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.