On the Poisson geometry of the Adler-Gel'fand-Dikii brackets

DOI10.1007/BF02921600zbMath0896.58028OpenAlexW2040816399MaRDI QIDQ1387672

Gloria Marí Beffa

Publication date: 10 August 1998

Published in: The Journal of Geometric Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02921600

zbMATH Keywords

normal formsLie-Poisson structuretransverse structureKdV Hamiltonian structuresAdler-Gel'fand-Dikij Poisson bracketHill's operatorsscalar differential operators with periodic coefficient

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

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Cites Work

• Unnamed Item
• The local structure of Poisson manifolds
• Symplectic leaves of the Gel'fand-Dikij brackets and homotopy classes of nondegenerate curves
• Normal forms for analytic Poisson structures
• Lie algebras and equations of Korteweg-de Vries type
• Reduction of Poisson manifolds
• Normal forms and versal deformations for Hill's equation
• On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
• A transverse structure for the Lie-Poisson bracket on the dual of the Virasoro algebra
• Invariants of Hamiltonian KdV-structures
• On the Virasoro Algebra as Reduced Poisson Submanifold of a Kac-Moody Algebra on the Circle
• Integrals of nonlinear equations of evolution and solitary waves

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