%0 Journal Article
%T On the discrete group analysis for the exact solutions of some classes of the nonlinear Abel and Burgers equations
%J Khayyam Journal of Mathematics
%I 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)
%Z 2423-4788
%A Darania, Parviz
%D 2021
%\ 07/01/2021
%V 7
%N 2
%P 257-265
%! On the discrete group analysis for the exact solutions of some classes of the nonlinear Abel and Burgers equations
%K Discrete group method
%K Abel equations
%K Burgers equations
%K Hopf-Cole transformation
%R 10.22034/kjm.2021.224570.1751
%X This article presents an account of the fundamentals of the discretegroup approach for analysis and integration of practicaldifferential equations. In this paper, by means of appropriatetransformations, the nonlinear Burgers equation is transformed intothe other class of the second-order differential equation of theEmden-Fowler type and this Emden-Fowler equation reduces to thenonlinear Abel equations. This approach shows that, under thistransformations of discrete group, the solution of referenceequation can be transformed into the solution of the transformedequation. Under such a conditions, we approach to the determine somesolutions for the Abel, Burgers, Emden-Fowler and heat equations.
%U http://www.kjm-math.org/article_130841_f5850a8d48e351b2b4da5292cbdc65f7.pdf