Traveling Wave Solutions for Some Nonlinear Partial Differential Equations by Using Modified(w⁄g)- Expansion Method

Modified(w⁄g)- Expansion Method

Abstract

In this paper, we use the modified $(\frac{w}{g})$- expansion method to find the traveling wave solutions for some nonlinear partial differential equations in mathematical physics namely the Zakharov – Kuznetsov – BBM (ZKBBM) equation and the Boussinesq equation . When $w$ and $g$ are taken some special choices, some families of direct expansion methods are obtained. we further give three forms of expansions methods via the modified $(\frac{g^{\prime}}{g^{n}})$-expansion method, modified $g^{\prime}$ -expansion method and modified $(\frac{w}{g})$- expansion function method when $w$ and $g$ satisfy decoupled differential equations $ w^{\prime}=\mu \,g $, $g^{\prime}=\lambda \,w$ , where $\,\mu\,$and$\,\lambda\,$ are arbitrary constants. When the parameters are taken some special values the solitary wave is derived from the traveling waves. This method is reliable, simple, and gives many new exact solutions.