Complete symmetry group for the generalized convection-reaction-diffusion equation

Abstract

In this paper, we perform a detailed group classification for a generalized convection-reaction-diffusion equation with three unknown functions. Specifically, we determine all the functional forms for the unknown functions where the given equation admits nontrivial Lie point symmetries. The classification problem provides us with eight families of equations summarized in four categories. The admitted Lie symmetries form the four Lie algebras [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. For the four families of the classification problem we calculate the one-dimensional optimal system and we derive all the similarity transformations which reduce the partial differential equation into an ordinary differential equation. Applications of the similarity transformations are presented while exact solutions are derived.