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arXiv · 1709.06763

Integrable deformations of the Bogoyavlenskij-Itoh Lotka-Volterra systems

Charalampos Evripidou·Pavlos Kassotakis·Pol Vanhaecke
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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 system, 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.

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Charalampos Evripidou, Pavlos Kassotakis, Pol Vanhaecke. 2017-09-20. Integrable deformations of the Bogoyavlenskij-Itoh Lotka-Volterra systems. https://doi.org/10.1134/s1560354717060090

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