Two Class Of New Auxiliary Equation And Their Applications

Finding the exact solution of nonlinear evolution equations is one of very important topic in soliton theory. This paper is devoted to find the exact solutions of the nonlinear evolution equations. We have get some interested results: such as, extended the auxiliary equation method, and which is also used to find the exact solitary wave solution of some nonlinear evolution equations. This paper contains three parts.Preface introduces the definition of evolution equation, the developments of soliton theory and some methods for finding the exact solutions of nonlinear evolution equations.In part two, the steps of finding the exact solutions of the nonlinear evolution equations by using the auxiliary eqution method are introduced.In part three , two class of new auxiliary equations are given, the solution of which is used to obtain the exact solitary wave solutions of some equations. For example, Boussinesq equation, modified Benjamin Bona Mahony eqution, Zakharov Kuznetsov equation, Korteweg-de Vries equation, Korteweg-de Vries Burgens eqaution, modified Kadomtsev-Petviashvili equations, two dimensional dispersive long wave equations, modified Korteweg-de Vries equation etc.