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Journal of Applied Mathematics
Volume 2013 (2013), Article ID 960798, 7 pages
http://dx.doi.org/10.1155/2013/960798
Research Article

The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations

Department of Mathematics, Honghe University, Mengzi, Yunnan 661100, China

Received 17 September 2013; Revised 7 November 2013; Accepted 7 November 2013

Academic Editor: Anjan Biswas

Copyright © 2013 Yun-Mei Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A good idea of finding the exact solutions of the nonlinear evolution equations is introduced. The idea is that the exact solutions of the elliptic-like equations are derived using the simplest equation method and the modified simplest equation method, and then the exact solutions of a class of nonlinear evolution equations which can be converted to the elliptic-like equation using travelling wave reduction are obtained. For example, the perturbed nonlinear Schrödinger’s equation (NLSE), the Klein-Gordon-Zakharov (KGZ) system, the generalized Davey-Stewartson (GDS) equations, the Davey-Stewartson (DS) equations, and the generalized Zakharov (GZ) equations are investigated and the exact solutions are presented using this method.