A Quasi-Lie Schemes Approach to Second-Order Gambier Equations

Autor: José F. Cariñena, Partha Guha, Javier de Lucas
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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