Some Investigation On The New Methods For Finding Exact Solutions Of Nonlinear Evolution Equations

Nonlinear dynamics is one of the important branches in nonlinear science, whereas study on how to solve nonlinear partial differential equations is one of the main contents in nonlinear dynamics. As a leading subject and hot interest in nonlinear science study on the solution method of nonlinear partial differential equations has become more and more challenging. At present, although a number of methods are proposed and developed to look for the exact solutions of nonlinear partial differential equations, unfortunately, not all these approaches are universally applicable for solving all kinds of nonlinear partial differential equations directly. As a consequence, it is still a very significant task to go on searching for various powerful and efficient approaches to solve nonlinear partial differential equations.In the first chapter, we simply introduce the background and the result of the article.In the second chapter, we discuss the Double Exp-function method, and apply it to Burgers equation, we obtain it's double solitary wave solutions.In the third chapter, we discuss the trigonometric function transform method, and apply it to a (2+1)-D laser equation and Ginzburg-Landau equation. More new explicit travelling wave solutions are obtained, which contain bright soliton, chirped bright soliton, dark soliton and chirped dark soliton.In the fourth chapter, we discuss the expand of Hirota method, and apply it to (3+1) dimensional K-P equation, (2+1)-D Nizhnik equations and Jimbo-Miwa equation. More new explicit travelling wave solutions are obtained, which contain periodic-soliton wave solutions, periodic double soliton wave solutions and double periodic double soliton wave solutions...