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

Modified(w⁄g)- Expansion Method

  • Abdel Rahman Shehata Minia University
  • Safaa Abu-Amra Omar Al-Mukhtar University
Keywords: Modified $(\frac{g^{\prime}}{g^{n}})$-expansion method, Modified $g^{\prime}$ -expansion method, Modified $(\frac{w}{g})$- expansion function method, Traveling Wave solutions, The Zakharov – Kuznetsov – BBM (ZKBBM) equation, The Boussinesq equation

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.

Author Biographies

Abdel Rahman Shehata, Minia University

Department of Mathematics, Faculty of Science, Minia University, Minia, Egypt

Safaa Abu-Amra, Omar Al-Mukhtar University

Department of Mathematics, Faculty of Science, Omar Al-Mukhtar University, Al-Bayda, Libya

Published
2018-12-01
How to Cite
Shehata, A. R., & Abu-Amra, S. (2018). Traveling Wave Solutions for Some Nonlinear Partial Differential Equations by Using Modified(w⁄g)- Expansion Method. European Journal of Mathematical Sciences, 4(2), 35-58. Retrieved from http://ejmathsci.org/index.php/ejmathsci/article/view/242
Section
Articles