The Exact Solutions For Some Nonlinear Evolution Equation

In this paper,a lot of solitary wave solutions and exact solutions of nonlinear evolution equations in mathematical physics are studied.The nonlinear evolution equations are widely applied and studied in maths , physics and biology.To obtain the solitary wave solutions and exact solutions of nonlinear evolution equation,people get hold of much important and effective methods, such as homogeneous balance method,tanh-function method and extend tanh-function method, inverse scattering method, Hirota method,Painlev(?) truncated method , Darboux transformations method,Censored auxiliar function method,etc. the exact solutions is different with different method. Based on thees methods,this paper studies the (2+1)-dimensional nonlinear coupled integrable generalization of the Kaup equation of nonlinear Schrodinger (NLS) type systems,and obtain a lot of new exact solutions, including solitary wave solutions and periodic solutions.This paper is composed of four charpter:In the first charpter,we mainly introduce the backgronud and recent researches of exact solutions of the nonlinear evolution equations,and introduce some different methods will be used in this paper , such as Censored auxiliar function method, homogeneous balance method,and tanh-function method,etc.In the second charpter,with the aid of computer algebra system and symbolic computation ,we make use of Censored auxiliar function method obtain a lot of new solitary wave solutions and periodic solutions of the (2+1)-dimensional nonlinear coupled integrable generalization of the Kaup equation of NLS type systems:In the third charpter, with the aid of computer algebra system and symbolic computation ,we make use of homogeneous balance method obtain B(a|¨) cklund Transformation a lot of new single solitary wave solutions and multi-solitary wave solutions of the (2+1)-dimensional nonlinear coupled integrable generalization of the Kaup equation with variable coefficient of NLS type systems:where,α(t),β(t),γ(t),η(t),μ(t),ω(t) are all nonzero function with the variable of t. In the fourth charpter, we generalize the conclusion obtained in this paper.