Integrable discretizations of the spin Ruijsenaars–Schneider models

DOI10.1063/1.532114zbMath0887.58025arXivsolv-int/9605001OpenAlexW2048014560MaRDI QIDQ4370767

Orlando Ragnisco, Yuri Borisovich Suris

Publication date: 6 January 1998

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9605001

zbMATH Keywords

integrable discretizationsspin Ruijsenaars-Schneider models

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Many-body theory; quantum Hall effect (81V70)

Related Items (6)

Poisson-Lie analogues of spin Sutherland models ⋮ Matrix Kadomtsev-Petviashvili hierarchy and spin generalization of trigonometric Calogero-Moser hierarchy ⋮ Time discretization of the spin Calogero-Moser model and the semi-discrete matrix KP hierarchy ⋮ Trigonometric real form of the spin RS model of Krichever and Zabrodin ⋮ On the Hamiltonian formulation of the trigonometric spin Ruijsenaars-Schneider system ⋮ Hilbert space theory for reflectionless relativistic potentials

Cites Work

• A generalisation of the Calogero-Moser system
• A new class of integrable systems and its relation to solitons
• Action-angle maps and scattering theory for some finite-dimensional integrable systems. I: The pure soliton case
• Integrable time-discretization of the Ruijsenaars-Schneider model
• The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems
• Exact Yangian symmetry in the classical Euler-Calogero-Moser model
• A time-discretized version of the Calogero-Moser model
• Bi-Hamiltonian structure of the \(qd\) algorithm and new discretizations of the Toda lattice
• The classical \(r\)-matrix for the relativistic Ruijsenaars-Schneider system.
• Why is the Ruijsenaars-Schneider hierarchy governed by the same \(R\)-operator as the Calogero-Moser one?
• Hamiltonian group actions and dynamical systems of calogero type
• A discrete-time relativistic Toda lattice
• Dynamicalr-matrix for the elliptic Ruijsenaars - Schneider system
• Integrable discretizations of the Bogoyavlensky lattices

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