Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations

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Campoamor-Stursberg, Rutwig (2016) Low Dimensional Vessiot-Guldberg-Lie Algebras of Second-Order Ordinary Differential Equations. Symmetry, 8 (3). p. 15. ISSN 2073-8994

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Official URL: https://doi.org/10.3390/sym8030015




Abstract

A direct approach to non-linear second-order ordinary differential equations admitting a superposition principle is developed by means of Vessiot-Guldberg-Lie algebras of a dimension not exceeding three. This procedure allows us to describe generic types of second-order ordinary differential equations subjected to some constraints and admitting a given Lie algebra as Vessiot-Guldberg-Lie algebra. In particular, well-known types, such as the Milne-Pinney or Kummer-Schwarz equations, are recovered as special cases of this classification. The analogous problem for systems of second-order differential equations in the real plane is considered for a special case that enlarges the generalized Ermakov systems.


Item Type:Article
Uncontrolled Keywords:Lie systems; Vessiot-Guldberg-Lie algebra; superposition rule; SODE Lie systems
Subjects:Sciences > Mathematics > Algebra
Sciences > Mathematics > Differential equations
ID Code:63198
Deposited On:30 Nov 2020 16:21
Last Modified:30 Nov 2020 16:21

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