Reduction of bi-Hamiltonian systems and separation of variables: An example from the Boussinesq hierarchy

DOI10.1007/BF02551195zbMath0983.37087arXivsolv-int/9906009MaRDI QIDQ1586710

Gregorio Falqui, Franco Magri, Giorgio Tondo

Publication date: 23 November 2000

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/solv-int/9906009

zbMATH Keywords

bi-Hamiltonian systemsBoussinesq hierarchyGelfand-Dickey hierarchy

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Hamilton-Jacobi equations in mechanics (70H20) Pseudodifferential operators and other generalizations of partial differential operators (35S99)

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Cites Work

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• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Reduction of Poisson manifolds
• Lax representation with a spectral parameter for the Kowalevski top and its generalizations
• The relationship between Hamiltonian formalisms of stationary and nonstationary problems
• A Lie algebraic generalization of the Mumford system, its symmetries and its multi-Hamiltonian structure
• Bi-Hamiltonian manifolds, quasi-bi-Hamiltonian systems and separation variables
• On the integrability of stationary and restricted flows of the KdV hierarchy
• On stationary problems for equations of korteweg-de vries type
• POISSON-NIJENHUIS STRUCTURES AND SATO HIERARCHY
• Quasi-bi-Hamiltonian systems and separability
• A note on fractional KdV hierarchies
• Two degrees of freedom quasi-bi-Hamiltonian systems