Superposition rules and second-order differential equations

Details Superposition rules and second-order differential equations Superposition rules and second-order differential equations

2011-02-07

arxiv.org/abs/1102.1299v2

In the book: "XIX International Fall Workshop on Geometry and Physics", eds. C. Herdeiro and R. Picken, AIP Conference Proceed

Physics

Mathematical Physics

6 pages. Corrected typos

Scientific paper

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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