Integrability of the $C_{n}$ and $BC_{n}$ Ruijsenaars-Schneider models

preprint2000arXivOpen access

We study the $C_{n}$ and $BC_{n}$ Ruijsenaars-Schneider(RS) models with interaction potential of trigonometric and rational types. The Lax pairs for these models are constructed and the involutive Hamiltonians are also given. Taking nonrelativistic limit, we also obtain the Lax pairs for the corresponding Calogero-Moser systems.

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Integrability of the $C_{n}$ and $BC_{n}$ Ruijsenaars-Schneider models

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Integrability of the CnC_{n}Cn​ and BCnBC_{n}BCn​ Ruijsenaars-Schneider models

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Integrability of the $C_{n}$ and $BC_{n}$ Ruijsenaars-Schneider models