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ISRN Mathematical Physics
Volume 2013 (2013), Article ID 146704, 5 pages
http://dx.doi.org/10.1155/2013/146704
Research Article

The Modified Simple Equation Method for Exact and Solitary Wave Solutions of Nonlinear Evolution Equation: The GZK-BBM Equation and Right-Handed Noncommutative Burgers Equations

1Department of Mathematics, Pabna Science and Technology University, Pabna 6600, Bangladesh
2Department of Applied Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh
3School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Pulau Pinang, Malaysia

Received 25 November 2012; Accepted 10 January 2013

Academic Editors: A. Herrera-Aguilar, W.-H. Steeb, and H. Zhou

Copyright © 2013 Kamruzzaman Khan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The modified simple equation method is significant for finding the exact traveling wave solutions of nonlinear evolution equations (NLEEs) in mathematical physics. In this paper, we bring in the modified simple equation (MSE) method for solving NLEEs via the Generalized Zakharov-Kuznetsov-Benjamin-Bona-Mahony (GZK-BBM) equation and the right-handed noncommutative Burgers' (nc-Burgers) equations and achieve the exact solutions involving parameters. When the parameters are taken as special values, the solitary wave solutions are originated from the traveling wave solutions. It is established that the MSE method offers a further influential mathematical tool for constructing the exact solutions of NLEEs in mathematical physics.