Study of the Emden–Fowler differential equation by complete classification of symmetry groups and dynamical analysis

Abstract The Emden–Fowler equation is a fundamental model in various fields of physics. In this work, we generalize this equation and conduct a thorough investigation of its symmetries and dynamical properties. Our results include a complete classification of the symmetry group, the derivation of the Lagrangian and conservation laws, and the computation of invariant solutions. By combining global and local analysis, we provide a comprehensive understanding of the dynamics of the reduced equations.