Classical r-matrix structure for elliptic Ruijsenaars chain and 1+1 field analogue of Ruijsenaars-Schneider model

2025/08/18 by Murinov, D., Zotov, A. · 1 citation
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2508.12656

Abstract

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.

Citations

• Classical integrable spin chains of Landau-Lifshitz type from R-matrix identities
• Integrable deformations of principal chiral model from solutions of associative Yang-Baxter equation
• On the field analogue of elliptic spin Calogero-Moser model: Lax pair and equations of motion
• Induced dynamics
• Elliptic Families of Solutions of the Kadomtsev-Petviashvili Equation and the Field Elliptic Calogero-Moser System
• Elliptic analog of the Toda lattice

Cited by

• Elliptic Ruijsenaars-Toda and elliptic Toda chains: classical r-matrix structure and relation to XYZ chain

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