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&lrm; P.O.Box 165&lrm; &lrm;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 - http://www.kjm-math.org/article_130841.html
L1 - http://www.kjm-math.org/article_130841_f5850a8d48e351b2b4da5292cbdc65f7.pdf
ER -