Recursion operator and bi-Hamiltonian structure for integrable multidimensional lattices

DOI10.1063/1.527907zbMath0656.70020OpenAlexW2032276040MaRDI QIDQ3804271

Orlando Ragnisco, Paolo Maria Santíni

Publication date: 1988

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

Full work available at URL: https://doi.org/10.1063/1.527907

zbMATH Keywords

recursion operatorbi-Hamiltonian structureToda chainintegrable two-dimensional versionnon-Abelian one-dimensional theories

Mathematics Subject Classification ID

Classical equilibrium statistical mechanics (general) (82B05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Hamiltonian and Lagrangian mechanics (70H99)

Related Items (3)

Cellular automata in \(1+1\), \(2+1\) and \(3+1\) dimensions, constants of motion and coherent structures ⋮ Two families of Liouville integrable lattice equations ⋮ Recursion operators and conservation laws for discrete Lax equations

Cites Work

• Reduction techniques for infinite-dimensional Hamiltonian systems: some ideas and applications
• The Hamiltonian structure of the nonabelian Toda hierarchy
• Evolution equations associated with the discrete analog of the matrix Schrödinger spectral problem solvable by the inverse spectral transform
• An example of ∂̄ problem arising in a finite difference context: Direct and inverse problem for the discrete analog of the equation ψx x+uψ=σψy
• The nonabelian Toda lattice: Discrete analogue of the matrix Schrödinger spectral problem
• Integrable three-dimensional lattices
• On the use of isospectral eigenvalue problems for obtaining hereditary symmetries for Hamiltonian systems
• The Recursion Operator of the Kadomtsev‐Petviashvili Equation and the Squared Eigenfunctions of the Schrödinger Operator

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