Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 424801, 11 pages
http://dx.doi.org/10.1155/2011/424801
Research Article

Hyperbolic, Trigonometric, and Rational Function Solutions of Hirota-Ramani Equation via ( 𝐺 ′ / 𝐺 ) -Expansion Method

Reza Abazari1 and Rasoul Abazari2

1Young Researchers Club, Ardabil Branch, Islamic Azad University, P.O. Box 56169-54184, Ardabil, Iran
2Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran

Received 13 November 2010; Accepted 22 February 2011

Academic Editor: Peter Wolenski

Copyright © 2011 Reza Abazari and Rasoul Abazari. 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 ( 𝐺 / 𝐺 ) -expansion method is proposed to construct the exact traveling solutions to Hirota-Ramani equation: 𝑢 𝑡 − 𝑢 𝑥 𝑥 𝑡 + 𝑎 𝑢 𝑥 ( 1 − 𝑢 𝑡 ) = 0 , where 𝑎 ≠ 0 . Our work is motivated by the fact that the ( 𝐺 / 𝐺 ) -expansion method provides not only more general forms of solutions but also periodic and solitary waves. If we set the parameters in the obtained wider set of solutions as special values, then some previously known solutions can be recovered. The method appears to be easier and faster by means of a symbolic computation system.