Abstract In this study, we present two different methods a sech-tanh method and extended tanh-method to obtained the soliton solutions of the two-dimensional Korteweg-de Vries-Burgers (KdVB) equation with the initial conditions. These solutions include bright and dark solitary wave solutions, triangular solutions and complex line soliton wave solution. These solutions are stable and have applic...

In this study, the numerical solution for the Modified Equal Width Wave (MEW) equation is presented using Fourier spectral method that use to discretize the space variable and Leap-frog method scheme for time dependence. Test problems including the single soliton wave motion, interaction of two solitary waves and interaction of three solitary waves will use to validate the proposed method. The ...

We establish soliton-like asymptotics for finite energy solutions to the Dirac equation coupled to a relativistic particle. Any solution with initial state close to the solitary manifold, converges in long time limit to a sum of traveling wave and outgoing free wave. The convergence holds in global energy norm. The proof uses spectral theory and symplectic projection onto solitary manifold in t...

We present a numerical study of solitary waves in one dimensional (1D) granular lattices. Our system consists of an array of deformable spheres which we model using Hertzian interactions between neighbouring bodies. A general discussion of the origin of solitary waves is presented. We then provide an analysis of the Hertz force. For the case of a uniform chain of spheres, we derive an approxima...

This research deals with the validation of fluid dynamic models, used for simulating shoaling and breaking solitary waves on slopes, based on experiments performed at the Ecole Supérieure d’Ingénieurs de Marseille’s (ESIM) laboratory. A separate paper, also presented at this conference, reports on experiments. In a first part of this work, a fully nonlinear potential flow model based on a Bound...

We investigate the interaction of a periodic solution and a one-soliton solution for the spin-polarized current in a uniaxial ferromagnetic nanowire. The amplitude and wave number of the periodic solution for the spin current give different contributions to the width, velocity, and amplitude of the soliton. Moreover, we found that the soliton can be trapped only in space with proper conditions....

In this part, we prove that the solitary wave solutions investigated in part I are extended as analytic functions in the complex plane, except at most countably many branch points and branch lines. We describe in detail how the limiting behavior of the complex singularities allows the creation of non-analytic solutions with corners and/or compact support. This is the second in a series of two p...

We study the nonlinear dynamics of a homogeneous DNA chain that is based on site-dependent finite stacking and pairing enthalpies. We introduce an extended nonlinear Schrödinger equation describing the dynamics of modulated wave in DNA model. We obtain envelope bright solitary waves with compact support as a solution. Analytical criteria of existence of this solution are derived. The stability ...

The solitary wave solution of the quadratic nonlinear Schrd̈inger equation is determined by the iterative method called Petviashvili method. This solution is also used for the initial condition for the time evolution to study the stability analysis. The spectral method is applied for the time evolution. Keywords—soliton, iterative method, spectral method, plasma

In this paper, Exp-function method is used for some exact solitary solutions of the generalized Pochhammer-Chree equation. It has been shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving nonlinear partial differential equations. As a result, some exact solitary solutions are obtained. It is shown that th...