Superposition rules and second-order differential equations
Mathematical Physics
2015-05-27 v2 math.MP
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.
Cite
@article{arxiv.1102.1299,
title = {Superposition rules and second-order differential equations},
author = {J. F. Cariñena and J. de Lucas},
journal= {arXiv preprint arXiv:1102.1299},
year = {2015}
}
Comments
6 pages. Corrected typos