by using bifurcation theory of planar ordinary differential equations all different bounded travelling wave solutions of the generalized zakharov equation are classified in different parametric regions . in each of these parametric regions the exact explicit parametric representation of all solitary , kink (anti kink) and periodic wave solutions as well as their numerical simulation and thei...

This paper studies the generalized (2 + 1)-dimensional Zakharov-Kuznetsov Equation using the (G'/G)-expand method, we obtain many new explicit solutions of the generalized (2 + 1)-dimensional Zakharov-Kuznetsov Equation, which include hyperbolic function solutions, trigonometric function solutions and rational function solutions and so on.

In this paper, we investigate the instability of one-dimensionally stable periodic traveling wave solutions of the generalized Korteweg-de Vries equation to long wavelength transverse perturbations in the generalized Zakharov-Kuznetsov equation in two space dimensions. By deriving appropriate asymptotic expansions of the periodic Evans function, we derive an index which yields sufficient condit...

This paper considers the existence of the generalized solution to the initial vale problem for a generalized Zakharov equation in dimension two. By a priori integral estimates and the Galerkin method, one can arrive at the global generalized solution to the problem.

We present a general result of transverse nonlinear instability of 1-d solitary waves for Hamiltonian PDE’s for both periodic or localized transverse perturbations. Our main structural assumption is that the linear part of the 1d model and the transverse perturbation “have the same sign”. Our result applies to the generalized KP-I equation, the Nonlinear Schrödinger equation, the generalized Bo...

With the help of the generalized hyperbolic function, the subsidiary ordinary differential equation method is improved and proposed to construct exact traveling wave solutions of the nonlinear partial differential equations in a unified way. A class of nonlinear Schrödinger-type equations including the generalized Zakharov system, the Rangwala-Rao equation, and the Chen-Lee-Liu equation are inv...

Abstract:In this paper, we utilize the Exp-function method with symbolic computational system Maple to constructing generalized solitary solutions of auxiliary equation. With the aid of auxiliary equation and its generalized solitary solutions, new exact solutions with three arbitrary functions of two nonlinear evolution equations in physics, namely, higher-order nonlinear Schrodinger equation ...

In this paper, we study a generalized Zakharov–Kuznetsov equation in three variables, which has applications in the nonlinear development of ion-acoustic waves in a magnetized plasma. Conservation laws for this equation are constructed for the first time by using the new conservation theorem of Ibragimov. Furthermore, new exact solutions are obtained by employing the Lie symmetry method along w...

In this paper, the well-known He’s variational iteration method (VIM) is used to construct solitary wave solutions for the generalized Zakharov equation (GZE). The chosen initial solution (trial function) can be in soliton form with some unknown parameters, which can be determined in the solution procedure. c © 2007 Elsevier Ltd. All rights reserved.