Analysis reveals Liouville integrability in the elliptic Ruijsenaars chain, indicating a new non-ultralocal structure for the Calogero-Moser model.
The classical dynamical r-matrix structure for the periodic elliptic Ruijsenaars chain is described. The Poisson brackets for the monodromy matrix are calculated as well, thus providing Liouville integrability of the model. Next, we study its continuous non-relativistic limit and reproduce the Maillet type non-ultralocal r-matrix structure for the field analogue of the elliptic Calogero-Moser model.
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Murinov et al. (2025) studied this question.
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