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arXiv · 2602.08143

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

D. Murinov·A. Zotov
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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 $r$-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.

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D. Murinov, A. Zotov. 2026-02-08. Elliptic Ruijsenaars-Toda and elliptic Toda chains: classical r-matrix structure and relation to XYZ chain. https://doi.org/10.1016/j.geomphys.2026.105848

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