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On the Integrability of Classical Ruijsenaars-Schneider Model of $BC_{2}$ Type

V. I. Inozemtsev·R. Sasaki
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Abstract

The problem of finding most general form of the classical integrable relativistic models of many-body interaction of the $BC_{n}$ type is considered. In the simplest nontrivial case of $n=2$,the extra integral of motion is presented in explicit form within the ansatz similar to the nonrelativistic Calogero-Moser models. The resulting Hamiltonian has been found by solving the set of two functional equations.

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V. I. Inozemtsev, R. Sasaki. 2001-08-22. On the Integrability of Classical Ruijsenaars-Schneider Model of $BC_{2}$ Type. https://doi.org/10.1142/s0217732301005382

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