Application Of Three Methods In Solving Nonlinear Partial Differential Equations

There is no specific method for solving nonlinear partial differential equations.It is of theoretical and practical value to construct a new method for solving equations.More and more methods are studied in developed time,so it is necessary to persistently explore new methods and summarize existing methods,and master the solution methods that have been developed.This paper mainly uses the first integral method,Riccati expansion method,(G'/G)-expansion method to solve several nonlinear partial differential equations for application and research.Firstly,the background and development of nonlinear partial differential equations are introduced,and the background of several equations studied in this paper is explained.Secondly,the common solving methods of nonlinear partial differential equations are introduced in detail.Then,the first integral method is used to solve the(3+1)-dimensional nonlinear Schrodinger equation and a class of nonlinear wave equation,and new traveling wave exact solutions are obtained.Then,the Riccati expansion method is used to solve the generalized KdV-mKdV equation and the(1+1)-dimensional Chaffee-Infante reaction-diffusion equation,and a large number of new non-traveling wave exact solutions are obtained,including hyperbolic and trigonometric solutions.Finally,the Sharma-Tasso-Olver equation is solved by (G'/G)-expansion method,and the new exact solutions is obtained based on the new auxiliary equation.