Nonlocal Symmetries, Telescopic Vector Fields and λ-Symmetries of Ordinary Differential Equations
This paper studies relationships between the order reductions of ordinary differential equations derived by the existence of λ-symmetries, telescopic vector fields and some nonlocal symmetries obtained by embedding the equation in an auxiliary system. The results let us connect such nonlocal symmetr...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2012 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2012
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/149189 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Nonlocal Symmetries, Telescopic Vector Fields and λ-Symmetries of Ordinary Differential Equations / C. Muriel, J.L. Romero // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 46 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862593164937789440 |
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| author | Muriel, C. Romero, J.L. |
| author_facet | Muriel, C. Romero, J.L. |
| citation_txt | Nonlocal Symmetries, Telescopic Vector Fields and λ-Symmetries of Ordinary Differential Equations / C. Muriel, J.L. Romero // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 46 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This paper studies relationships between the order reductions of ordinary differential equations derived by the existence of λ-symmetries, telescopic vector fields and some nonlocal symmetries obtained by embedding the equation in an auxiliary system. The results let us connect such nonlocal symmetries with approaches that had been previously introduced: the exponential vector fields and the λ-coverings method. The λ-symmetry approach let us characterize the nonlocal symmetries that are useful to reduce the order and provides an alternative method of computation that involves less unknowns. The notion of equivalent λ-symmetries is used to decide whether or not reductions associated to two nonlocal symmetries are strictly different.
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| first_indexed | 2025-11-27T09:33:04Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-149189 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-27T09:33:04Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Muriel, C. Romero, J.L. 2019-02-19T18:24:29Z 2019-02-19T18:24:29Z 2012 Nonlocal Symmetries, Telescopic Vector Fields and λ-Symmetries of Ordinary Differential Equations / C. Muriel, J.L. Romero // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 46 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 34A05; 34A34 DOI: http://dx.doi.org/10.3842/SIGMA.2012.106 https://nasplib.isofts.kiev.ua/handle/123456789/149189 This paper studies relationships between the order reductions of ordinary differential equations derived by the existence of λ-symmetries, telescopic vector fields and some nonlocal symmetries obtained by embedding the equation in an auxiliary system. The results let us connect such nonlocal symmetries with approaches that had been previously introduced: the exponential vector fields and the λ-coverings method. The λ-symmetry approach let us characterize the nonlocal symmetries that are useful to reduce the order and provides an alternative method of computation that involves less unknowns. The notion of equivalent λ-symmetries is used to decide whether or not reductions associated to two nonlocal symmetries are strictly different. This paper is a contribution to the Special Issue “Symmetries of Dif ferential Equations: Frames, Invariants and Applications”. The full collection is available at http://www.emis.de/journals/SIGMA/SDE2012.html.
 The authors would like to thank the anonymous referees for their useful comments and suggestions to improve the paper. The support of DGICYT project MTM2009-11875 and Junta de Andaluc´ıa group FQM-201 are gratefully acknowledged. C. Muriel also acknowledges the partial support from the University of C´adiz to participate in the conference “Symmetries of Dif ferential Equations: Frames, Invariants and Applications” in honor of the 60th birthday of Peter Olver. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Nonlocal Symmetries, Telescopic Vector Fields and λ-Symmetries of Ordinary Differential Equations Article published earlier |
| spellingShingle | Nonlocal Symmetries, Telescopic Vector Fields and λ-Symmetries of Ordinary Differential Equations Muriel, C. Romero, J.L. |
| title | Nonlocal Symmetries, Telescopic Vector Fields and λ-Symmetries of Ordinary Differential Equations |
| title_full | Nonlocal Symmetries, Telescopic Vector Fields and λ-Symmetries of Ordinary Differential Equations |
| title_fullStr | Nonlocal Symmetries, Telescopic Vector Fields and λ-Symmetries of Ordinary Differential Equations |
| title_full_unstemmed | Nonlocal Symmetries, Telescopic Vector Fields and λ-Symmetries of Ordinary Differential Equations |
| title_short | Nonlocal Symmetries, Telescopic Vector Fields and λ-Symmetries of Ordinary Differential Equations |
| title_sort | nonlocal symmetries, telescopic vector fields and λ-symmetries of ordinary differential equations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149189 |
| work_keys_str_mv | AT murielc nonlocalsymmetriestelescopicvectorfieldsandλsymmetriesofordinarydifferentialequations AT romerojl nonlocalsymmetriestelescopicvectorfieldsandλsymmetriesofordinarydifferentialequations |