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Journal of Applied Mathematics
Volume 2012, Article ID 438928, 20 pages
http://dx.doi.org/10.1155/2012/438928
Research Article

The Improved (𝐺/𝐺)-Expansion Method for the (2+1)-Dimensional Modified Zakharov-Kuznetsov Equation

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

Received 24 April 2012; Accepted 22 May 2012

Academic Editor: Shiping Lu

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 apply the improved (𝐺/𝐺)-expansion method for constructing abundant new exact traveling wave solutions of the (2+1)-dimensional Modified Zakharov-Kuznetsov equation. In addition, 𝐺+𝜆𝐺+𝜇𝐺=0 together with 𝑏(𝛼)=𝑤𝑞=𝑤𝑝𝑞(𝐺/𝐺)𝑞 is employed in this method, where 𝑝𝑞(𝑞=0,±1,±2,,±𝑤), 𝜆 and 𝜇 are constants. Moreover, the obtained solutions including solitons and periodic solutions are described by three different families. Also, it is noteworthy to mention out that, some of our solutions are coincided with already published results, if parameters taken particular values. Furthermore, the graphical presentations are demonstrated for some of newly obtained solutions.