Bi-Hamiltonian structure of the \(qd\) algorithm and new discretizations of the Toda lattice

DOI10.1016/0375-9601(95)00647-LzbMath1020.35531OpenAlexW1994931211MaRDI QIDQ1965711

Yuri Borisovich Suris

Publication date: 8 February 2000

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0375-9601(95)00647-l

Mathematics Subject Classification ID

Related Items (13)

INTEGRABLE DISCRETIZATIONS FOR LATTICE SYSTEM: LOCAL EQUATIONS OF MOTION AND THEIR HAMILTONIAN PROPERTIES ⋮ Integrable discretizations of the Bogoyavlensky lattices ⋮ Composite integrators for bi-Hamiltonian systems ⋮ The quadratic-form identity for constructing the Hamiltonian structures of the discrete integrable systems ⋮ Reduction groups and related integrable difference systems of nonlinear Schrödinger type ⋮ Some integrable maps and their Hirota bilinear forms ⋮ On an integrable discretization of the modified Korteweg-de Vries equation. ⋮ Integrable discretizations of the spin Ruijsenaars–Schneider models ⋮ Discrete time Toda systems ⋮ Integrable seven-point discrete equations and second-order evolution chains ⋮ Legendre transforms on a triangular lattice ⋮ On the Structure of the Bäcklund Transformations for the Relativistic Lattices ⋮ On a discrete analogue of the two-dimensional Toda lattice hierarchy

Cites Work

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• Integrable symplectic maps
• A new integrable case of the motion of the 4-dimensional rigid body
• Orthogonal polynomial approach to discrete Lax pairs for initial boundary-value problems of the QD algorithm
• Integrable time-discretization of the Ruijsenaars-Schneider model
• A discrete-time Garnier system
• Dynamical \(r\)-matrices for integrable maps
• Nonlinear Partial Difference Equations. IV. Bäcklund Transformation for the Discrete-Time Toda Equation
• The Bidiagonal Singular Value Decomposition and Hamiltonian Mechanics
• Loop groups, discrete versions of some classical integrable systems, and rank 2 extensions

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