Nonlocal Symmetries, Telescopic Vector Fields and λ-Symmetries of Ordinary Differential Equations

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Фізико-технічні та математичні науки
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2012, том 8
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dc.contributor.author	Muriel, C.
dc.contributor.author	Romero, J.L.
dc.date.accessioned	2019-02-19T18:24:29Z
dc.date.available	2019-02-19T18:24:29Z
dc.date.issued	2012
dc.identifier.citation	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.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 34A05; 34A34
dc.identifier.other	DOI: http://dx.doi.org/10.3842/SIGMA.2012.106
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/149189
dc.description.abstract	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.	uk_UA
dc.description.sponsorship	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.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Nonlocal Symmetries, Telescopic Vector Fields and λ-Symmetries of Ordinary Differential Equations	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA