Method of Conservation Laws for Solving Nonlinear Schrödinger Equation

Abstract

In this paper, we solve the nonlinear Schrödinger equation of the form, (Remark: Graphics omitted.), by means of conservation laws. For ε=0, the two soliton solution is obtained and is compared with numerical solution. For ε≠0, we consider plasma waves with linear and nonlinear Landau damping and obtain an approximate one soliton solution where the amplitude or velocity changes in time.