Journal of Advances in Applied Mathematics

9

Authors: Qingmei Zhang, Mei Xiong, Longwei Chen

In this paper, exact travelling wave solutions of two higher order nonlinear Schrödinger equations (NLSEs) are studied by using the first integral method. Firstly, two higher order nonlinear Schrödinger equations are reduced to nonlinear ordinary differential equations (ODEs) by simple travelling wave transformations. Then the division theorem of polynomial is used to calculate first integrals of dynamic systems. Finally, the soliton wave solutions, kink wave solutions and periodic wave solutions of two higher order nonlinear Schrödinger equations are obtained. The results show that this method is effective for solving exact solutions of nonlinear partial differential equations (PDEs).

12

Authors: Beibei Zhang, Mei Xiong, Longwei Chen

The novel (G‘/G)-expansion method is applied to solve generalized Davey-Stewartson equations with arbitrary power nonlinearities and obtain some exact traveling wave solutions. Via this method, we obtain kink wave solutions, anti-kink wave solutions, exact solitary wave solutions, periodic wave solutions. Also, it is shown that this method is influential for solving nonlinear partial differential equations (PDEs) in mathematical physics and engineering.