Integrable time-discretization of the Ruijsenaars-Schneider model
From MaRDI portal
Publication:1918080
DOI10.1007/BF02099255zbMath0851.58025arXivhep-th/9412170OpenAlexW3102702853MaRDI QIDQ1918080
Orlando Ragnisco, Frank W. Nijhoff, Vadim B. Kuznetsov
Publication date: 24 November 1996
Published in: Communications in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/hep-th/9412170
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Continuum limits in quantum field theory (81T27) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)
Related Items
Integrable discretizations of the Bogoyavlensky lattices ⋮ On different integrable systems sharing the same nondynamical r-matrix ⋮ On a technique to identify solvable discrete-time many-body problems ⋮ Quantum Bäcklund transformations: some ideas and examples ⋮ On integrability of the deformed Ruijsenaars-Schneider system ⋮ The Lagrangian structure of Calogero's goldfish model ⋮ Matrix Kadomtsev-Petviashvili hierarchy and spin generalization of trigonometric Calogero-Moser hierarchy ⋮ Monodromy free linear equations and many-body systems ⋮ Self-dual form of Ruijsenaars-Schneider models and ILW equation with discrete Laplacian ⋮ Ermakov-Pinney and Emden-Fowler equations: new solutions from novel Bäcklund transformations ⋮ Time discretization of the spin Calogero-Moser model and the semi-discrete matrix KP hierarchy ⋮ Bi-Hamiltonian structure of the \(qd\) algorithm and new discretizations of the Toda lattice ⋮ The nondynamical \(r\)-matrix for the Ruijsenaars-Schneider model and the classical Sklyanin algebra. ⋮ Elliptic (N, N′)-soliton solutions of the lattice Kadomtsev-Petviashvili equation ⋮ Algebraic Linearization of Hyperbolic RuijsenaarsSchneider Systems ⋮ Integrable discretizations of the spin Ruijsenaars–Schneider models ⋮ The dynamical twisting and nondynamical r-matrix structure of the elliptic Ruijsenaars–Schneider model ⋮ Ising correlations and elliptic determinants ⋮ L-A-B representation for nonlinear evolution equations and its applications ⋮ Hilbert space theory for reflectionless relativistic potentials ⋮ Integrable and solvable many-body problems in the plane via complexification ⋮ Equations of motion and conserved quantities in non-abelian discrete integrable models ⋮ Hirota equation and Bethe ansatz ⋮ Integrable lattices ⋮ A gauge equivalent pair with two different \(r\)-matrices ⋮ Elliptic solutions to integrable nonlinear equations and many-body systems ⋮ Field analogue of the Ruijsenaars-Schneider model ⋮ A super-integrable discretization of the Calogero model ⋮ New solvable discrete-time many-body problem featuring several arbitrary parameters ⋮ Kernel functions and Bäcklund transformations for relativistic Calogero-Moser and Toda systems ⋮ Bäcklund transformations for finite-dimensional integrable systems: a geometric approach. ⋮ Toda lattice hierarchy and trigonometric Ruijsenaars–Schneider hierarchy
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Integrable symplectic maps
- Some algebraic structures connected with the Yang-Baxter equation
- A new class of integrable systems and its relation to solitons
- The Lax representation for an integrable class of relativistic dynamical systems
- Action-angle maps and scattering theory for some finite-dimensional integrable systems. I: The pure soliton case
- Poisson structure of a periodic classical XYZ-chain
- Complete integrability of relativistic Calogero-Moser systems and elliptic function identities
- Growth and integrability in the dynamics of mappings
- Three integrable Hamiltonian systems connected with isospectral deformations
- Rational solutions of the Kadomtsev-Petviashvili equation and integrable systems of \(n\) particles on a line
- Integration of quantum many-body problems by affine Knizhnik- Zamolodchikov equations
- Gaudin model, Bethe ansatz and critical level
- A time-discretized version of the Calogero-Moser model
- ALGEBRAIC ASPECTS OF THE BETHE ANSATZ
- The analogue of the Backlund transformation for integrable many-body systems
- Integrable maps
- Generalized Bethe ansatz with the general spin representations of the Sklyanin algebra
- The lattice Gel'fand-Dikii hierarchy
- Rational and elliptic solutions of the korteweg-de vries equation and a related many-body problem
- Integrability of difference Calogero–Moser systems
- Boundary conditions for integrable quantum systems
