On the discrete group analysis for the exact solutions of some classes of the nonlinear Abel and Burgers equations

Abstract

This article presents an account of the fundamentals of the discrete group approach for analysis and integration of practical differential equations. In this paper, by means of appropriate transformations, the nonlinear Burgers equation is transformed into the other class of the second-order differential equation of the Emden-Fowler type and this Emden-Fowler equation reduces to the nonlinear Abel equations. This approach shows that, under this transformations of discrete group, the solution of reference equation can be transformed into the solution of the transformed equation. Under such a conditions, we approach to the determine some solutions for the Abel, Burgers, Emden-Fowler and heat equations.