Abstract and Applied Analysis
Volume 2013 (2013), Article ID 791863, 5 pages
http://dx.doi.org/10.1155/2013/791863
Research Article

Exact Solutions and Conservation Laws of a (2+1)-Dimensional Nonlinear KP-BBM Equation

Khadijo Rashid Adem and Chaudry Masood Khalique

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 23 January 2013; Accepted 25 March 2013

Academic Editor: Shi Weichen

Copyright © 2013 Khadijo Rashid Adem 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

In this paper, we study the two-dimensional nonlinear Kadomtsov-Petviashivilli-Benjamin-Bona-Mahony (KP-BBM) equation. This equation is the Benjamin-Bona-Mahony equation formulated in the KP sense. We first obtain exact solutions of this equation using the Lie group analysis and the simplest equation method. The solutions obtained are solitary waves. In addition, the conservation laws for the KP-BBM equation are constructed by using the multiplier method.