C.A. Evripidou, P. Kassotakis, P. Vanhaecke, “Integrable Deformations of the Bogoyavlenskij–Itoh Lotka–Volterra Systems”, Regul. Chaotic Dyn., 2017, Volume 22, Issue 6,Pages <nobr>721

This article is cited in 11 papers

Integrable Deformations of the Bogoyavlenskij–Itoh Lotka–Volterra Systems

C.A. Evripidou^a, P. Kassotakis^b, P. Vanhaecke^c

^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.

MSC: 37J35, 39A22

Received: 19.09.2017
Accepted: 01.11.2017

Language: English

DOI: 10.1134/S1560354717060090