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Regul. Chaotic Dyn., 2008, Volume 13, Issue 6, Pages 543–556 (Mi rcd600)  

This article is cited in 3 scientific papers (total in 3 papers)

JÜRGEN MOSER – 80

Integrable Lotka–Volterra systems

O.I. Bogoyavlenskijab

a V. A. Steklov Institute of Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
b Department of Mathematics, Queen’s University, Kingston, K7L 3N6, Canada

Abstract: Infinite- and finite-dimensional lattices of Lotka–Volterra type are derived that possess Lax representations and have large families of first integrals. The obtained systems are Hamiltonian and contain perturbations of Volterra lattice. Examples of Liouville-integrable 4-dimensional Hamiltonian Lotka-Volterra systems are presented. Several 5-dimensional Lotka–Volterra systems are found that have Lax representations and are Liouville-integrable on constant levels of Casimir functions.

Keywords: Lax representation, Hamiltonian structures, Casimir functions, Riemannian surfaces, Lotka–Volterra systems, integrable lattices

DOI: https://doi.org/10.1134/S1560354708060051


Bibliographic databases:

MSC: 58F05
Received: 06.09.2008
Accepted:28.10.2008
Language:

Citation: O.I. Bogoyavlenskij, “Integrable Lotka–Volterra systems”, Regul. Chaotic Dyn., 13:6 (2008), 543–556

Citation in format AMSBIB
\Bibitem{Bog08}
\by O.I. Bogoyavlenskij
\paper Integrable Lotka–Volterra systems
\jour Regul. Chaotic Dyn.
\yr 2008
\vol 13
\issue 6
\pages 543--556
\mathnet{http://mi.mathnet.ru/rcd600}
\crossref{https://doi.org/10.1134/S1560354708060051}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2465723}
\zmath{https://zbmath.org/?q=an:1229.37097}


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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. Pantelis A. Damianou, Hervé Sabourin, Pol Vanhaecke, “Intermediate Toda Systems”, Regul. Chaotic Dyn., 20:3 (2015), 277–292  mathnet  crossref  mathscinet  zmath  adsnasa
    2. C.A. Evripidou, P. Kassotakis, P. Vanhaecke, “Integrable Deformations of the Bogoyavlenskij–Itoh Lotka–Volterra Systems”, Regul. Chaotic Dyn., 22:6 (2017), 721–739  mathnet  crossref  mathscinet
    3. Charalampos A. Evripidou, Peter H. van der Kamp, Cheng Zhang, “Dressing the Dressing Chain”, SIGMA, 14 (2018), 059, 14 pp.  mathnet  crossref
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