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Lie Group Classification for a Generalised Coupled Lane-Emden System in Dimension One

Published online by Cambridge University Press:  16 July 2018

Ben Muatjetjeja  and
Chaudry Masood Khalique
Ben Muatjetjeja*
Affiliation:
International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, Republic of South Africa.
Chaudry Masood Khalique*
Affiliation:
International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University, Mafikeng Campus, Private Bag X 2046, Mmabatho 2735, Republic of South Africa.
*
* Corresponding author. Email address:Ben.Muatjetjeja@nwu.ac.za
Corresponding author. Email address:Masood.Khalique@nwu.ac.za
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Abstract

In this article, we discuss the generalised coupled Lane-Emden system u” + H(v) = 0, v” + G(u) = 0 that applies to several physical phenomena. The Lie group classification of the underlying system shows that it admits a ten-dimensional equivalence Lie algebra. We also show that the principal Lie algebra in one dimension has several possible extensions, and obtain an exact solution for an interesting particular case via Noether integrals.

Keywords

02.30.Jr02.30.Ik02.70.Wz05.45.Yv47.10.ab47.35.Fg52.35.SbLie group classificationgeneralised Lane-Emden systemprincipal Lie algebraequivalence transformationsLie point symmetriesNoether integrals

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Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 4 , Issue 4 , November 2014 , pp. 301 - 311
Copyright
Copyright © Global-Science Press 2014

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