\({\mathcal R}\)-matrix approach to multi-Hamiltonian Lax dynamics

DOI10.1016/S0034-4877(97)85891-0zbMath0899.35108MaRDI QIDQ1387111

Maciej Błaszak

Publication date: 2 June 1998

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Lie algebraLie-Poisson bracketlattice systemsLax equationsLax representationspseudodifferential Lax operatorsfield systems

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 (5)

New hierarchies of integrable lattice equations and associated properties: Darboux transformation, conservation laws and integrable coupling ⋮ A Few Integrable Dynamical Systems, Recurrence Operators, Expanding Integrable Models and Hamiltonian Structures by the r -Matrix Method ⋮ Lie algebraic approach to the construction of (2+1)-dimensional lattice-field and field integrable Hamiltonian equations ⋮ COMPATIBLE POISSON STRUCTURES OF TODA TYPE DISCRETE HIERARCHY ⋮ Central extension approach to integrable field and lattice-field systems in \((2+1)\)-dimensions

Cites Work

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• A note on the Poisson brackets associated with Lax operators
• The Hamiltonian structure of the (2+1)-dimensional Ablowitz–Kaup–Newell–Segur hierarchy
• Bi-Hamiltonian formulation of the Kadomtsev–Petviashvili and Benjamin–Ono equations
• Hamiltonian theory over noncommutative rings and integrability in multidimensions
• R-matrix approach to lattice integrable systems
• Dressing transformations and Poisson group actions

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