Journal of Applied Mathematics
Volume 2012 (2012), Article ID 405978, 10 pages
http://dx.doi.org/10.1155/2012/405978
Research Article

Lie Group Classification of a Generalized Lane-Emden Type System in Two Dimensions

Motlatsi Molati1,2 and Chaudry Masood Khalique1

1International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, South Africa
2Department of Mathematics and Computer Science, National University of Lesotho, Roma 180, Lesotho

Received 18 September 2012; Accepted 13 October 2012

Academic Editor: Fazal M. Mahomed

Copyright © 2012 Motlatsi Molati 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

The aim of this work is to perform a complete Lie symmetry classification of a generalized Lane-Emden type system in two dimensions which models many physical phenomena in biological and physical sciences. The classical approach of group classification is employed for classification. We show that several cases arise in classifying the arbitrary parameters, the forms of which include amongst others the power law nonlinearity, and exponential and quadratic forms.