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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 169694, 5 pages
http://dx.doi.org/10.1155/2014/169694
Research Article

Conservation Laws for a Variable Coefficient Variant Boussinesq System

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

Received 21 November 2013; Accepted 6 January 2014; Published 12 February 2014

Academic Editor: Hossein Jafari

Copyright © 2014 Ben Muatjetjeja 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 construct the conservation laws for a variable coefficient variant Boussinesq system, which is a third-order system of two partial differential equations. This system does not have a Lagrangian and so we transform it to a system of fourth-order, which admits a Lagrangian. Noether’s approach is then utilized to obtain the conservation laws. Lastly, the conservation laws are presented in terms of the original variables. Infinite numbers of both local and nonlocal conserved quantities are derived for the underlying system.