Homogenous balance method for solving exact solutions of the nonlinear Benny -luke equation and Vakhnenko-Parkes equation

Abstract

In this article, We apply the homogeneous balance method to construct the many families of exact solution of travelling wave solution of nonlinear equations, the Benny -Luke equation and vakhnenko-parkes equation. As the result, many solitary wave solution are obtained from the solution by hyperbolic function when the parameters were taken at special values and we compared the result with the solution of F-expansion method and -expansion method, we obtained the same results by certain hypotheses. Also we drew a 3D graph of exact solution for the special Benny -luke equation and vakhnenko-parkes equation by help of the maple.

Keywords

• Application
• Homogeneous balance method
• The Benny-Luke equation
• The Vakhenko-Parkes equation