Some Methods For Solving Exact Solutions Of Nonlinear Evolution Equations

With the continuous development of science and technology,more and more people realize that the nature of nature is nonlinear.Therefore,the study of exact solutions of nonlinear evolution equations is paid more and more attention by experts and scholars.A lot of effective solving method has been proposed,but these methods are mostly used for solving nonlinear evolution equations with constant coefficients,the development of equations with variable coefficients is relatively few,and we know that it can be of variable coefficient nonlinear evolution equations in nature,reaction nature more realistic and objective.Therefore,solving nonlinear evolution equations with variable coefficients becomes more and more popular.This is also the focus of this article.In this paper,on the basis of previous studies,three methods for solving nonlinear evolution equations with variable coefficients are introduced.In the first expansion method(G'/G)based on the improvement and promotion,use G'/(G+G')expansion method to solve nonlinear evolution equations with variable coefficients,and take Gardner equation with variable coefficients,BBM equation with variable coefficients and the(2+1)-dimensional BLP equations with variable coefficients for example.Finally,obtained the exact solutions about them.Secondly,we use the double auxiliary equation expansion method to solve the(2+1)-dimensional BLP equations with variable coefficients,and the influence of the number of auxiliary equations on the solutions is discussed.Finally,we use the improved System technique expansion method to solve two kinds of nonlinear KdV equation with variable coefficients and the Fisher equation with variable coefficients,and get very good results.The full text is divided into five chapters.The first chapter introduces the origin and development of nonlinear evolution equation and soliton,and the research status of evolution equation with variable coefficients,and summarizes the main work of this paper.In the second chapter,we introduce the G'/(G+G')expansion method,and apply this method to the Gardner equation with variable coefficients,the BBM equation with variable coefficients and the(2+1)dimensional BLP equations with variable coefficients.Finally,we obtain their exact solutions.In the third chapter,using the double auxiliaryequation expansion method to solve the(2+1)dimensional BLP equations with variable coefficients,and the exact solution of the equation is obtained.Finally,the influence of the number of auxiliary equations on the solution is discussed.In the fourth chapter,we introduce the improved System technique expansion method,and take the two kinds of nonlinear KdV equation with variable coefficients and Fisher equation with variable coefficients for example,and we get the new exponential function solution form of the equation successfully.In the fifth chapter,the full text is summarized and the direction of the research is prospected.