IJPAM: Volume 106, No. 4 (2016)
EQUATIONS IN MATHEMATICAL PHYSICS



Faculty of Science
Taif University
KINGDOM SAUDI ARABIA

Faculty of Science
City Zagazig University
Zagazig, EGYPT

Faculty of Science
El-Minia University
EGYPT
Abstract. In this article, we use the modified ()- expansionmethod to
find the traveling wave solutions for some nonlinear partial
differential equations in mathematical physicsvia the nonlinear
variant Boussinesq differential equations.When
and
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
- expansion method and modified
- 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 ()-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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This work is licensed under the Creative Commons Attribution International License (CC BY).