Variations for Some Painlevé Equations

dc.creatorAcosta-Humañez, Primitivo B.
dc.creatorVan Der Put, Marius
dc.creatorTop, Jaap
dc.date.accessioned2019-11-12T20:08:30Z
dc.date.accessioned2022-11-14T19:38:00Z
dc.date.available2019-11-12T20:08:30Z
dc.date.available2022-11-14T19:38:00Z
dc.date.created2019-11-12T20:08:30Z
dc.date.issued2019
dc.identifier18150659
dc.identifierhttps://hdl.handle.net/20.500.12442/4330
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/5180440
dc.description.abstractThis paper rst discusses irreducibility of a Painlev e equation P. We explain how the Painlev e property is helpful for the computation of special classical and algebraic solutions. As in a paper of Morales-Ruiz we associate an autonomous Hamiltonian H to a Painlev e equation P. Complete integrability of H is shown to imply that all solutions to P are classical (which includes algebraic), so in particular P is solvable by \quadratures". Next, we show that the variational equation of P at a given algebraic solution coincides with the normal variational equation of H at the corresponding solution. Finally, we test the Morales-Ramis theorem in all cases P2 to P5 where algebraic solutions are present, by showing how our results lead to a quick computation of the component of the identity of the di erential Galois group for the rst two variational equations. As expected there are no cases where this group is commutative.
dc.publisherSIGMA
dc.rightshttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rightsinfo:eu-repo/semantics/closedAccess
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 Internacional
dc.sourceSymmetry, Integrability and Geometry: Methods and Applications
dc.sourceVol. 15, (2019)
dc.sourcehttps://www.emis.de/journals/SIGMA/2019/088/sigma19-088.pdf
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dc.subjectHamiltonian systems
dc.subjectVariational equations
dc.subjectPainlevé equations
dc.subjectdifferential Galois groups
dc.titleVariations for Some Painlevé Equations
dc.typearticle


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