The Exp -Expansion Method and its Application for Solving Nonlinear Evolution Equations

In this paper, we employ the exp method to find the exact traveling wave solutions involving parameters of a nonlinear the system of shallow water wave equations. Comparison between this two method and another method which have been solved it. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave solutions. It is shown that the proposed methods provides a more powerful mathematical tool for constructing exact traveling wave solutions for many other nonlinear evolution equations.