On the Continuous Limit of Integrable Lattices II. Volterra Systems and SP(N) Theories

DOI10.1142/S0129055X98000070zbMath0921.35155OpenAlexW2024718285MaRDI QIDQ4221347

Carlo Morosi, Livio Pizzocchero

Publication date: 26 July 1999

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

Full work available at URL: https://doi.org/10.1142/s0129055x98000070

zbMATH Keywords

Hamiltonian structureLax operatorsimple Lie algebraLax formulationgeneralized \(N\)-fields Volterra latticezero-spacing limit

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Lattice dynamics; integrable lattice equations (37K60)

Related Items (5)

A KIND OF NEW CONTINUOUS LIMITS OF AN INTEGRABLE COUPLING SYSTEM FOR DISCRETE AKNS HIERARCHY ⋮ An integrable coupling system of lattice hierarchy and its continuous limits ⋮ The relation between the Toda hierarchy and the KdV hierarchy ⋮ Continuous limits for an integrable coupling system of Toda equation hierarchy ⋮ Continuous Correspondence of Conservation Laws of the Semi-discrete AKNS System

Cites Work

• Nonlinear Poisson structures and r-matrices
• Lie algebras and equations of Korteweg-de Vries type
• The initial value problem for the sequence of generalized Korteweg-de Vries equations
• On the continuous limit of integrable lattices. I: The Kac-Moerbeke system and KdV theory
• Korteweg-de Vries and nonlinear equations related to the Toda lattice
• R-matrices and higher Poisson brackets for integrable systems
• The nonabelian Toda lattice: Discrete analogue of the matrix Schrödinger spectral problem
• A novel hierarchy of integrable lattices
• Multiple Hamiltonian structures for Toda-type systems
• Continuous limits for the Kac-Van Moerbeke hierarchy and for their restricted flows
• ON THE BIHAMILTONIAN INTERPRETATION OF THE LAX FORMALISM
• R-matrix theory, formal Casimirs and the periodic Toda lattice

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