Nonlocal quadratic Poisson algebras, monodromy map, and Bogoyavlensky lattices

DOI10.1063/1.532090zbMath0883.58015arXivsolv-int/9610001OpenAlexW3100127513MaRDI QIDQ4351642

Yuri Borisovich Suris

Publication date: 28 August 1997

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

Full work available at URL: https://arxiv.org/abs/solv-int/9610001

zbMATH Keywords

Lax representation\(r\)-matrixmonodromy mapBogoyavlensky latticenonlocal quadratic Poisson structure

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)

Related Items (6)

INTEGRABLE DISCRETIZATIONS FOR LATTICE SYSTEM: LOCAL EQUATIONS OF MOTION AND THEIR HAMILTONIAN PROPERTIES ⋮ Lax representations and integrable time discretizations of the DDKdV, DDmKdV, and DDHOKdV ⋮ On quadratic Poisson brackets ⋮ A new multi-component discrete integrable hierarchy and multi-component cubic Volterra integrable hierarchy as well as their coupling systems ⋮ r-Matrices for Relativistic Deformations of Integrable Systems ⋮ A generalized cubic Volterra lattice hierarchy and its integrable couplings system

Cites Work

• What is a classical r-matrix?
• Nonlinear Poisson structures and r-matrices
• Poisson geometry of the analog of the Miura maps and Bäcklund-Darboux transformations for equations of Toda type and periodic Toda flows
• Two results on a class of Poisson structures on Lie groups
• A note on the Poisson brackets associated with Lax operators
• On the \(r\)-matrix interpretation of Bogoyavlensky lattices
• R-matrices and higher Poisson brackets for integrable systems
• Dual moment maps into loop algebras
• The toda flow on a generic orbit is integrable
• THE LAX REPRESENTATION WITH A SPECTRAL PARAMETER FOR CERTAIN DYNAMICAL SYSTEMS
• The lattice Gel'fand-Dikii hierarchy

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