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

Cariñena, José F.

Symmetry, integrability and geometry, methods and applications, 2013-01, Vol.9, p.026 [Periódico revisado por pares]

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Título:
A Quasi-Lie Schemes Approach to Second-Order Gambier Equations
Autor: Cariñena, José F.
Assuntos: Kummer-Schwarz equation ; Lie system ; Milne-Pinney equation ; quasi-Lie scheme ; quasi-Lie system ; second-order Gambier equation ; second-order Riccati equation ; superposition rule
É parte de: Symmetry, integrability and geometry, methods and applications, 2013-01, Vol.9, p.026
Descrição: 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. [ProQuest: [...] denotes formulae omitted.]
Editor: Kiev: National Academy of Sciences of Ukraine
Idioma: Inglês

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