Group Classification of a Generalized Lane-Emden System

Abstract

We perform the group classification of the generalized Lane-Emden system ${xu}^{\mathrm{\prime }\mathrm{\prime }}+n{u}^{\mathrm{\prime }}+xH\left(v\right)=0,x{v}^{\mathrm{\prime }\mathrm{\prime }}+n{v}^{\mathrm{\prime }}+xg\left(u\right)=0$, which occurs in many applications of physical phenomena such as pattern formation, population evolution, and chemical reactions. We obtain four cases depending on the values of n.