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arXiv · 1712.00286

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

José F. Cariñena·Faruk Güngör·Pedro J. Torres
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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.

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José F. Cariñena, Faruk Güngör, Pedro J. Torres. 2017-12-01. Invariance of second order ordinary differential equations under two-dimensional affine subalgebras of EP Lie algebra. https://arxiv.org/abs/1712.00286

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