Author(s)

Qingmei Zhang, Mei Xiong, Longwei Chen

College of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, China.

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 Schrödinger equation and the generalized nonlinear Schrödinger 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 Schrödinger equations are obtained. The results show that this method is effective for solving exact solutions of nonlinear partial differential equations.

The Special Kind of (G’/G)-Expansion Method, the New Mapping Method, the Partial Differential Equations, the Exact Travelling Wave Solutions

Zhang, Q. , Xiong, M. and Chen, L. (2019) Exact Travelling Wave Solutions of Two Nonlinear Schrödinger Equations by Using Two Methods. Journal of Applied Mathematics and Physics, 7, 3101-3115. doi: 10.4236/jamp.2019.712218.