Superposition rules and second-order differential equations

DOI10.1063/1.3599137zbMATH Open1241.34043arXiv1102.1299OpenAlexW3100015050MaRDI QIDQ3105572

Publication date: 5 January 2012

Published in: AIP Conference Proceedings (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1102.1299

zbMATH Keywords

Riccati equations Lie systems superposition rules SODE Lie systems

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Explicit solutions, first integrals of ordinary differential equations (34A05)