Group classification and exact solutions of a generalized Emden–Fowler equation

The aim of this work is to perform a complete symmetry classification of a generalized Emden-Fowler equation. The various forms of this equation are extensively studied in the literature and they have applications in astrophysical and physiological phenomena. The classical approach of group classification and the procedure based upon the Lie algebras of low dimension are employed for classification. Exact solutions of the invariant equations are derived.

► Complete group classification of a generalized Emden–Fowler equation is performed.
► Functional forms of the arbitrary parameters are specified through two approaches.
► These are the classical approach and the approach based upon low-dimensional Lie algebras.
► Exact solutions of the submodels are presented.