Exact Solutions for the Modified KdV and the Generalized KdV Equations via Exp-Function Method

An application of the Exp-function method (EFM) to search for exact solutions of nonlinear partial di®erential equations is analyzed. This method is used for the modi¯ed KdV equation and the generalized KdV equation. The EFM was used to construct peri- odic wave and solitary wave solutions of nonlinear evolution equations (NLEEs). This method is developed for searching exact travelling wave solutions of nonlinear partial di®erential equations. It is shown that the Exp-function method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics and applied mathematics.