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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 548975, 8 pages
http://dx.doi.org/10.1155/2013/548975
Research Article

Solutions and Conservation Laws of a (2+1)-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 6 July 2013; Accepted 19 August 2013

Academic Editor: Maria Gandarias

Copyright © 2013 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 study a nonlinear evolution partial differential equation, namely, the (2+1)-dimensional Boussinesq equation. For the first time Lie symmetry method together with simplest equation method is used to find the exact solutions of the (2+1)-dimensional Boussinesq equation. Furthermore, the new conservation theorem due to Ibragimov will be utilized to construct the conservation laws of the (2+1)-dimensional Boussinesq equation.