Integrable deformations of the Bogoyavlenskij–Itoh Lotka–Volterra systems

C.A. Evripidou; P. Kassotakis; P. Vanhaecke

doi:10.1134/S1560354717060090

Integrable deformations of the Bogoyavlenskij–Itoh Lotka–Volterra systems

Authors: Evripidou C.¹, Kassotakis P.¹, Vanhaecke P.²
Affiliations:
1. Department of Mathematics and Statistics
2. Laboratoire de Mathématiques et Applications
Issue: Vol 22, No 6 (2017)
Pages: 721-739
Section: Article
URL: https://ogarev-online.ru/1560-3547/article/view/218788
DOI: https://doi.org/10.1134/S1560354717060090
ID: 218788

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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.