Study On New Methods For Solving Nonlinear Partial Differential Equations Based On(G'/G)-Expansion Method

Solving nonlinear partial differential equations has an important position and role in nonlinear science research.The exact solution as an analytical solution,it can help people to explain the nonlinear phenomenon,reveal inner laws and essential attribute of development of any phenomenon.Through many efforts of scientists,many methods have been established to solve nonlinear partial differential equations,but the method for constructing exact solutions of nonlinear partial differential equations is not universally applicable.So looking for some new effective methods to solve nonlinear partial differential equations has important significance.In the summary of all kinds of methods for solving nonlinear partial differential equations,the paper mostly study some integrable nonlinear partial differential equations which have a wide application background,improve and generalize the(G'/G)-expansion method.With the help of mathematical computation software Mathematica,the exact solutions of these nonlinear partial differential equations are obtained.Not only the existing results are obtained,but also some new results are obtained.The full-text is divided into five chapters.In chapter 1,we describe the research background,research progress and nowadays work of nonlinear partial differential equations,as well as the main work of this paper.In chapter 2,a new(G'/(G+G'))-expansion method is studied.We apply the new(G'/(G+G'))-expansion method to determine the new exact solutions for a class of generalized nonlinear Schrodinger equation and coupled nonlinear Schrodinger equations.The solutions can be expressed by the hyperbolic cotangent functions,the cotangent functions and the rational functions.In chapter 3,we improve the(G'/G)-expansion method and propose a multiple(G'/G)-expansion method to look for the double traveling wave solutions of the coupled nonlinear Klein-Gordon equations and the coupled Schrodinger-Boussinesq equations.In chapter 4,based on the(G'/G)-expansion method,we study a new mixed(G'/G)-(F'/F)-expansion method that differs from the method in Chapter 3.More rich,complex and diverse double traveling wave solutions of(2+1)-dimensional Burgers equation and Hirota-Satsuma equation are obtained by the new mixed(G'/G)(F'/F)-expansion method.In chapter 5,the summary and expectation are given.