Integrable discretizations of the spin Ruijsenaars-Schneider models

Abstract

Integrable discretizations are introduced for the rational and hyperbolic spin Ruijsenaars--Schneider models. These discrete dynamical systems are demonstrated to belong to the same integrable hierarchies as their continuous--time counterparts. Explicit solutions are obtained for arbitrary flows of the hierarchies, including the discrete time ones.

LaTeX file

References in corpus (11)

• Spin generalization of the Ruijsenaars-Schneider model, non-abelian 2D Toda chain and representations of Sklyanin algebra
• A discrete time relativistic Toda lattice
• The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems
• Peakons, R-Matrix and Toda-Lattice
• Dynamical r-matrix for the elliptic Ruijsenaars-Schneider system
• Discrete time Bogoyavlensky lattices
• Affine Toda Solitons and Systems of Calogero-Moser Type
• Elliptic Ruijsenaars-Schneider and Calogero-Moser hierarchies are governed by the same r-matrix
• Why are the rational and hyperbolic Ruijsenaars-Schneider hierarchies governed by the same R-operators as the Calogero-Moser ones?
• A discrete time peakons lattice
• The Classical $r$-Matrix for the Relativistic Ruijsenaars-Schneider System

Cited by in corpus (6)

• Poisson-Lie analogues of spin Sutherland models
• On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system
• On Hamiltonian structure of the spin Ruijsenaars-Schneider model
• Spin versions of the complex trigonometric Ruijsenaars-Schneider model from cyclic quivers
• Bäcklund Transformations as exact integrable time-discretizations for the trigonometric Gaudin model
• Time discretization of the spin Calogero-Moser model and the semi-discrete matrix KP hierarchy