Standard And Extended Tanh Function Expansion Method For Solving Nonlinear Evolution Equations

With the development of nonlinear science, the study of nonlinear phenomena is becoming more and more clear, and the field of the study becomes very wide, such as the method to solve evolution equations and the method to discuss the existence, uniqueness, stability of exact solutions. The study of exact solutions is an important topic. There are a number of methods to solve evolution equations, but they are only applicable to certain types of equations. In fact, there is no method can be worked on all nonlinear evolution equations.This paper, we use a standard tanh-function method and the extended tanh-function method to solve some nonlinear evolution equations, and obtain a large number of exact solutions. It shows the effectiveness of tanh-function method.The structure of this paper is as follows:Chapter 1, we introduce several common methods to solve nonlinear evolution equations, and briefly review the present condition for the study of exact solutions.Chapter 2, we use the standard tanh-function method to solve several nonlinear evolution equations, which include (3+1)-dimensional KP, sine-Gordon, Higher-order KdV-like and Klein-Gordon-type equations.Chapter 3, exact solutions of Boussinesq-type equation and breaking equation are obtained by using extended tanh-function method.In the end, we summarize the work of this paper, and bring up a number of problems to be solved in the future.