Ermakov's Superintegrable Toy and Nonlocal Symmetries

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dc.creatorLeach, P. G. L.
dc.creatorKarasu, A.
dc.creatorNucci, M. C.
dc.creatorAndriopoulos, K.
dc.date2005-11-25
dc.date.accessioned2026-07-07T09:34:37Z
dc.date.available2026-07-07T09:34:37Z
dc.descriptionWe investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2,R). The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.
dc.descriptionPublished in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/
dc.identifierhttps://arxiv.org/abs/nlin/0511055
dc.identifierhttp://arxiv.org/abs/nlin/0511055
dc.identifierSIGMA 1 (2005), 018, 15 pages
dc.identifierdoi:10.3842/SIGMA.2005.018
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159556
dc.subjectExactly Solvable and Integrable Systems
dc.subjectMathematical Physics
dc.titleErmakov's Superintegrable Toy and Nonlocal Symmetries
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