Geometric discretisation of the Toda system.
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Publication:1968453
DOI10.1016/S0375-9601(97)00477-5zbMath1044.37527arXivsolv-int/9612006OpenAlexW3103658216WikidataQ104434216 ScholiaQ104434216MaRDI QIDQ1968453
Publication date: 7 March 2000
Published in: Physics Letters. A (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/solv-int/9612006
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Discrete version of topics in analysis (39A12)
Related Items (26)
INTEGRABLE DISCRETIZATIONS FOR LATTICE SYSTEM: LOCAL EQUATIONS OF MOTION AND THEIR HAMILTONIAN PROPERTIES ⋮ Discrete Toda lattices and the Laplace method ⋮ Darboux transformations for 5-point and 7-point self-adjoint schemes and an integrable discretization of the 2D Schrödinger operator ⋮ Geometric discretization of the Koenigs nets ⋮ Pentagram maps and refactorization in Poisson-Lie groups ⋮ Integrability and geometry of the Wynn recurrence ⋮ Hermite-Padé approximation and integrability ⋮ Integral preserving discretization of 2D Toda lattices ⋮ Discrete Laplace cycles of period four ⋮ Vector-relation configurations and plabic graphs ⋮ The affine Weyl group symmetry of Desargues maps and of the non-commutative Hirota-Miwa system ⋮ The integrable discrete analogues of orthogonal coordinate systems are multi-dimensional circular lattices ⋮ Multidimensional quadrilateral lattices are integrable. ⋮ Integrable lattices and their sublattices. II. From the B-quadrilateral lattice to the self-adjoint schemes on the triangular and the honeycomb lattices ⋮ Asymptotic Lattices and W-Congruences in Integrable Discrete Geometry ⋮ Transformations of quadrilateral lattices ⋮ Characteristic algebras and integrable exponential systems ⋮ The Darboux-type transformations of integrable lattices. ⋮ The pentagon relation and incidence geometry ⋮ The C-(symmetric) quadrilateral lattice, its transformations and the algebro-geometric construction ⋮ Geometric discretization of the Bianchi system ⋮ Discrete asymptotic nets and \(W\)-congruences in Plücker line geometry ⋮ Affine Spheres: Discretization via Duality Relations ⋮ An extension of the Hirota bilinear difference equation ⋮ Quadratic reductions of quadrilateral lattices ⋮ The symmetric, \(d\)-invariant and Egorov reductions of the quadrilateral lattice
Cites Work
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- Holomorphic curves and Toda systems
- Theory of nonlinear lattices
- Discrete Toda field equations
- Nonlinear Partial Difference Equations. II. Discrete-Time Toda Equation
- Nonlinear Partial Difference Equations III; Discrete Sine-Gordon Equation
- Integrable three-dimensional lattices
- Lectures on the Inverse Scattering Transform
- Harmonic maps and periodic Toda systems
- Integrable dynamics of a discrete curve and the Ablowitz–Ladik hierarchy
- Discrete isothermic surfaces.
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