Application Of Exp-Function Method And (G'/G)-Expansion Method To Solve Nonlinear Evolution Equations

As is known to all, many important science and engineering problems are attributed to study on nonlinear evolution equations, thus it is very important to find exact solutions.Using Exp-function method and (G'/G) -expansion method, we study exact solutions for generalized Burger-Huxley equation, modified Kawahara equation and fifth-order KdV equation respectively in this thesis. The main results derived are as follows:(1) Based on Exp-function method, a series of new exact solutions of the generalized Burger-Huxley equation have been obtained and the solutions given by first-integral method are only our special cases. It is shown that the Exp-function method is straightforward and concise, and its applications are promising.(2) The (G'/G) -expansion method has been successfully used to seek exact travelling wave solutions of the modified Kawahara equation and the fifth-order KdV equation. As a result, a series of new exact solutions are obtained and the solutions given before are only our special cases. The solution procedure is very simple and the travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions and the rational functions. It is shown that the (G'/G) -expansion method provides a very effective and powerful mathematical tool for solving nonlinear evolution equations.Finally, the summary of this thesis and the prospect of study on constructing exact solution to nonlinear evolution equations in soliton are given.