Exact Solutions To Some Nonlinear Evolutionary Equations

This paper mainly focuses on the issues of finding exact solutions of nonlinear evolution equation. Based on the existing method, we have improved traditional Jacobi elliptic expansion method, which extended and enriched the method we have known. The basic content of this paper is given as following:Chapter one is devoted to reviewing the history development and current situation of our research work and summarizing the main works of thesis at last in this chapter.In chapter two, we introduce some primary conception and denotation relate to this paper, give the concept and classification of soliton, make out some explain to exact solutions, approximately solutions and similar solutions which tend to be confused.In chapter three, we introduce several methods to obtain solutions of the nonlinear equation. Such as, traditional Jacobian elliptic expansion method, generalized Jacobian elliptic function expansion method, homogeneous balance method, Wu elimination method.In chapter four, we ameliorate to the traditional Jacobian elliptic function expansion method, and give the unified expression of form solutions of Jacobian elliptic functions, and use this method to research the exact solutions of Klein-Gordon equation and Zakharov equation and mKdV-ZK equation. With the aid of mathematica software, we obtain a lot of new solutions except many solutions which we have known. Compared to traditional methods, our method has many advantages. Such as, having unified forms, easy to use, and the results is more comprehensive, etc. The method has active meaning for us to find new solutions and research structure of solitons.