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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| Дата: | 2012 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2012
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149189 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1491892019-02-20T01:24:35Z Nonlocal Symmetries, Telescopic Vector Fields and λ-Symmetries of Ordinary Differential Equations Muriel, C. Romero, J.L. 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. 2012 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149189 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 |
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. |
| format |
Article |
| author |
Muriel, C. Romero, J.L. |
| spellingShingle |
Muriel, C. Romero, J.L. Nonlocal Symmetries, Telescopic Vector Fields and λ-Symmetries of Ordinary Differential Equations Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Muriel, C. Romero, J.L. |
| author_sort |
Muriel, C. |
| title |
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_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_sort |
nonlocal symmetries, telescopic vector fields and λ-symmetries of ordinary differential equations |
| publisher |
Інститут математики НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149189 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT murielc nonlocalsymmetriestelescopicvectorfieldsandlsymmetriesofordinarydifferentialequations AT romerojl nonlocalsymmetriestelescopicvectorfieldsandlsymmetriesofordinarydifferentialequations |
| first_indexed |
2023-05-20T17:31:41Z |
| last_indexed |
2023-05-20T17:31:41Z |
| _version_ |
1796153493094924288 |