude periodic wave solution, and kink-periodic wave interaction solution. We also obtain the bright soliton solution, kind bright soliton solution, double well dark soliton solution and kink-bright soliton interaction solution by using Painlevé truncated expansion method. And we investigate interactive properties of solitons and periodic waves. Supported by the National Natural Science Foundation of Zhejiang Province under Grant No. LZ15A050001 and the National Natural Science Foundation of China under Grant No. 11675164
Anti-periodic traveling wave solution to a forced two-dimensional generalized KdV-Burgers equation
TAN Junyu
2003-01-01
The anti-periodic traveling wave solutions to a forced two-dimensional generalized KdV-Burgers equation are studied.Some theorems concerning the boundness, existence and uniqueness of the solution to this equation are proved.
A Class of Traveling Wave Solutions to Some Nonlinear Partial Differential Equations
BAI Cheng-Lin
2003-01-01
For the Noyes-Fields equations, two-dimensional hyperbolic equations of conversation laws, and theBurgers-KdV equation, a class of traveling wave solutions has been obtained by constructing appropriate functiontransformations. The main idea of solving the equations is that nonlinear partial differential equations are changed intosolving algebraic equations. This method has a wide-rangingpracticability.
A Class of Traveling Wave Solutions to Some Nonlinear Partial Differential Equations
BAICheng-Lin
2003-01-01
For the Noyes-Fields equations, two-dimenslonal hyperbolic equations of conversation laww and the Burgers-KdV equation, a class of travellng wave solutions has been obtained by constructhag appropriate function transformations. The main idea of solving the equations is that nonlinear partial differential equations are changed into solving algebraic equations. This method has a wide-ranging practicability.
Nibbering, Erik T.J.; Duppen, Koos; Wiersma, Douwe A.
1992-01-01
The results of line shape analysis, resonance light scattering and femtosecond four-wave mixing measurements are reported on several organic molecules in solution. It is shown that a Brownian oscillator model for line broadening provides a full description for the optical dynamics in aprotic solutio
The adiabatic approximation solutions of cylindrical and spherical dust ion-acoustic solitary waves
吕克璞; 豆福全; 孙建安; 段文山; 石玉仁
2005-01-01
By using the equivalent particle theory, the adiabatic approximation solutions of the Korteweg-de Vries type equation (including KdV equation, cylindrical KdV equation and spherical KdV equation) in dust ion-acoustic solitary waves were obtained. The method can be extended to other nonlinear evolution equations.
A null coframe formulation of quadratic curvature gravity and gravitational wave solutions
Baykal, Ahmet
2014-01-01
Quadratic curvature gravity equations are projected to a complex null coframe by using the algebra of exterior forms and expressed in terms of the spinor quantities defined originally by Newman and Penrose. As an application, a new family of impulsive gravitational wave solutions propagating in various type D backgrounds are introduced.
Minimum Wave Speed Solution of Fisher's Equation by the Method of Least Squares - A Note
K. N. Mehta
1989-04-01
Full Text Available The paper presents a simple solution of travelling-wave type (corresponding to the minimum speed c=2 of Fisher's equation. which can be readily adapted for modelling neutron density in nuclear reactors, reaction-diffusion processes'in propulsion systems and growth of new advantageous gene in one-dimensional habitat
On Global Smooth Solution of A Semi-Linear System of Wave Equations in R3
WU Haigen
2009-01-01
In this paper we consider the Cauchy problem for a semi-linear system of wave equations with Hamilton structure. We prove the existence of global smooth so-lution of the system for subcritical case by using conservation of energy and Strichartz's estimate. On the basis of Morawetz-Poho2ev identity, we obtain the same result for the critical case.
Global Existence of Solutions to the Fowler Equation in a Neighbourhood of Travelling-Waves
Afaf Bouharguane
2011-01-01
Full Text Available We investigate a fractional diffusion/anti-diffusion equation proposed by Andrew C. Fowler to describe the dynamics of sand dunes sheared by a fluid flow. In this paper, we prove the global-in-time well-posedness in the neighbourhood of travelling-waves solutions of the Fowler equation.
Exact solution of planar and nonplanar weak shock wave problem in gasdynamics
Singh, L.P. [Department of Applied Mathematics, Institute of Technology, Bananas Hindu University, Varanasi 221 005 (India); Ram, S.D., E-mail: sram.rs.apm@itbhu.ac.in [Department of Applied Mathematics, Institute of Technology, Bananas Hindu University, Varanasi 221 005 (India); Singh, D.B. [Department of Applied Mathematics, Institute of Technology, Bananas Hindu University, Varanasi 221 005 (India)
2011-11-15
Highlights: > An exact solution is derived for a problem of weak shock wave in adiabatic gas dynamics. > The density ahead of the shock is taken as a power of the position from the origin of the shock wave. > For a planar and non-planar motion, the total energy carried by the wave varies with respect to time. > The solution obtained for the planer, and cylindrically symmetric flow is new one. > The results obtained are also presented graphically for different Mach numbers. - Abstract: In the present paper, an analytical approach is used to determine a new exact solution of the problem of one dimensional unsteady adiabatic flow of planer and non-planer weak shock waves in an inviscid ideal fluid. Here it is assumed that the density ahead of the shock front varies according to the power law of the distance from the source of disturbance. The solution of the problem is presented in the form of a power in the distance and the time.
GLOBAL SOLUTION AND ITS LONG TIME BEHAVIOR FOR THE GENERALIZED LONG-SHORT WAVE EQUATIONS
Zhang Ruifeng; Guo Boling
2005-01-01
The long time behavior of the solutions of the generalized long-short wave equations with dissipation term is studied. The existence of global attractor of the initial periodic boundary value is proved by means of a uniform a priori estimate for time. And also the dimensions of the global attractor are estimated.
Global existence of solutions for semilinear damped wave equation in 2-D exterior domain
Ikehata, Ryo
We consider a mixed problem of a damped wave equation utt-Δ u+ ut=| u| p in the two dimensional exterior domain case. Small global in time solutions can be constructed in the case when the power p on the nonlinear term | u| p satisfies p ∗=2Japon. 55 (2002) 33) plays an effective role.
