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Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 871724, 17 pages
http://dx.doi.org/10.1155/2012/871724
Research Article

Some New Traveling Wave Solutions of the Nonlinear Reaction Diffusion Equation by Using the Improved (𝐺/𝐺)-Expansion Method

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

Received 5 December 2011; Revised 23 February 2012; Accepted 24 February 2012

Academic Editor: Jun-Juh Yan

Copyright © 2012 Hasibun Naher and Farah Aini Abdullah. 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 new exact traveling wave solutions involving free parameters of the nonlinear reaction diffusion equation by using the improved (𝐺/𝐺)-expansion method. The second-order linear ordinary differential equation with constant coefficients is used in this method. The obtained solutions are presented by the hyperbolic and the trigonometric functions. The solutions become in special functional form when the parameters take particular values. It is important to reveal that our solutions are in good agreement with the existing results.