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Advances in Mathematical Physics
Volume 2014 (2014), Article ID 672679, 8 pages
http://dx.doi.org/10.1155/2014/672679
Research Article

Symmetries, Traveling Wave Solutions, and Conservation Laws of a -Dimensional Boussinesq Equation

International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa

Received 5 April 2014; Accepted 15 June 2014; Published 2 July 2014

Academic Editor: Xiao-Yan Gu

Copyright © 2014 Letlhogonolo Daddy Moleleki and Chaudry Masood Khalique. 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 analyze the -dimensional Boussinesq equation, which has applications in fluid mechanics. We find exact solutions of the -dimensional Boussinesq equation by utilizing the Lie symmetry method along with the simplest equation method. The solutions obtained are traveling wave solutions. Moreover, we construct the conservation laws of the -dimensional Boussinesq equation using the new conservation theorem, which is due to Ibragimov.