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The Scientific World Journal
Volume 2014, Article ID 724759, 6 pages
http://dx.doi.org/10.1155/2014/724759
Research Article

Water Wave Solutions of the Coupled System Zakharov-Kuznetsov and Generalized Coupled KdV Equations

1Mathematics Department, Faculty of Science, Taibah University, Al-Ula 41921-259, Saudi Arabia
2Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt
3Mathematics Department, College of Arts and Science, Taif University, Ranyah, Saudi Arabia

Received 19 July 2014; Revised 8 September 2014; Accepted 9 September 2014; Published 12 October 2014

Academic Editor: Praveen Agarwal

Copyright © 2014 A. R. Seadawy and K. El-Rashidy. 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

An analytic study was conducted on coupled partial differential equations. We formally derived new solitary wave solutions of generalized coupled system of Zakharov-Kuznetsov (ZK) and KdV equations by using modified extended tanh method. The traveling wave solutions for each generalized coupled system of ZK and KdV equations are shown in form of periodic, dark, and bright solitary wave solutions. The structures of the obtained solutions are distinct and stable.