New Exact Solutions of the Drinfel'd-Sokolov-Wilson Equations ⋆

The first integral method is an important method to solve nonlinear partial differential equations. It can be applied to non-integrable systems as well as to integrable ones. In this paper, it aims to find out the exact solutions of Drinfel’d-Sokolov-Wilson equations by using the first integral method. Many kinds of solutions can be obtained, such as shock wave solutions, Exp-function solutions, rational function solutions and so on. Several solutions are found firstly. It has been proved that this method is effective.