A Number Of Exact Solutions For Nonlinear Evolution Equations,

Searching for exact solutions of nonlinear evolution equation has long been a popular research subject for mathematicians and physicists.At present, there has been established and developed a lot of effective method to solve nonlinear evolution equations, but a large number of nonlinear evolution equations are still unable to solve for complexity of nonlinear equations themselves.As a con-sequence,it is a very important research and valuable work to go on searching for some effective and feasible method to solve nonlinear evolution equation.In this paper, the first integral method of thinking and successor to make improvements to this method is introduced.By using this approach,a lot of exact solutions for some nonlinear evolution equations which have important physical significance are easily presented. The results include not only a number of known exact solutions, but also a number of new exact solutions.This enriched and improved the content of exact solutions of nonlinear evolution equations.This paper is composed of four chapters:In the fist chapter, we introduce the basic profiles of nonlinear evolution equations and the research status of exact solutions for nonlinear evolution equa-tions.The main work of this article is introduced.In the second chapter,we elaborate the first integral method and its appli-cation procedure in detail.In the third chapter, we make use of first integral method to obtain a lot of new exact solutions of Modified Improved Boussinesq equation, (2+1)-dimensional dispersive long wave equations and (2+1)-dimensional Konopelchenko-Dubrovsky equations.In the end, we summarize the work of this paper and look into the distance of research in future as well.