Elliptic Ruijsenaars-Toda and elliptic Toda chains: classical r-matrix structure and relation to XYZ chain
Exactly Solvable and Integrable Systems
2026-04-23 v3 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
We discuss the classical elliptic Toda chain introduced by Krichever and the elliptic Ruijsenaars-Toda chain introduced by Adler, Shabat and Suris. It is shown that these models can be obtained as particular cases of the elliptic Ruijsenaars chain. We explain how the classical -matrix structures are derived for these chains. Also, as a by-product, we prove that the elliptic Ruijsenaars-Toda chain is gauge equivalent to discrete Landau-Lifshitz model of XYZ type. The elliptic Toda chain is also gauge equivalent to XYZ chain with special values of the Casimir functions at each site.
Cite
@article{arxiv.2602.08143,
title = {Elliptic Ruijsenaars-Toda and elliptic Toda chains: classical r-matrix structure and relation to XYZ chain},
author = {D. Murinov and A. Zotov},
journal= {arXiv preprint arXiv:2602.08143},
year = {2026}
}
Comments
29 pages, minor changes, details added to Section 5