Lie group classification for a generalised coupld lane–emden system in dimension one

Abstract

n 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.