Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 218216, 11 pages
http://dx.doi.org/10.1155/2011/218216
Research Article

The ( 𝐺 ′ / 𝐺 ) -Expansion Method for Abundant Traveling Wave Solutions of Caudrey-Dodd-Gibbon Equation

Hasibun Naher, Farah Aini Abdullah, and M. Ali Akbar

School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia

Received 24 June 2011; Accepted 22 September 2011

Academic Editor: Kue-Hong Chen

Copyright © 2011 Hasibun Naher 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

We construct the traveling wave solutions of the fifth-order Caudrey-Dodd-Gibbon (CDG) equation by the ( 𝐺 / 𝐺 ) -expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, the trigonometric, and the rational functions. It is shown that the ( 𝐺 / 𝐺 ) -expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations.