A quasi-Lie schemes approach to second-order Gambier equations

Cariñena Marzo, José Fernando; Guha ,P.; Lucas Araujo, Javier De

doi:10.3842/SIGMA.2013.026

A quasi-Lie schemes approach to second-order Gambier equations

Cariñena Marzo, José Fernando (Universidad de Zaragoza) ; Guha ,P. ; Lucas Araujo, Javier De

Resumen: 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.
Idioma: Inglés
DOI: 10.3842/SIGMA.2013.026
Año: 2013
Publicado en: Symmetry Integrability and Geometry-Methods and Applications 9, 26 (2013), [23 pp]
ISSN: 1815-0659
Factor impacto JCR: 1.299 (2013)
Categ. JCR: PHYSICS, MATHEMATICAL rank: 25 / 55 = 0.455 (2013) - Q2 - T2
Financiación: info:eu-repo/grantAgreement/ES/DGA/E24-1
Financiación: info:eu-repo/grantAgreement/ES/DGA/FMI40-10
Financiación: info:eu-repo/grantAgreement/ES/MICINN/MTM2009-11154
Tipo y forma: Article (Published version)
Área (Departamento): Física Teórica (Departamento de Física Teórica)
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A quasi-Lie schemes approach to second-order Gambier equations