The Evolution Equation About Its Exact Solution

In this dissertation, dual function of the proposed algorithm and Lie sym-metry group method are applied to reduce some classical evolution equation. The main results contained here are as follows:First, dual-function algorithm is used to reduce KdV-Burgers equation to ordinary differential equations by travelling wave reduction, the physical meaning of the new soliton solutions are obtained.Second, Lie symmetry group method is applied to reduce Future-Options equation to ordinary differential equations by symmetry reduction, not only the Lie symmetry of the financial equation are obtained, but also the group invariant solutions of this equation are obtained.Third, Lie symmetry group method is also applied to reduce Kuramoto-Sivashinsky equation to ordinary differential equations by symmetry reduction, the Lie symmetry and exact solutions of this equation are obtained.The paper is structured as follows:Chapter one, outlined for solving the evolution equations and its important role in the historical background, and then introduce the relevant reduction of equations of the basic method and symbols used in this article.Chapter two, the method which described in the previous chapter is used to reduce different evolution equation, and then construct exact solutions.