Exciton localization in solution-processed organolead trihalide perovskites
He, Haiping; Yu, Qianqian; LI, Hui; Li, Jing; Si, Junjie; Jin, Yizheng; Wang, Nana; Wang, Jianpu; He, Jingwen; Wang, Xinke; Zhang, Yan; Ye, Zhizhen
2016-01-01
Organolead trihalide perovskites have attracted great attention due to the stunning advances in both photovoltaic and light-emitting devices. However, the photophysical properties, especially the recombination dynamics of photogenerated carriers, of this class of materials are controversial. Here we report that under an excitation level close to the working regime of solar cells, the recombination of photogenerated carriers in solution-processed methylammonium–lead–halide films is dominated b...
FAN Hong-Yi; ZHU Jia-Min; WANG Tong-Tong; LU Zhi-Ming; LIU Yu-Lu
2008-01-01
One of the advantages of the variational iteration method is the free choice of initial guess. In this paper we use the basic idea of the Jacobian-function method to construct a generalized trial function with some unknown parameters. The Jaulent-Miodek equations are used to illustrate effectiveness and convenience of this method, some new explicit exact travelling wave solutions have been obtained, which include bell-type soliton solution, kink-type soliton solutions, solitary wave solutions, and doubly periodic wave solutions.
Dobrokhotov, S. Yu.; Nazaikinskii, V. E.
2017-01-01
The following results are obtained for the Cauchy problem with localized initial data for the crystal lattice vibration equations with continuous and discrete time: (i) the asymptotics of the solution is determined by Lagrangian manifolds with singularities ("punctured" Lagrangian manifolds); (ii) Maslov's canonical operator is defined on such manifolds as a modification of a new representation recently obtained for the canonical operator by the present authors together with A. I. Shafarevich (Dokl. Ross. Akad. Nauk 46 (6), 641-644 (2016)); (iii) the projection of the Lagrangian manifold onto the configuration plane specifies a bounded oscillation region, whose boundary (which is naturally referred to as the leading edge front) is determined by the Hamiltonians corresponding to the limit wave equations; (iv) the leading edge front is a special caustic, which possibly contains stronger focal points. These observations, together with earlier results, lead to efficient formulas for the wave field in a neighborhood of the leading edge front.
The local structure factor near an interface; beyond extended capillary-wave models
Parry, A. O.; Rascón, C.; Evans, R.
2016-06-01
We investigate the local structure factor S (zq) at a free liquid-gas interface in systems with short-ranged intermolecular forces and determine the corrections to the leading-order, capillary-wave-like, Goldstone mode divergence of S (zq) known to occur for parallel (i.e. measured along the interface) wavevectors q\\to 0 . We show from explicit solution of the inhomogeneous Ornstein-Zernike equation that for distances z far from the interface, where the profile decays exponentially, S (zq) splits unambiguously into bulk and interfacial contributions. On each side of the interface, the interfacial contributions can be characterised by distinct liquid and gas wavevector dependent surface tensions, {σ l}(q) and {σg}(q) , which are determined solely by the bulk two-body and three-body direct correlation functions. At high temperatures, the wavevector dependence simplifies and is determined almost entirely by the appropriate bulk structure factor, leading to positive rigidity coefficients. Our predictions are confirmed by explicit calculation of S (zq) within square-gradient theory and the Sullivan model. The results for the latter predict a striking temperature dependence for {σ l}(q) and {σg}(q) , and have implications for fluctuation effects. Our results account quantitatively for the findings of a recent very extensive simulation study by Höfling and Dietrich of the total structure factor in the interfacial region, in a system with a cut-off Lennard-Jones potential, in sharp contrast to extended capillary-wave models which failed completely to describe the simulation results.
BHARDWAJ S B; SINGH RAM MEHAR; SHARMA KUSHAL; MISHRA S C
2016-06-01
Attempts have been made to explore the exact periodic and solitary wave solutions of nonlinear reaction diffusion (RD) equation involving cubic–quintic nonlinearity along with timedependent convection coefficients. Effect of varying model coefficients on the physical parameters of solitary wave solutions is demonstrated. Depending upon the parametric condition, the periodic,double-kink, bell and antikink-type solutions for cubic–quintic nonlinear reaction-diffusion equation are extracted. Such solutions can be used to explain various biological and physical phenomena.
Joint Inversion of Earthquake Source Parameters with local and teleseismic body waves
Chen, W.; Ni, S.; Wang, Z.
2011-12-01
In the classical source parameter inversion algorithm of CAP (Cut and Paste method, by Zhao and Helmberger), waveform data at near distances (typically less than 500km) are partitioned into Pnl and surface waves to account for uncertainties in the crustal models and different amplitude weight of body and surface waves. The classical CAP algorithms have proven effective for resolving source parameters (focal mechanisms, depth and moment) for earthquakes well recorded on relatively dense seismic network. However for regions covered with sparse stations, it is challenging to achieve precise source parameters . In this case, a moderate earthquake of ~M6 is usually recorded on only one or two local stations with epicentral distances less than 500 km. Fortunately, an earthquake of ~M6 can be well recorded on global seismic networks. Since the ray paths for teleseismic and local body waves sample different portions of the focal sphere, combination of teleseismic and local body wave data helps constrain source parameters better. Here we present a new CAP mothod (CAPjoint), which emploits both teleseismic body waveforms (P and SH waves) and local waveforms (Pnl, Rayleigh and Love waves) to determine source parameters. For an earthquake in Nevada that is well recorded with dense local network (USArray stations), we compare the results from CAPjoint with those from the traditional CAP method involving only of local waveforms , and explore the efficiency with bootstraping statistics to prove the results derived by CAPjoint are stable and reliable. Even with one local station included in joint inversion, accuracy of source parameters such as moment and strike can be much better improved.
Uzunov, Ivan M.; Georgiev, Zhivko D.
2014-10-01
We study the dynamics of the localized pulsating solutions of generalized complex cubic- quintic Ginzburg-Landau equation (CCQGLE) in the presence of intrapulse Raman scattering (IRS). We present an approach for identification of periodic attractors of the generalized CCQGLE. At first using ansatz of the travelling wave, and fixing some relations between the material parameters, we derive the strongly nonlinear Lienard - Van der Pol equation for the amplitude of the nonlinear wave. Next, we apply the Melnikov method to this equation to analyze the possibility of existence of limit cycles. For a set of fixed material parameters we show the existence of limit cycle that arises around a closed phase trajectory of the unperturbed system and prove its stability.
