48 research outputs found
Cheng Equation: A Revisit Through Symmetry Analysis
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.Comment: 10 pages. Accepted for publication in Quaestiones Mathematicae
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Algebraic Structures of Generalised Symmetries of n th-order Scalar Ordinary Differential Equations of Maximal Lie Point Symmetry
We compute for the representative scalar ordinary differential equation of maximal point symmetry the generalised symmetries of order-one and two. We examine the Lie Brackets for the generalised symmetries and see that closure does not occur for generalised symmetries of order-two. Consequently all generalised symmetries up to the maximum order possible must be admitted