A Quasi-Lie Schemes Approach to Second-Order Gambier Equations
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
A Quasi-Lie Schemes Approach to Second-Order Gambier Equations
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| Creator |
Cariñena, J.F.
Guha, P. de Lucas, J. |
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| Description |
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.
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| Date |
2019-02-19T19:03:08Z
2019-02-19T19:03:08Z 2013 |
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| Type |
Article
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| Identifier |
A Quasi-Lie Schemes Approach to Second-Order Gambier Equations / J.F. Cariñena, P. Guha, L. de Lucas // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 56 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 34A26; 34A05; 34A34; 17B66; 53Z05 DOI: http://dx.doi.org/10.3842/SIGMA.2013.026 http://dspace.nbuv.gov.ua/handle/123456789/149230 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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