Cao, Yanpeng; Tisse, Christel-Loic
2014-02-01
In this Letter, we propose an efficient and accurate solution to remove temperature-dependent nonuniformity effects introduced by the imaging optics. This single-image-based approach computes optics-related fixed pattern noise (FPN) by fitting the derivatives of correction model to the gradient components, locally computed on an infrared image. A modified bilateral filtering algorithm is applied to local pixel output variations, so that the refined gradients are most likely caused by the nonuniformity associated with optics. The estimated bias field is subtracted from the raw infrared imagery to compensate the intensity variations caused by optics. The proposed method is fundamentally different from the existing nonuniformity correction (NUC) techniques developed for focal plane arrays (FPAs) and provides an essential image processing functionality to achieve completely shutterless NUC for uncooled long-wave infrared (LWIR) imaging systems.
Hui Cheng YIN
2001-01-01
For a class of three-dimensional quasilinear wave equations with small initial data, we givea complete asymptotic expansion of the lifespan of classical solutions, that is, we solve a conjectureposed by John and Hormander. As an application of our result, we show that the solution of three-dimensional isentropic compressible Euler equations with irrotational initial data which are a smallperturbation from a constant state will develop singularity in the first-order derivatives in finite timewhile the solution itself is continuous. Furthermore, for this special case, we also solve a conjecture ofAlinhac.
Solitary and Jacobi elliptic wave solutions of the generalized Benjamin-Bona-Mahony equation
Belobo, Didier Belobo; Das, Tapas
2017-07-01
Exact bright, dark, antikink solitary waves and Jacobi elliptic function solutions of the generalized Benjamin-Bona-Mahony equation with arbitrary power-law nonlinearity will be constructed in this work. The method used to carry out the integration is the F-expansion method. Solutions obtained have fractional and integer negative or positive power-law nonlinearities. These solutions have many free parameters such that they may be used to simulate many experimental situations, and to precisely control the dynamics of the system.
Multi-Order Exact Solutions for a generalized shallow water wave equation and other nonlinear PDEs
Bagchi, Bijan; Ganguly, Asish
2011-01-01
We seek multi-order exact solutions of a generalized shallow water wave equation along with those corresponding to a class of nonlinear systems described by the KdV, modified KdV, Boussinesq, Klein-Gordon and modified Benjamin-Bona-Mahony equation. We employ a modified version of a generalized Lame equation and subject it to a perturbative treatment identifying the solutions order by order in terms of Jacobi elliptic functions. Our solutions are new and hold the key feature that they are expressible in terms of an auxiliary function f in a generic way. For appropriate choices of f we recover the previous results reported in the literature.
Travelling wave solutions of the Schamel–Korteweg–de Vries and the Schamel equations
Figen Kangalgil
2016-10-01
Full Text Available In this paper, the extended (G′/G-expansion method has been suggested for constructing travelling wave solutions of the Schamel–Korteweg–de Vries (s-KdV and the Schamel equations with aid of computer systems like Maple or Mathematica. The hyperbolic function solutions and the trigonometric function solutions with free parameters of these equations have been obtained. Moreover, it has been shown that the suggested method is elementary, effective and has been used to solve nonlinear evolution equations in applied mathematics, engineering and mathematical physics.
Local solutions of Maximum Likelihood Estimation in Quantum State Tomography
Gonçalves, Douglas S; Lavor, Carlile; Farías, Osvaldo Jiménez; Ribeiro, P H Souto
2011-01-01
Maximum likelihood estimation is one of the most used methods in quantum state tomography, where the aim is to find the best density matrix for the description of a physical system. Results of measurements on the system should match the expected values produced by the density matrix. In some cases however, if the matrix is parameterized to ensure positivity and unit trace, the negative log-likelihood function may have several local minima. In several papers in the field, authors associate a source of errors to the possibility that most of these local minima are not global, so that optimization methods can be trapped in the wrong minimum, leading to a wrong density matrix. Here we show that, for convex negative log-likelihood functions, all local minima are global. We also show that a practical source of errors is in fact the use of optimization methods that do not have global convergence property or present numerical instabilities. The clarification of this point has important repercussion on quantum informat...
Energy decay of a variable-coefficient wave equation with nonlinear time-dependent localized damping
Jieqiong Wu
2015-09-01
Full Text Available We study the energy decay for the Cauchy problem of the wave equation with nonlinear time-dependent and space-dependent damping. The damping is localized in a bounded domain and near infinity, and the principal part of the wave equation has a variable-coefficient. We apply the multiplier method for variable-coefficient equations, and obtain an energy decay that depends on the property of the coefficient of the damping term.
The Peano-series solution for modeling shear horizontal waves in piezoelectric plates
Ben Ghozlen M.H.
2012-06-01
Full Text Available The shear horizontal (SH wave devices have been widely used in electroacoustic. To improve their performance, the phase velocity dispersion and the electromechanical coupling coefficient of the Lamb wave should be calculated exactly in the design. Therefore, this work is to analyze exactly the Lamb waves polarized in the SH direction in homogeneous plate pie.zoelectric material (PZT-5H. An alternative method is proposed to solve the wave equation in such a structure without using the standard method based on the electromechanical partial waves. This method is based on an analytical solution, the matricant explicitly expressed under the Peano series expansion form. Two types of configuration have been addressed, namely the open circuited and the short circuited. Results confirm that the SH wave provides a number of attractive properties for use in sensing and signal processing applications. It has been found that the phase velocity remains nearly constant for all values of h/λ (h is the plate thickness, λ the acoustic wavelength. Secondly the SH0 wave mode can provide very high electromechanical coupling. Graphical representations of electrical and mechanical amounts function of depth are made, they are in agreement with the continuity rules. The developed Peano technique is in agreement with the classical approach, and can be suitable with cylindrical geometry.
Fractal dimensions of wave functions and local spectral measures on the Fibonacci chain
Macé, Nicolas; Jagannathan, Anuradha; Piéchon, Frédéric
2016-05-01
We present a theoretical framework for understanding the wave functions and spectrum of an extensively studied paradigm for quasiperiodic systems, namely the Fibonacci chain. Our analytical results, which are obtained in the limit of strong modulation of the hopping amplitudes, are in good agreement with published numerical data. In the perturbative limit, we show a symmetry of wave functions under permutation of site and energy indices. We compute the wave-function renormalization factors and from them deduce analytical expressions for the fractal exponents corresponding to individual wave functions, as well as their global averages. The multifractality of wave functions is seen to appear at next-to-leading order in ρ . Exponents for the local spectral density are given, in extremely good accord with numerical calculations. Interestingly, our analytical results for exponents are observed to describe the system rather well even for values of ρ well outside the domain of applicability of perturbation theory.
