Tanh Function Expansion Method CRE Method In The Application Of The Nonlinear Partial Differential Equations

Nonlinear equations are one of the important fields of nonlinear science. Thus, calculating the solutions of the nonlinear equations is the key of nonlinear science. People have been es-tablishing and developing a lot of methods for calculating the solutions of nonlinear equations due to the effort of many scientists, such as the inverse scattering transformation, the Dar-boux transformation, the bilinear method and multilinear method, the truncated Painleve expansion and function expansion method, and so on. Professor Lou also puts forward a simple and straightforward method-" CRE method " based on these.This paper first introduces several methods for studing integrability of nonlinear partial differential equations, later we use the generalized truncated Painleve expansion method to obtain new solutions of the Burgers equation.As prior knowledge, this paper introduces the tanh function expansion method of the nonlinear equations. Then some soliton solutions are obtained through the analysis of KdV equations and the coupled KdV equations.Through the master of some basic knowledge, we introduce the CRE method naturally. First, showing Riccati function expansion to mKdV equation, then the consistent equation of mKdV can be given. Many exact solutions with special structure can be obtained, by solving the consistent equations.