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

Document Type : Original Article


Department of Mathematics, Urmia university‎ P.O.Box 165‎ ‎Urmia-Iran



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.