A Quasi-Lie Schemes Approach to Second-Order Gambier Equations
Autor: | José F. Cariñena, Partha Guha, Javier de Lucas |
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Jazyk: | angličtina |
Rok vydání: | 2013 |
Předmět: | |
Zdroj: | Symmetry, Integrability and Geometry: Methods and Applications, Vol 9, p 026 (2013) |
Druh dokumentu: | article |
ISSN: | 1815-0659 |
DOI: | 10.3842/SIGMA.2013.026 |
Popis: | A quasi-Lie scheme is a geometric structure that provides t-dependent changes of variables transforming members of an associated family of systems of first-order differential equations into members of the same family. In this note we introduce two quasi-Lie schemes for studying second-order Gambier equations in a geometric way. This allows us to study the transformation of these equations into simpler canonical forms, which solves a gap in the previous literature, and other relevant differential equations, which leads to derive new constants of motion for families of second-order Gambier equations. Additionally, we describe general solutions of certain second-order Gambier equations in terms of particular solutions of Riccati equations, linear systems, and t-dependent frequency harmonic oscillators. |
Databáze: | Directory of Open Access Journals |
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