Lotka–Volterra systems satisfying a strong Painlevé property

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dc.contributor.authorBountis, Tassos
dc.contributor.authorVanhaecke, Pol
dc.creatorTassos, Bountis
dc.date.accessioned2017-12-26T10:12:55Z
dc.date.available2017-12-26T10:12:55Z
dc.date.issued2016-12-09
dc.description.abstractAbstract We use a strong version of the Painlevé property to discover and characterize a new class of n-dimensional Hamiltonian Lotka–Volterra systems, which turn out to be Liouville integrable as well as superintegrable. These systems are in fact Nambu systems, they posses Lax equations and they can be explicitly integrated in terms of elementary functions. We apply our analysis to systems containing only quadratic nonlinearities of the form aijxixj,i≠j, and require that all variables diverge as t−1. We also require that the leading terms depend on n−2 free parameters. We thus discover a cocycle relation among the coefficients aij of the equations of motion and by integrating the cocycle equations we show that they are equivalent to the above strong version of the Painlevé property. We also show that these systems remain explicitly solvable even if a linear term bixi is added to the i-th equation, even though this violates the Painlevé property, as logarithmic singularities are introduced in the Laurent solutions, at the first terms following the leading order pole.en_US
dc.identifierDOI:10.1016/j.physleta.2016.09.034
dc.identifier.citationTassos Bountis, Pol Vanhaecke, Lotka–Volterra systems satisfying a strong Painlevé property, In Physics Letters A, Volume 380, Issue 47, 2016, Pages 3977-3982en_US
dc.identifier.issn03759601
dc.identifier.urihttps://www.sciencedirect.com/science/article/pii/S0375960116309963
dc.identifier.urihttp://nur.nu.edu.kz/handle/123456789/3070
dc.language.isoenen_US
dc.publisherPhysics Letters Aen_US
dc.relation.ispartofPhysics Letters A
dc.rights.license© 2016 Elsevier B.V. All rights reserved.
dc.subjectIntegrable Lotka Volterra systemsen_US
dc.subjectStrong Painlevé propertyen_US
dc.titleLotka–Volterra systems satisfying a strong Painlevé propertyen_US
dc.typeArticleen_US
elsevier.aggregationtypeJournal
elsevier.coverdate2016-12-09
elsevier.coverdisplaydate9 December 2016
elsevier.endingpage3982
elsevier.identifier.doi10.1016/j.physleta.2016.09.034
elsevier.identifier.eid1-s2.0-S0375960116309963
elsevier.identifier.piiS0375-9601(16)30996-3
elsevier.identifier.scopusid84992518950
elsevier.issue.identifier47
elsevier.openaccess0
elsevier.openaccessarticlefalse
elsevier.openarchivearticlefalse
elsevier.startingpage3977
elsevier.teaserWe use a strong version of the Painlevé property to discover and characterize a new class of n-dimensional Hamiltonian Lotka–Volterra systems, which turn out to be Liouville integrable as well as superintegrable....
elsevier.volume380
workflow.import.sourcescience

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