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arXiv · 1102.1299

Superposition rules and second-order differential equations

J. F. Cariñena·J. de Lucas
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Abstract

The main purpose of this work is to introduce and analyse some generalizations of diverse superposition rules for first-order differential equations to the setting of second-order differential equations. As a result, we find a way to apply the theories of Lie and quasi-Lie systems to analyse second-order differential equations. In order to illustrate our results, several second-order differential equations appearing in the physics and mathematical literature are analysed and some superposition rules for these equations are derived by means of our methods.

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J. F. Cariñena, J. de Lucas. 2011-07-14. Superposition rules and second-order differential equations. https://doi.org/10.1063/1.3599137

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