TY - JOUR ID - 130841 TI - On the discrete group analysis for the exact solutions of some classes of the nonlinear Abel and Burgers equations JO - Khayyam Journal of Mathematics JA - KJM LA - en SN - AU - Darania, Parviz AD - Department of Mathematics, Urmia university‎ P.O.Box 165‎ ‎Urmia-Iran Y1 - 2021 PY - 2021 VL - 7 IS - 2 SP - 257 EP - 265 KW - Discrete group method KW - Abel equations KW - Burgers equations KW - Hopf-Cole transformation DO - 10.22034/kjm.2021.224570.1751 N2 - 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. UR - https://www.kjm-math.org/article_130841.html L1 - https://www.kjm-math.org/article_130841_f5850a8d48e351b2b4da5292cbdc65f7.pdf ER -