Department of Pure Mathematics, Ferdowsi University of Mashhad (in cooperation with the Center of Excellence in Analysis on Algebraic Structures and Tusi Mathematical Research Group)Khayyam Journal of Mathematics2423-47887220210701On the discrete group analysis for the exact solutions of some classes of the nonlinear Abel and Burgers equations25726513084110.22034/kjm.2021.224570.1751ENParvizDaraniaDepartment of Mathematics, Urmia university&lrm; P.O.Box 165&lrm; &lrm;Urmia-Iran0000-0003-4996-6925Journal Article20200326This article presents an account of the fundamentals of the discrete<br />group approach for analysis and integration of practical<br />differential equations. In this paper, by means of appropriate<br />transformations, the nonlinear Burgers equation is transformed into<br />the other class of the second-order differential equation of the<br />Emden-Fowler type and this Emden-Fowler equation reduces to the<br />nonlinear Abel equations. This approach shows that, under this<br />transformations of discrete group, the solution of reference<br />equation can be transformed into the solution of the transformed<br />equation. Under such a conditions, we approach to the determine some<br />solutions for the Abel, Burgers, Emden-Fowler and heat equations.http://www.kjm-math.org/article_130841_f5850a8d48e351b2b4da5292cbdc65f7.pdf