Experimental Study on Local Scour Around A Large Circular Cylinder Under Irregular Waves
周益人; 陈国平
2004-01-01
A series of physical model tests are conducted for local scour around a circular cylinder of a relatively large diameter (0.15 ＜ D/L ＜ 0.5) under the action of irregular waves. The laws of change of the topography around the cylinder are systematically studied. The effects of wave height, wave period, water depth, sediment grain size and cylinder diameter are taken into account. The mechanism of formation of the topography around the cylinder is analyzed. A detailed analysis is given to bed sediment grain size, and it is considered that the depth of scour around the cylinder under wave action is not inversely proportional to the sediment grain diameter. On such a basis, an equation is proposed for calculation of the maximum depth of scour around a cylinder as well as its position under the action of irregular waves.
Non-local features of a hydrodynamic pilot-wave system
Nachbin, Andre; Couchman, Miles; Bush, John
2016-11-01
A droplet walking on the surface of a vibrating fluid bath constitutes a pilot-wave system of the form envisaged for quantum dynamics by Louis de Broglie: a particle moves in resonance with its guiding wave field. We here present an examination of pilot-wave hydrodynamics in a confined domain. Specifically, we present a one-dimensional water wave model that describes droplets walking in single and multiple cavities. The cavities are separated by a submerged barrier, and so allow for the study of tunneling. They also highlight the non-local dynamical features arising due to the spatially-extended wave field. Results from computational simulations are complemented by laboratory experiments.
Localized atomic basis set in the projector augmented wave method
Larsen, Ask Hjorth; Vanin, Marco; Mortensen, Jens Jørgen
2009-01-01
representation. The possibility to switch seamlessly between the two representations implies that simulations employing the local basis can be fine tuned at the end of the calculation by switching to the grid, thereby combining the strength of the two representations for optimal performance. The implementation...... is tested by calculating atomization energies and equilibrium bulk properties of a variety of molecules and solids, comparing to the grid results. Finally, it is demonstrated how a grid-quality structure optimization can be performed with significantly reduced computational effort by switching between...
Hossein Jafari
2016-04-01
Full Text Available In this paper, we consider the local fractional decomposition method, variational iteration method, and differential transform method for analytic treatment of linear and nonlinear local fractional differential equations, homogeneous or nonhomogeneous. The operators are taken in the local fractional sense. Some examples are given to demonstrate the simplicity and the efficiency of the presented methods.
Regularity for solutions of non local, non symmetric equations
Lara, Hector Chang
2011-01-01
We study the regularity for solutions of fully nonlinear integro differential equations with respect to nonsymmetric kernels. More precisely, we assume that our operator is elliptic with respect to a family of integro differential linear operators where the symmetric part of the kernels have a fixed homogeneity $\\sigma$ and the skew symmetric part have strictly smaller homogeneity $\\tau$. We prove a weak ABP estimate and $C^{1,\\alpha}$ regularity. Our estimates remain uniform as we take $\\sigma \\to 2$ and $\\tau \\to 1$ so that this extends the regularity theory for elliptic differential equations with dependence on the gradient.
Identification and mitigation of T-S waves using localized dynamic surface modification
Amitay, Michael; Tuna, Burak A.; Dell'Orso, Haley
2016-06-01
The control of transition from a laminar to a turbulent flow over a flat plate using localized dynamic surface modifications was explored experimentally in Rensselaer Polytechnic Institute's subsonic wind tunnel. Dynamic surface modification, via a pair of Piezoelectrically Driven Oscillating Surface (PDOS) actuators, was used to excite and control the T-S wave over a flat plate. Creating an upstream, localized small disturbance at the most amplified frequency of fact = 250 Hz led to phase-locking the T-S wave. This enabled observation of the excited T-S wave using phase-locked stereoscopic particle image velocimetry. The growth of the T-S wave as it moved downstream was also measured using this technique (25% growth over four wavelengths of the excited wave). Activation of a downstream PDOS actuator (in addition to the upstream PDOS) at the appropriate amplitude and phase shift resulted in attenuation of the peak amplitude of the coherent velocity fluctuations (by up to 68%) and a substantial reduction of the degree of coherence of the T-S wave. Since the PDOS actuators used in this work were localized, the effect of the control strategy was confined to the region directly downstream of the PDOS actuator.
Broadband Lamb wave trapping in cellular metamaterial plates with multiple local resonances.
Zhao, De-Gang; Li, Yong; Zhu, Xue-Feng
2015-03-20
We have investigated the Lamb wave propagation in cellular metamaterial plates constructed by bending-dominated and stretch-dominated unit-cells with the stiffness differed by orders of magnitude at an ultralow density. The simulation results show that ultralight metamaterial plates with textured stubs deposited on the surface can support strong local resonances for both symmetric and anti-symmetric modes at low frequencies, where Lamb waves at the resonance frequencies are highly localized in the vibrating stubs. The resonance frequency is very sensitive to the geometry of textured stubs. By reasonable design of the geometry of resonant elements, we establish a simple loaded-bar model with the array of oscillators having a gradient relative density (or weight) that can support multiple local resonances, which permits the feasibility of a broadband Lamb wave trapping. Our study could be potentially significant in designing ingenious weight-efficient acoustic devices for practical applications, such as shock absorption, cushioning, and vibrations traffic, etc.
Traveling wave solutions of the one-dimensional Boussinesq paradigm equation
Vassilev, V. M.; Djondjorov, P. A.; Hadzhilazova, M. Ts.; Mladenov, I. M.
2013-10-01
The one-dimensional quasi-stationary flow of inviscid liquid in a shallow layer with free surface is described by the so-called Boussinesq Paradigm Equation (BPE). Slightly generalized this equation appears also in the theory of longitudinal vibrations of rods and in the continuum limit for lattices. It is well known that the one-dimensional (1-D) BPE admits a one-parameter family of traveling wave solutions expressed in an analytic form through the "sech" function. In the present contribution, new analytic solutions to the 1-D BPE representing traveling waves are obtained. These solutions are expressed through Weierstrass and Jacobi elliptic functions, which in some cases reduce to elementary functions.
