The variable separation approach and study on solving the variable-coefficient nonlinear Schr?dinger equation

Abstract

In this paper, a variable separation approach is proposed and successfully extended to the (1+1)dimensional physics models. The new exact solution of two classes of variable-coefficient nonlinear Schrdinger equations are obtained. As a specific example, the envelope soliton solution for nonlinear Schr?dinger equations are a by-product, which is somewhat different in form, from the present result.