A Generalized (G'/G)-Expansion Method for the Nonlinear Schrödinger Equation with Variable Coefficients

Abstract

In this paper, a generalized (G' /G)-expansion method, combined with suitable transformations, is used to construct exact solutions of the nonlinear Schrödinger equation with variable coefficients. As a result, hyperbolic function solutions, trigonometric function solutions, and rational solutions with parameters are obtained. When the parameters are taken as special values, some solutions including the known kink-type solitary wave solution and the singular travelling wave solution are derived from these obtained solutions. It is shown that the generalized (G' /G)-expansion method is direct, effective, and can be used for many other nonlinear evolution equations with variable coefficients in mathematical physics.