Research Article

Cheng equation: a revisit through symmetry analysis

Published in: Quaestiones Mathematicae
Volume 43, issue 7, 2020 , pages: 857–867
DOI: 10.2989/16073606.2019.1584593
Author(s): Amlan K. Halder, India, P.G.L. Leach, South Africa, A. Paliathanasis, Republic of South Africa, R. Sinuvasan, India

Abstract

The symmetry analysis of the Cheng equation is performed. The Cheng equation is reduced to a first-order equation of either Abel’s equations, the analytic solution of which is given in terms of special functions. Moreover, for a particular symmetry the system is reduced to the Riccati equation or to the linear nonhomogeneous equation of Euler type. Henceforth, the general solution of the Cheng equation with the use of the Lie theory is discussed, as also the application of Lie symmetries in a generalized Cheng equation.

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