Integrable extensions of classical elliptic integrable systems

TL;DR

This paper explores integrable extensions of classical elliptic integrable systems, specifically the elliptic Calogero-Moser model with spin and the Euler-Arnold top, adding degrees of freedom and describing them via Darboux variables.

Contribution

It introduces specific integrable extensions of well-known elliptic systems, expanding their degrees of freedom and providing a Darboux variable framework.

Findings

Extended elliptic Calogero-Moser model with spin

Extended Euler-Arnold top with additional degrees of freedom

Description of extended systems using Darboux variables

Abstract

In this article we consider two particular examples of general construction proposed in arXiv:2012.15529. We consider the integrable extensions of the classical elliptic Calogero-Moser model of N particles with spin and the integrable Euler-Arnold top related to the group SL(N,C). The extended systems has additional N-1 degrees of freedom and can be described in terms of the Darboux variables.