Lotka–Volterra systems satisfying a strong Painlevé property

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dc.contributor.authorBountis, Tassos
dc.contributor.authorVanhaecke, Pol
dc.date.accessioned2018-08-23T09:29:51Z
dc.date.available2018-08-23T09:29:51Z
dc.date.issued2016-09
dc.description.abstractWe 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 −2free parameters. We thus discover a cocycle relation among the coefficients aijof 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 bixiis 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.identifier.citationTassos Bountisa, Pol Vanhaecke. 2016. Lotka–Volterra systems satisfying a strong Painlevé property. Physics Letters Aen_US
dc.identifier.urihttp://nur.nu.edu.kz/handle/123456789/3397
dc.language.isoenen_US
dc.publisherPhysics Letters Aen_US
dc.rightsAttribution-NonCommercial-ShareAlike 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/us/*
dc.subjectIntegrable Lotka Volterra systemsen_US
dc.subjectStrong Painlevé propertyen_US
dc.titleLotka–Volterra systems satisfying a strong Painlevé propertyen_US
dc.typeArticleen_US
workflow.import.sourcescience

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