IJPAM: Volume 106, No. 4 (2016)

ANALYTIC SOLUTIONS FOR NONLINEAR EVOLUTION
EQUATIONS IN MATHEMATICAL PHYSICS

Khaled A. Gepreel$^{1,2}$, Taher A. Nofal$^{1,3}$
$^1$Department of Mathematics
Faculty of Science
Taif University
KINGDOM SAUDI ARABIA
$^2$Department of Mathematics
Faculty of Science
City Zagazig University
Zagazig, EGYPT
$^3$Department of Mathematics
Faculty of Science
El-Minia University
EGYPT


Abstract. In this article, we use the modified ($w/g$)- expansionmethod to find the traveling wave solutions for some nonlinear partial differential equations in mathematical physicsvia the nonlinear variant Boussinesq differential equations.When $w$ and $g$ are taken special choices, some families of direct expansion methods are obtained to obtain the exact solutions for the nonlinear evolutions equations in the mathematical physics. Based on these interesting results, we further give two forms of expansions via the modified $g'/g^{2} $- expansion method and modified $g'$- expansion methods. When the parameters are taken some special values, the solitary wave are derived from the traveling waves.This method is reliable, simple, and gives many new exact solutions.

Received: October 29, 2015

AMS Subject Classification: 35K99, 35P05, 35P99

Key Words and Phrases: the modified ($w/g$)-expansion method, traveling wave solutions, the nonlinear variant Boussinesq differential equations

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DOI: 10.12732/ijpam.v106i4.3 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 106
Issue: 4
Pages: 1003 - 1016


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CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).