First Integral Method to Study Nonlinear Evolution Equations

In this paper, we apply the first integral method to generalized ZK-BBM equation and Drinefel’d-Sokolov- Wilson system and one-dimensional modified EW-Burgers equation. The first integral method is a powerful solution method for obtaining exact solutions of some nonlinear evolution equations. This method was first proposed by Feng [8] in solving Burgers– KdV equation which is based on the ring theory of commutative algebra. This method can be applied to nonintegrable equations as well as to integrable ones. Key words First integral method; Generalized ZK-BBM equation ; Drinefel’d-Sokolov-Wilson system; One-dimensional modified EW-Burgers equation