Deformations of Calogero-Moser systems and finite Toda chains

DOI10.1007/BF01016137zbMath0851.58021arXivsolv-int/9310001OpenAlexW2151992938MaRDI QIDQ1918818

Jan Felipe van Diejen

Publication date: 1994

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9310001

zbMATH Keywords

complete integrabilityCalogero-Moser systemsToda chains

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)

Related Items

Trigonometric and elliptic Ruijsenaars-Schneider systems on the complex projective space, Duality between the trigonometricBC_nSutherland system and a completed rational Ruijsenaars–Schneider–van Diejen system, The full phase space of a model in the Calogero-Ruijsenaars family, Stable equilibria for the roots of the symmetric continuous Hahn and Wilson polynomials, Integrability of conformal blocks. I: Calogero-Sutherland scattering theory, Poisson-Lie interpretation of trigonometric Ruijsenaars duality, The action–angle dual of an integrable Hamiltonian system of Ruijsenaars–Schneider–van Diejen type, Scattering theory of the hyperbolic \(BC_n\) Sutherland and the rational \(BC_n\) Ruijsenaars-Schneider-Van Diejen models, The hyperbolic \(BC_n\) Sutherland and the rational \(BC_n\) Ruijsenaars-Schneider-Van Diejen models: Lax matrices and duality, Action-angle duality between the \(C_n\)-type hyperbolic Sutherland and the rational Ruijsenaars-Schneider-van Diejen models, Lax matrices for a 1-parameter subfamily of van Diejen-Toda chains, Global description of action-angle duality for a Poisson-Lie deformation of the trigonometric \(\mathrm {BC}_n\) Sutherland system, Self-duality and scattering map for the hyperbolic van Diejen systems with two coupling parameters (with an Appendix by S. Ruijsenaars), Equivalence of two sets of Hamiltonians associated with the rational \(\operatorname{BC}_n\) Ruijsenaars-Schneider-van Diejen system, Lax representation of the hyperbolic van Diejen dynamics with two coupling parameters, Integrable boundary interactions for Ruijsenaars' difference Toda chain, Commuting difference operators with polynomial eigenfunctions, On the classical \(r\)-matrix structure of the rational \(BC_n\) Ruijsenaars-Schneider-van Diejen system, Gradient system for the roots of the Askey-Wilson polynomial, On the r-matrix structure of the hyperbolic BC n Sutherland model, A new model in the Calogero-Ruijsenaars family, On a Poisson-Lie deformation of the \(\mathrm{BC}_{n}\) Sutherland system

Cites Work

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• Relativistic Toda systems
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