R-matrix theory, formal Casimirs and the periodic Toda lattice

DOI10.1063/1.531639zbMath0863.58038OpenAlexW2093411332MaRDI QIDQ5284871

Livio Pizzocchero, Carlo Morosi

Publication date: 3 June 1997

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

Full work available at URL: https://doi.org/10.1063/1.531639

zbMATH Keywords

periodic Toda lattice\(r\)-matrix theorybiHamiltoniantriHamiltonian schemes

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) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (12)

INTEGRABLE DISCRETIZATIONS FOR LATTICE SYSTEM: LOCAL EQUATIONS OF MOTION AND THEIR HAMILTONIAN PROPERTIES ⋮ A trihamiltonian extension of the Toda lattice ⋮ Lattice Geometry of the Discrete Darboux, KP, BKP and CKP Equations. Menelaus' and Carnot's Theorems ⋮ Poisson quasi-Nijenhuis deformations of the canonical PN structure ⋮ Bihamiltonian Geometry and Separation of Variables for Toda Lattices ⋮ Compatible Lie algebroids and the periodic Toda lattice ⋮ Poisson quasi-Nijenhuis manifolds and the Toda system ⋮ TRI–HAMILTONIAN VECTOR FIELDS, SPECTRAL CURVES AND SEPARATION COORDINATES ⋮ Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations ⋮ Singularities of bi-Hamiltonian systems ⋮ On the Continuous Limit of Integrable Lattices II. Volterra Systems and SP(N) Theories ⋮ The negative Toda hierarchy and rational Poisson brackets

Cites Work

• What is a classical r-matrix?
• Nonlinear Poisson structures and r-matrices
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Some algebraic structures connected with the Yang-Baxter equation
• Lie algebras and equations of Korteweg-de Vries type
• Reduction of Poisson manifolds
• Reduction techniques for infinite-dimensional Hamiltonian systems: some ideas and applications
• The solution to a generalized Toda lattice and representation theory
• Completely integrable systems, Euclidean Lie algebras, and curves
• Systems of Toda type, inverse spectral problems, and representation theory
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• R-matrices and higher Poisson brackets for integrable systems
• A simple model of the integrable Hamiltonian equation
• R-matrix approach to lattice integrable systems
• Multiple Hamiltonian structures for Toda-type systems
• Integrals of the Toda lattice
• The Toda lattice. II. Existence of integrals
• Integrability condition and finite-periodic Toda lattice

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