The Research And Application Of Methods To A Class Of Nonlinear Evolution Equations

The study of methods to nonlinear evolution equations has become one of the main researches in areas of Mathematics and physics. Find the exact solutions to nonlinear evolution equations can provide theory support to further understand the theory of nonlinear phenomena. This article describes some methods appeared in recent years for solving nonlinear equations, and obtained a number of exact solutions to nonlinear evolution equations, which including some new solitary wave solutions and periodic wave solutions. This paper consists of the following four chapters:Chapter1:The first chapter described the (G’/G)-expansion method, and used this method for solving the Kdv equation, Sharma-Tasso-Olver (STO) equations and Benjamin equation, a lot of exact solutions were obtained, including new solitary wave solutions and periodic wave solutions, and some solutions were simulated by computer.Chapter2:By using the extended mapping method and computer algebra systems, some exact solutions for the Boussinesq equation and Klein-Gordon equation were obtained,which including some new solutions and some solutions have not been found from the previous studies.Chapter3:By using the Riccati equations as the secondary, the solutions of Riccati equations could be get by the homogeneous balance method. Solutions of nonlinear evolution equations can be constructed in the form of index, it may be eventually expressed by the hyperbolic functions. This process is simple, clear and concise, and could have the guiding significance for solving a class of nonlinear evolution equations.Chapter4:By making use of the F expansion method and computer algebra systems for solving double ZK equations, a series of exact solutions expressed by Jacobi elliptic functions were obtained.