Exact solutions of unsteady Korteweg-de Vries and time regularized long wave equations.
Islam, S M Rayhanul; Khan, Kamruzzaman; Akbar, M Ali
2015-01-01
In this paper, we implement the exp(-Φ(ξ))-expansion method to construct the exact traveling wave solutions for nonlinear evolution equations (NLEEs). Here we consider two model equations, namely the Korteweg-de Vries (KdV) equation and the time regularized long wave (TRLW) equation. These equations play significant role in nonlinear sciences. We obtained four types of explicit function solutions, namely hyperbolic, trigonometric, exponential and rational function solutions of the variables in the considered equations. It has shown that the applied method is quite efficient and is practically well suited for the aforementioned problems and so for the other NLEEs those arise in mathematical physics and engineering fields. PACS numbers: 02.30.Jr, 02.70.Wz, 05.45.Yv, 94.05.Fq.
Z. Hashemiyan
2016-01-01
Full Text Available Properties of soft biological tissues are increasingly used in medical diagnosis to detect various abnormalities, for example, in liver fibrosis or breast tumors. It is well known that mechanical stiffness of human organs can be obtained from organ responses to shear stress waves through Magnetic Resonance Elastography. The Local Interaction Simulation Approach is proposed for effective modelling of shear wave propagation in soft tissues. The results are validated using experimental data from Magnetic Resonance Elastography. These results show the potential of the method for shear wave propagation modelling in soft tissues. The major advantage of the proposed approach is a significant reduction of computational effort.
Packo, P.; Staszewski, W. J.; Uhl, T.
2016-01-01
Properties of soft biological tissues are increasingly used in medical diagnosis to detect various abnormalities, for example, in liver fibrosis or breast tumors. It is well known that mechanical stiffness of human organs can be obtained from organ responses to shear stress waves through Magnetic Resonance Elastography. The Local Interaction Simulation Approach is proposed for effective modelling of shear wave propagation in soft tissues. The results are validated using experimental data from Magnetic Resonance Elastography. These results show the potential of the method for shear wave propagation modelling in soft tissues. The major advantage of the proposed approach is a significant reduction of computational effort. PMID:26884808
Local probing of magnetic films by optical excitation of magnetostatic waves
Chernov, A. I.; Kozhaev, M. A.; Vetoshko, P. M.; Dodonov, D. V.; Prokopov, A. R.; Shumilov, A. G.; Shaposhnikov, A. N.; Berzhanskii, V. N.; Zvezdin, A. K.; Belotelov, V. I.
2016-06-01
Excitation of volume and surface magnetostatic spin waves in ferrite garnet films by circularly polarized laser pulses utilizing to the inverse magnetooptical Faraday effect has been studied experimentally. The region of excitation of the magnetostatic spin waves is determined by the diameter of the laser beam (˜10 μm). At the same time, the characteristic propagation length of the modes is 30 μm. A method of finding the local characteristics of a magnetic film, in particular, the cubic and uniaxial anisotropy constants, based on the analysis of the azimuthal-angle dependence of the spectrum of the magnetostatic spin waves has been proposed.
Abbott, B. P.; Abbott, R.; Abbott, T. D.; Abernathy, M. R.; Acernese, F.; Ackley, K.; Adams, C.; Adams, T.; Addesso, P.; Adhikari, R. X.; Adya, V. B.; Affeldt, C.; Agathos, M.; Agatsuma, K.; Aggarwal, N.; Aguiar, O. D.; Ain, A.; Ajith, P.; Allen, B.; Allocca, A.; Altin, P. A.; Amariutei, D. V.; Anderson, S. B.; Anderson, W. G.; Arai, K.; Araya, M. C.; Arceneaux, C. C.; Areeda, J. S.; Arnaud, N.; Arun, K. G.; Ashton, G.; Ast, M.; Aston, S. M.; Astone, P.; Aufmuth, P.; Aulbert, C.; Babak, S.; Baker, P. T.; Baldaccini, F.; Ballardin, G.; Ballmer, S. W.; Barayoga, J. C.; Barclay, S. E.; Barish, B. C.; Barker, D.; Barone, F.; Barr, B.; Barsotti, L.; Barsuglia, M.; Barta, D.; Bartlett, J.; Bartos, I.; Bassiri, R.; Basti, A.; Batch, J. C.; Baune, C.; Bavigadda, V.; Bazzan, M.; Behnke, B.; Bejger, M.; Belczynski, C.; Bell, A. S.; Bell, C. J.; Berger, B. K.; Bergman, J.; Bergmann, G.; Berry, C. P. L.; Bersanetti, D.; Bertolini, A.; Betzwieser, J.; Bhagwat, S.; Bhandare, R.; Bilenko, I. A.; Billingsley, G.; Birch, J.; Birney, R.; Biscans, S.; Bisht, A.; Bitossi, M.; Biwer, C.; Bizouard, M. A.; Blackburn, J. K.; Blair, C. D.; Blair, D.; Blair, R. M.; Bloemen, S.; Bock, O.; Bodiya, T. P.; Boer, M.; Bogaert, G.; Bogan, C.; Bohe, A.; Bojtos, P.; Bond, C.; Bondu, F.; Bonnand, R.; Bork, R.; Boschi, V.; Bose, S.; Bozzi, A.; Bradaschia, C.; Brady, P. R.; Braginsky, V. B.; Branchesi, M.; Brau, J. E.; Briant, T.; Brillet, A.; Brinkmann, M.; Brisson, V.; Brockill, P.; Brooks, A. F.; Brown, D. A.; Brown, D. D.; Brown, N. M.; Buchanan, C. C.; Buikema, A.; Bulik, T.; Bulten, H. J.; Buonanno, A.; Buskulic, D.; Buy, C.; Byer, R. L.; Cadonati, L.; Cagnoli, G.; Cahillane, C.; Calderón Bustillo, J.; Callister, T.; Calloni, E.; Camp, J. B.; Cannon, K. C.; Cao, J.; Capano, C. D.; Capocasa, E.; Carbognani, F.; Caride, S.; Casanueva Diaz, J.; Casentini, C.; Caudill, S.; Cavaglià, M.; Cavalier, F.; Cavalieri, R.; Cella, G.; Cepeda, C.; Cerboni Baiardi, L.; Cerretani, G.; Cesarini, E.; Chakraborty, R.; Chalermsongsak, T.; Chamberlin, S. J.; Chan, M.; Chao, S.; Charlton, P.; Chassande-Mottin, E.; Chen, H. Y.; Chen, Y.; Cheng, C.; Chincarini, A.; Chiummo, A.; Cho, H. S.; Cho, M.; Chow, J. H.; Christensen, N.; Chu, Q.; Chua, S.; Chung, S.; Ciani, G.; Clara, F.; Clark, J. A.; Cleva, F.; Coccia, E.; Cohadon, P.-F.; Colla, A.; Collette, C. G.; Constancio, M.; Conte, A.; Conti, L.; Cook, D.; Corbitt, T. R.; Cornish, N.; Corsi, A.; Cortese, S.; Costa, C. A.; Coughlin, M. W.; Coughlin, S. B.; Coulon, J.-P.; Countryman, S. T.; Couvares, P.; Coward, D. M.; Cowart, M. J.; Coyne, D. C.; Coyne, R.; Craig, K.; Creighton, J. D. E.; Cripe, J.; Crowder, S. G.; Cumming, A.; Cunningham, L.; Cuoco, E.; Dal Canton, T.; Danilishin, S. L.; D'Antonio, S.; Danzmann, K.; Darman, N. S.; Dattilo, V.; Dave, I.; Daveloza, H. P.; Davier, M.; Davies, G. S.; Daw, E. J.; Day, R.; DeBra, D.; Debreczeni, G.; Degallaix, J.; De Laurentis, M.; Deléglise, S.; Del Pozzo, W.; Denker, T.; Dent, T.; Dereli, H.; Dergachev, V.; DeRosa, R.; De Rosa, R.; DeSalvo, R.; Dhurandhar, S.; Díaz, M. C.; Di Fiore, L.; Di Giovanni, M.; Di Lieto, A.; Di Palma, I.; Di Virgilio, A.; Dojcinoski, G.; Dolique, V.; Donovan, F.; Dooley, K. L.; Doravari, S.; Douglas, R.; Downes, T. P.; Drago, M.; Drever, R. W. P.; Driggers, J. C.; Du, Z.; Ducrot, M.; Dwyer, S. E.; Edo, T. B.; Edwards, M. C.; Effler, A.; Eggenstein, H.-B.; Ehrens, P.; Eichholz, J. M.; Eikenberry, S. S.; Engels, W.; Essick, R. C.; Etzel, T.; Evans, M.; Evans, T. M.; Everett, R.; Factourovich, M.; Fafone, V.; Fair, H.; Fairhurst, S.; Fan, X.; Fang, Q.; Farinon, S.; Farr, B.; Farr, W. M.; Favata, M.; Fays, M.; Fehrmann, H.; Fejer, M. M.; Ferrante, I.; Ferreira, E. C.; Ferrini, F.; Fidecaro, F.; Fiori, I.; Fisher, R. P.; Flaminio, R.; Fletcher, M.; Fournier, J.-D.; Franco, S.; Frasca, S.; Frasconi, F.; Frei, Z.; Freise, A.; Frey, R.; Fricke, T. T.; Fritschel, P.; Frolov, V. V.; Fulda, P.; Fyffe, M.; Gabbard, H. A. G.; Gair, J. R.; Gammaitoni, L.; Gaonkar, S. G.; Garufi, F.; Gatto, A.; Gaur, G.; Gehrels, N.; Gemme, G.; Gendre, B.; Genin, E.; Gennai, A.; George, J.; Gergely, L.; Germain, V.; Ghosh, A.; Ghosh, S.; Giaime, J. A.; Giardina, K. D.; Giazotto, A.; Gill, K.; Glaefke, A.; Goetz, E.; Goetz, R.; Gondan, L.; González, G.; Gonzalez Castro, J. M.; Gopakumar, A.; Gordon, N. A.; Gorodetsky, M. L.; Gossan, S. E.; Gosselin, M.; Gouaty, R.; Graef, C.; Graff, P. B.; Granata, M.; Grant, A.; Gras, S.; Gray, C.; Greco, G.; Green, A. C.; Groot, P.; Grote, H.; Grunewald, S.; Guidi, G. M.; Guo, X.; Gupta, A.; Gupta, M. K.; Gushwa, K. E.; Gustafson, E. K.; Gustafson, R.; Hacker, J. J.; Hall, B. R.; Hall, E. D.; Hammond, G.; Haney, M.; Hanke, M. M.; Hanks, J.; Hanna, C.; Hannam, M. D.; Hanson, J.; Hardwick, T.; Harms, J.; Harry, G. M.; Harry, I. W.; Hart, M. J.; Hartman, M. T.; Haster, C.-J.; Haughian, K.; Heidmann, A.; Heintze, M. C.; Heitmann, H.; Hello, P.; Hemming, G.; Hendry, M.; Heng, I. S.; Hennig, J.; Heptonstall, A. W.; Heurs, M.; Hild, S.; Hoak, D.; Hodge, K. A.; Hofman, D.; Hollitt, S. E.; Holt, K.; Holz, D. E.; Hopkins, P.; Hosken, D. J.; Hough, J.; Houston, E. A.; Howell, E. J.; Hu, Y. M.; Huang, S.; Huerta, E. A.; Huet, D.; Hughey, B.; Husa, S.; Huttner, S. H.; Huynh-Dinh, T.; Idrisy, A.; Indik, N.; Ingram, D. R.; Inta, R.; Isa, H. N.; Isac, J.