The Expansion Method for Solving Nonlinear Partial Differential Equations

Abstract

The -expansion method, for solving nonlinear evolution equations is reviewed and applied to solve selected equations, which have positive integer homogeneous balance number. For the equations with non integer homogeneous balance number, we suggested an approach to write a transform to reduce the homogeneous balance number to a positive integer, and as an application, we apply this approach successfully to find a traveling wave solution to the general KdV equation for . For both cases and with help of Maple tools, we compared our results with the results obtained by other methods. Theses study show that this method is an effective method, and can be used to solve many types of nonlinear evolution equations.