Exact Travelling Wave Solutions of Two Nonlinear Schrödinger Equations by Using Two Methods

The special kind of (G’/G)-expansion method and the new mapping method are easy and significant mathematical methods. In this paper, exact travelling wave solutions of the higher order dispersive Cubic-quintic nonlinear Schrodinger equation and the generalized nonlinear Schrodinger equation are studied by using the two methods. Finally, the solitary wave solutions, singular soliton solutions, bright and dark soliton solutions and periodic solutions of the two nonlinear Schrodinger equations are obtained. The results show that this method is effective for solving exact solutions of nonlinear partial differential equations.