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

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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