-M.; Isi, M.; Islas, G.; Isogai, T.; Iyer, B. R.; Izumi, K.; Jacqmin, T.; Jang, H.; Jani, K.; Jaranowski, P.; Jawahar, S.; Jiménez-Forteza, F.; Johnson, W. W.; Jones, D. I.; Jones, R.; Jonker, R. J. G.; Ju, L.; K, Haris; Kalaghatgi, C. V.; Kalogera, V.; Kandhasamy, S.; Kang, G.; Kanner, J. B.; Karki, S.; Kasprzack, M.; Katsavounidis, E.; Katzman, W.; Kaufer, S.; Kaur, T.; Kawabe, K.; Kawazoe, F.; Kéfélian, F.; Kehl, M. S.; Keitel, D.; Kelley, D. B.; Kells, W.; Kennedy, R.; Key, J. S.; Khalaidovski, A.; Khalili, F. Y.; Khan, S.; Khan, Z.; Khazanov, E. A.; Kijbunchoo, N.; Kim, C.; Kim, J.; Kim, K.; Kim, N.; Kim, N.; Kim, Y.-M.; King, E. J.; King, P. J.; Kinzel, D. L.; Kissel, J. S.; Kleybolte, L.; Klimenko, S.; Koehlenbeck, S. M.; Kokeyama, K.; Koley, S.; Kondrashov, V.; Kontos, A.; Korobko, M.; Korth, W. Z.; Kowalska, I.; Kozak, D. B.; Kringel, V.; Krishnan, B.; Królak, A.; Krueger, C.; Kuehn, G.; Kumar, P.; Kuo, L.; Kutynia, A.; Lackey, B. D.; Landry, M.; Lange, J.; Lantz, B.; Lasky, P. D.; Lazzarini, A.; Lazzaro, C.; Leaci, P.; Leavey, S.; Lebigot, E.; Lee, C. H.; Lee, H. K.; Lee, H. M.; Lee, K.; Lenon, A.; Leonardi, M.; Leong, J. R.; Leroy, N.; Letendre, N.; Levin, Y.; Levine, B. M.; Li, T. G. F.; Libson, A.; Littenberg, T. B.; Lockerbie, N. A.; Logue, J.; Lombardi, A. L.; Lord, J. E.; Lorenzini, M.; Loriette, V.; Lormand, M.; Losurdo, G.; Lough, J. D.; Lück, H.; Lundgren, A. P.; Luo, J.; Lynch, R.; Ma, Y.; MacDonald, T.; Machenschalk, B.; MacInnis, M.; Macleod, D. M.; Magana-Sandoval, F.; Magee, R. M.; Mageswaran, M.; Majorana, E.; Maksimovic, I.; Malvezzi, V.; Man, N.; Mandel, I.; Mandic, V.; Mangano, V.; Mansell, G. L.; Manske, M.; Mantovani, M.; Marchesoni, F.; Marion, F.; Márka, S.; Márka, Z.; Markosyan, A. S.; Maros, E.; Martelli, F.; Martellini, L.; Martin, I. W.; Martin, R. M.; Martynov, D. V.; Marx, J. N.; Mason, K.; Masserot, A.; Massinger, T. J.; Masso-Reid, M.; Matichard, F.; Matone, L.; Mavalvala, N.; Mazumder, N.; Mazzolo, G.; McCarthy, R.; McClelland, D. E.; McCormick, S.; McGuire, S. C.; McIntyre, G.; McIver, J.; McManus, D. J.; McWilliams, S. T.; Meacher, D.; Meadors, G. D.; Meidam, J.; Melatos, A.; Mendell, G.; Mendoza-Gandara, D.; Mercer, R. A.; Merilh, E.; Merzougui, M.; Meshkov, S.; Messenger, C.; Messick, C.; Meyers, P. M.; Mezzani, F.; Miao, H.; Michel, C.; Middleton, H.; Mikhailov, E. E.; Milano, L.; Miller, J.; Millhouse, M.; Minenkov, Y.; Ming, J.; Mirshekari, S.; Mishra, C.; Mitra, S.; Mitrofanov, V. P.; Mitselmakher, G.; Mittleman, R.; Moggi, A.; Mohan, M.; Mohapatra, S. R. P.; Montani, M.; Moore, B. C.; Moore, C. J.; Moraru, D.; Moreno, G.; Morriss, S. R.; Mossavi, K.; Mours, B.; Mow-Lowry, C. M.; Mueller, C. L.; Mueller, G.; Muir, A. W.; Mukherjee, Arunava; Mukherjee, D.; Mukherjee, S.; Mullavey, A.; Munch, J.; Murphy, D. J.; Murray, P. G.; Mytidis, A.; Nardecchia, I.; Naticchioni, L.; Nayak, R. K.; Necula, V.; Nedkova, K.; Nelemans, G.; Neri, M.; Neunzert, A.; Newton, G.; Nguyen, T. T.; Nielsen, A. B.; Nissanke, S.; Nitz, A.; Nocera, F.; Nolting, D.; Normandin, M. E. N.; Nuttall, L. K.; Oberling, J.; Ochsner, E.; O'Dell, J.; Oelker, E.; Ogin, G. H.; Oh, J. J.; Oh, S. H.; Ohme, F.; Oliver, M.; Oppermann, P.; Oram, Richard J.; O'Reilly, B.; O'Shaughnessy, R.; Ott, C. D.; Ottaway, D. J.; Ottens, R. S.; Overmier, H.; Owen, B. J.; Pai, A.; Pai, S. A.; Palamos, J. R.; Palashov, O.; Palomba, C.; Pal-Singh, A.; Pan, H.; Pankow, C.; Pannarale, F.; Pant, B. C.; Paoletti, F.; Paoli, A.; Papa, M. A.; Paris, H. R.; Parker, W.; Pascucci, D.; Pasqualetti, A.; Passaquieti, R.; Passuello, D.; Patrick, Z.; Pearlstone, B. L.; Pedraza, M.; Pedurand, R.; Pekowsky, L.; Pele, A.; Penn, S.; Pereira, R.; Perreca, A.; Phelps, M.; Piccinni, O.; Pichot, M.; Piergiovanni, F.; Pierro, V.; Pillant, G.; Pinard, L.; Pinto, I. M.; Pitkin, M.; Poggiani, R.; Post, A.; Powell, J.; Prasad, J.; Predoi, V.; Premachandra, S. S.; Prestegard, T.; Price, L. R.; Prijatelj, M.; Principe, M.; Privitera, S.; Prodi, G. A.; Prokhorov, L.; Punturo, M.; Puppo, P.; Pürrer, M.; Qi, H.; Qin, J.; Quetschke, V.; Quintero, E. A.; Quitzow-James, R.; Raab, F. J.; Rabeling, D. S.; Radkins, H.; Raffai, P.; Raja, S.; Rakhmanov, M.; Rapagnani, P.; Raymond, V.; Razzano, M.; Re, V.; Read, J.; Reed, C. M.; Regimbau, T.; Rei, L.; Reid, S.; Reitze, D. H.; Rew, H.; Ricci, F.; Riles, K.; Robertson, N. A.; Robie, R.; Robinet, F.; Rocchi, A.; Rolland, L.; Rollins, J. G.; Roma, V. J.; Romano, J. D.; Romano, R.; Romanov, G.; Romie, J. H.; Rosińska, D.; Rowan, S.; Rüdiger, A.; Ruggi, P.; Ryan, K.; Sachdev