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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 630282, 5 pages
Research Article

Nonlinearly Self-Adjoint, Conservation Laws and Solutions for a Forced BBM Equation

1Departamento de Matemáticas, Universidad de Cádiz, P.O. Box 40, Puerto Real, 11510 Cádiz, Spain
2International 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 31 January 2014; Accepted 2 March 2014; Published 3 April 2014

Academic Editor: Mariano Torrisi

Copyright © 2014 Maria Luz Gandarias 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.


We study a forced Benjamin-Bona-Mahony (BBM) equation. We prove that the equation is not weak self-adjoint; however, it is nonlinearly self-adjoint. By using a general theorem on conservation laws due to Nail Ibragimov and the symmetry generators, we find conservation laws for these partial differential equations without classical Lagrangians. We also present some exact solutions for a special case of the equation.