Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 459879, 22 pages
http://dx.doi.org/10.1155/2012/459879
Research Article

A Generalized and Improved ( 𝐺 ′ / 𝐺 ) -Expansion Method for Nonlinear Evolution Equations

M. Ali Akbar,1,2 Norhashidah Hj. Mohd. Ali,1 and E. M. E. Zayed3

1School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia
2Department of Applied Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh
3Mathematics Department, Faculty of Science, Zagazig University, Zagazig 44519, Egypt

Received 22 September 2011; Revised 14 December 2011; Accepted 20 December 2011

Academic Editor: Jaromir Horacek

Copyright © 2012 M. Ali Akbar 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

A generalized and improved ( 𝐺 / 𝐺 ) -expansion method is proposed for finding more general type and new travelling wave solutions of nonlinear evolution equations. To illustrate the novelty and advantage of the proposed method, we solve the KdV equation, the Zakharov-Kuznetsov-Benjamin-Bona-Mahony (ZKBBM) equation and the strain wave equation in microstructured solids. Abundant exact travelling wave solutions of these equations are obtained, which include the soliton, the hyperbolic function, the trigonometric function, and the rational functions. Also it is shown that the proposed method is efficient for solving nonlinear evolution equations in mathematical physics and in engineering.