, S.; Sadecki, T.; Sadeghian, L.; Saleem, M.; Salemi, F.; Samajdar, A.; Sammut, L.; Sanchez, E. J.; Sandberg, V.; Sandeen, B.; Sanders, J. R.; Sassolas, B.; Sathyaprakash, B. S.; Saulson, P. R.; Sauter, O.; Savage, R. L.; Sawadsky, A.; Schale, P.; Schilling, R.; Schmidt, J.; Schmidt, P.; Schnabel, R.; Schofield, R. M. S.; Schönbeck, A.; Schreiber, E.; Schuette, D.; Schutz, B. F.; Scott, J.; Scott, S. M.; Sellers, D.; Sentenac, D.; Sequino, V.; Sergeev, A.; Serna, G.; Setyawati, Y.; Sevigny, A.; Shaddock, D. A.; Shah, S.; Shahriar, M. S.; Shaltev, M.; Shao, Z.; Shapiro, B.; Shawhan, P.; Sheperd, A.; Shoemaker, D. H.; Shoemaker, D. M.; Siellez, K.; Siemens, X.; Sigg, D.; Silva, A. D.; Simakov, D.; Singer, A.; Singer, L. P.; Singh, A.; Singh, R.; Sintes, A. M.; Slagmolen, B. J. J.; Smith, J. R.; Smith, N. D.; Smith, R. J. E.; Son, E. J.; Sorazu, B.; Sorrentino, F.; Souradeep, T.; Srivastava, A. K.; Staley, A.; Steinke, M.; Steinlechner, J.; Steinlechner, S.; Steinmeyer, D.; Stephens, B. C.; Stone, R.; Strain, K. A.; Straniero, N.; Stratta, G.; Strauss, N. A.; Strigin, S.; Sturani, R.; Stuver, A. L.; Summerscales, T. Z.; Sun, L.; Sutton, P. J.; Swinkels, B. L.; Szczepanczyk, M. J.; Tacca, M.; Talukder, D.; Tanner, D. B.; Tápai, M.; Tarabrin, S. P.; Taracchini, A.; Taylor, R.; Theeg, T.; Thirugnanasambandam, M. P.; Thomas, E. G.; Thomas, M.; Thomas, P.; Thorne, K. A.; Thorne, K. S.; Thrane, E.; Tiwari, S.; Tiwari, V.; Tokmakov, K. V.; Tomlinson, C.; Tonelli, M.; Torres, C. V.; Torrie, C. I.; Töyrä, D.; Travasso, F.; Traylor, G.; Trifirò, D.; Tringali, M. C.; Trozzo, L.; Tse, M.; Turconi, M.; Tuyenbayev, D.; Ugolini, D.; Unnikrishnan, C. S.; Urban, A. L.; Usman, S. A.; Vahlbruch, H.; Vajente, G.; Valdes, G.; van Bakel, N.; van Beuzekom, M.; van den Brand, J. F. J.; van den Broeck, C.; Vander-Hyde, D. C.; van der Schaaf, L.; van der Sluys, M. V.; van Heijningen, J. V.; van Veggel, A. A.; Vardaro, M.; Vass, S.; Vasúth, M.; Vaulin, R.; Vecchio, A.; Vedovato, G.; Veitch, J.; Veitch, P. J.; Venkateswara, K.; Verkindt, D.; Vetrano, F.; Viceré, A.; Vinciguerra, S.; Vine, D. J.; Vinet, J.-Y.; Vitale, S.; Vo, T.; Vocca, H.; Vorvick, C.; Vousden, W. D.; Vyatchanin, S. P.; Wade, A. R.; Wade, L. E.; Wade, M.; Walker, M.; Wallace, L.; Walsh, S.; Wang, G.; Wang, H.; Wang, M.; Wang, X.; Wang, Y.; Ward, R. L.; Warner, J.; Was, M.; Weaver, B.; Wei, L.-W.; Weinert, M.; Weinstein, A. J.; Weiss, R.; Welborn, T.; Wen, L.; Weßels, P.; Westphal, T.; Wette, K.; Whelan, J. T.; White, D. J.; Whiting, B. F.; Williams, R. D.; Williamson, A. R.; Willis, J. L.; Willke, B.; Wimmer, M. H.; Winkler, W.; Wipf, C. C.; Wittel, H.; Woan, G.; Worden, J.; Wright, J. L.; Wu, G.; Yablon, J.; Yam, W.; Yamamoto, H.; Yancey, C. C.; Yap, M. J.; Yu, H.; Yvert, M.; Zadrożny, A.; Zangrando, L.; Zanolin, M.; Zendri, J.-P.; Zevin, M.; Zhang, F.; Zhang, L.; Zhang, M.; Zhang, Y.; Zhao, C.; Zhou, M.; Zhou, Z.; Zhu, X. J.; Zucker, M. E.; Zuraw, S. E.; Zweizig, J.; LIGO Scientific Collaboration; Virgo Collaboration
2016-12-01
We present a possible observing scenario for the Advanced LIGO and Advanced Virgo gravitational-wave detectors over the next decade, with the intention of providing information to the astronomy community to facilitate planning for multi-messenger astronomy with gravitational waves. We determine the expected sensitivity of the network to transient gravitational-wave signals, and study the capability of the network to determine the sky location of the source. We report our findings for gravitational-wave transients, with particular focus on gravitational-wave signals from the inspiral of binary neutron-star systems, which are considered the most promising for multi-messenger astronomy. The ability to localize the sources of the detected signals depends on the geographical distribution of the detectors and their relative sensitivity, and 90% credible regions can be as large as thousands of square degrees when only two sensitive detectors are operational. Determining the sky position of a significant fraction of detected signals to areas of 5 deg2 to 20 deg2 will require at least three detectors of sensitivity within a factor of ˜ 2 of each other and with a broad frequency bandwidth. Should the third LIGO detector be relocated to India as expected, a significant fraction of gravitational-wave signals will be localized to a few square degrees by gravitational-wave observations alone.