Invariance of second order ordinary differential equations under two-dimensional affine subalgebras of EP Lie algebra

Abstract

Using the only admissible rank-two realisations of the Lie algebra of the affine group in one dimension in terms of the Lie algebra of Lie symmetries of the Ermakov-Pinney (EP) equation, some classes of second order nonlinear ordinary differential equations solvable by reduction method are constructed. One class includes the standard EP equation as a special case. A new EP equation with a perturbed potential but admitting the same solution formula as EP itself arises. The solution of the dissipative EP equation is also discussed.

References in corpus (3)

• Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities
• Recent Applications of the Theory of Lie Systems in Ermakov Systems
• Coefficient characterization of linear differential equations with maximal symmetries