The simplest equation method and its application for solving the nonlinear NLSE,KGZ,GDS,DS,and GZ equations

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. © 2013 yun-mei zhao et al.