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Regul. Chaotic Dyn., 2017, Volume 22, Issue 6, Pages 721–739 (Mi rcd285)  

This article is cited in 1 scientific paper (total in 1 paper)

Integrable Deformations of the Bogoyavlenskij–Itoh Lotka–Volterra Systems

C.A. Evripidoua, P. Kassotakisb, P. Vanhaeckec

a Department of Mathematics and Statistics, La Trobe University, Melbourne, Victoria 3086, Australia
b Department of Mathematics and Statistics, University of Cyprus, Nicosia 1678, Cyprus
c Laboratoire de Mathématiques et Applications, UMR 7348 du CNRS, Université de Poitiers, 86962 Futuroscope Chasseneuil Cedex, France

Abstract: We construct a family of integrable deformations of the Bogoyavlenskij–Itoh systems and construct a Lax operator with spectral parameter for it. Our approach is based on the construction of a family of compatible Poisson structures for the undeformed systems, whose Casimirs are shown to yield a generating function for the integrals in involution of the deformed systems.We show how these deformations are related to the Veselov–Shabat systems.

Keywords: Integrable systems, deformations

Funding Agency Grant Number
Australian Research Council
The work of C.A.Evripidou was partially supported by a postdoctoral fellowship of the University of Cyprus and by the Australian Research Council.


DOI: https://doi.org/10.1134/S1560354717060090

References: PDF file   HTML file

Bibliographic databases:

MSC: 37J35, 39A22
Received: 19.09.2017
Accepted:01.11.2017
Language:

Citation: C.A. Evripidou, P. Kassotakis, P. Vanhaecke, “Integrable Deformations of the Bogoyavlenskij–Itoh Lotka–Volterra Systems”, Regul. Chaotic Dyn., 22:6 (2017), 721–739

Citation in format AMSBIB
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\by C.A. Evripidou, P. Kassotakis, P. Vanhaecke
\paper Integrable Deformations of the Bogoyavlenskij–Itoh Lotka–Volterra Systems
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 6
\pages 721--739
\mathnet{http://mi.mathnet.ru/rcd285}
\crossref{https://doi.org/10.1134/S1560354717060090}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3736470}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. P. H. van der Kamp, Ch. A. Evripidou, Ch. Zhang, “Dressing the Dressing Chain”, SIGMA, 14 (2018), 059, 14 pp.  mathnet  crossref
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