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Elliptic Ruijsenaars-Toda and elliptic Toda chains: classical r -matrix structure and relation to XYZ chain
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We discuss the classical elliptic Toda chain introduced by Krichever and the elliptic RuijsenaarsToda 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.
Title: Elliptic Ruijsenaars-Toda and elliptic Toda chains: classical r -matrix structure and relation to XYZ chain
Description:
We discuss the classical elliptic Toda chain introduced by Krichever and the elliptic RuijsenaarsToda 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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