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ISRN Mathematical Physics
Volume 2012 (2012), Article ID 837241, 9 pages
http://dx.doi.org/10.5402/2012/837241
Research Article

Symmetry Reduction, Exact Solutions, and Conservation Laws of the ZK-BBM Equation

1Taizhou Institute of Science and Technology, (NUST), Taizhou, Jiangsu 225300, China
2Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013, China
3Department of Mathematics, National Institute of Technology, Jamshedpur, Jharkhand 831014, India

Received 22 April 2012; Accepted 4 July 2012

Academic Editors: A. Aghamohammadi and S. del Campo

Copyright © 2012 Wenbin Zhang 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

Employing the classical Lie method, we obtain the symmetries of the ZK-BBM equation. Applying the given Lie symmetry, we obtain the similarity reduction, group invariant solution, and new exact solutions. We also obtain the conservation laws of ZK-BBM equation of the corresponding Lie symmetry.