Group Classification of a Generalized Lane-Emden System

where n is a real constant andf(y) is a real-valued function of the variabley, hasmany applications inmathematical physics and astrophysics. Equation (1), for certain fixed values of n and f(y), models several phenomena such as the theory of stellar structure, the thermal behavior of a spherical cloud of gas, isothermal gaseous sphere, and the theory of thermionic currents [1–3]. Several methods for the solution and many applications of the Lane-Emden Equation (1) can be found in the literature. The interested reader is referred to [4] and the references therein. It is worth mentioning that Wong [5], in his review paper of 1975, presented more than 140 references on this topic. A natural extension of (1), called the generalized LaneEmden system [6], is given by