A Quasi-Lie Schemes Approach to Second-Order Gambier Equations
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...
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| Datum: | 2013 |
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| Sprache: | English |
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Інститут математики НАН України
2013
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| Schriftenreihe: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/149230 |
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| Zitieren: | 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. |
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irk-123456789-1492302019-02-20T01:23:13Z A Quasi-Lie Schemes Approach to Second-Order Gambier Equations Cariñena, J.F. Guha, P. de Lucas, J. 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. 2013 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Cariñena, J.F. Guha, P. de Lucas, J. |
| spellingShingle |
Cariñena, J.F. Guha, P. de Lucas, J. A Quasi-Lie Schemes Approach to Second-Order Gambier Equations Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Cariñena, J.F. Guha, P. de Lucas, J. |
| author_sort |
Cariñena, J.F. |
| title |
A Quasi-Lie Schemes Approach to Second-Order Gambier Equations |
| title_short |
A Quasi-Lie Schemes Approach to Second-Order Gambier Equations |
| title_full |
A Quasi-Lie Schemes Approach to Second-Order Gambier Equations |
| title_fullStr |
A Quasi-Lie Schemes Approach to Second-Order Gambier Equations |
| title_full_unstemmed |
A Quasi-Lie Schemes Approach to Second-Order Gambier Equations |
| title_sort |
quasi-lie schemes approach to second-order gambier equations |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149230 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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