Integrability of the $C_n$ and $B{C}_n$ Ruijsenaars-Schneider models

Abstract

We study the $C_n$ and $B{C}_n$ 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.

20 pages, LaTeX2e, no figures

References in corpus (4)

• Generalised Calogero-Moser models and universal Lax pair operators
• Elliptic Ruijsenaars-Schneider and Calogero-Moser Models Represented by Sklyanin Algebra and sl(n) Gaudin Algebra
• Diagonalization of the elliptic Macdonald-Ruijsenaars difference system of type C_2
• Theta Functions Associated with the Affine Root Systems and the Elliptic Ruijsenaars Operators

Cited by in corpus (10)

• Quantum vs Classical Integrability in Ruijsenaars-Schneider Systems
• On factorized Lax pairs for classical many-body integrable systems
• Eigenvalues of Ruijsenaars-Schneider models associated with $A_{n-1}$ root system in Bethe ansatz formalism
• Scattering theory of the hyperbolic BC(n) Sutherland and the rational BC(n) Ruijsenaars--Schneider--van Diejen models
• The Dn Ruijsenaars-Schneider model
• On the scattering theory of the classical hyperbolic C(n) Sutherland model
• The Lax pairs for elliptic C_n and BC_n Ruijsenaars-Schneider models and their spectral curves
• Structures in BC_N Ruijsenaars-Schneider models
• On the classical r-matrix structure of the rational BC(n) Ruijsenaars-Schneider-van Diejen system
• On the Integrability of Classical Ruijsenaars-Schneider Model of $B{C}_2$ Type