Volume 4, Issue 4
Lie Group Classification for a Generalised Coupled Lane-Emden System in Dimension One

East Asian J. Appl. Math., 4 (2014), pp. 301-311.

Published online: 2018-02

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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

Lie group classification, generalised Lane-Emden system, principal Lie algebra, equivalence transformations, Lie point symmetries, Noether integrals.

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@Article{EAJAM-4-301, author = {}, title = {Lie Group Classification for a Generalised Coupled Lane-Emden System in Dimension One}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {4}, number = {4}, pages = {301--311}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.080214.230814a}, url = {http://global-sci.org/intro/article_detail/eajam/10838.html} }
TY - JOUR T1 - Lie Group Classification for a Generalised Coupled Lane-Emden System in Dimension One JO - East Asian Journal on Applied Mathematics VL - 4 SP - 301 EP - 311 PY - 2018 DA - 2018/02 SN - 4 DO - http://doi.org/10.4208/eajam.080214.230814a UR - https://global-sci.org/intro/article_detail/eajam/10838.html KW - Lie group classification, generalised Lane-Emden system, principal Lie algebra, equivalence transformations, Lie point symmetries, Noether integrals. AB -

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.

Ben Muatjetjeja & Chaudry Masood Khalique. (1970). Lie Group Classification for a Generalised Coupled Lane-Emden System in Dimension One. East Asian Journal on Applied Mathematics. 4 (4). 301-311. doi:10.4208/eajam.080214.230814a
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