Differential geometric Poisson bivectors in one space variable

DOI10.1063/1.530213zbMath0778.58022OpenAlexW2060167982WikidataQ115331117 ScholiaQ115331117MaRDI QIDQ4201706

Philip W. Doyle

Publication date: 6 September 1993

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

Full work available at URL: https://doi.org/10.1063/1.530213

zbMATH Keywords

Poisson bivectors

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Classical field theories (70Sxx)

Related Items (18)

On deformations of one-dimensional Poisson structures of hydrodynamic type with degenerate metric ⋮ Systems of conservation laws with third-order Hamiltonian structures ⋮ On a class of third-order nonlocal Hamiltonian operators ⋮ Projective geometry of homogeneous second-order Hamiltonian operators ⋮ Projective-geometric aspects of bi-Hamiltonian structures of KdV type ⋮ Miura-reciprocal transformations and localizable Poisson pencils ⋮ Applications of Nijenhuis geometry. III: Frobenius pencils and compatible non-homogeneous Poisson structures ⋮ Bi-Hamiltonian structures of KdV type ⋮ Geometry of inhomogeneous Poisson brackets, multicomponent Harry Dym hierarchies, and multicomponent Hunter-Saxton equations ⋮ Bi-Hamiltonian structure of a WDVV equation in \(2\)-d topological field theory ⋮ WDVV equations and invariant bi-Hamiltonian formalism ⋮ Remarks on the Lagrangian representation of bi-Hamiltonian equations ⋮ Flat pencils of symplectic connections and Hamiltonian operators of degree 2 ⋮ Homogeneous Hamiltonian operators and the theory of coverings ⋮ Projective-geometric aspects of homogeneous third-order Hamiltonian operators ⋮ On the cohomology groups of complexes of homogeneous forms on loop spaces of smooth manifolds ⋮ Applications of Nijenhuis geometry II: maximal pencils of multi-Hamiltonian structures of hydrodynamic type ⋮ On the bi-Hamiltonian geometry of WDVV equations

Cites Work

• Darboux' theorem for Hamiltonian differential operators
• Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
• Hamiltonian structures for systems of hyperbolic conservation laws
• Hamiltonian perturbation theory and water waves
• On the Hamiltonian structure of evolution equations
• Classification results and the Darboux theorem for low-order Hamiltonian operators
• THE GEOMETRY OF HAMILTONIAN SYSTEMS OF HYDRODYNAMIC TYPE. THE GENERALIZED HODOGRAPH METHOD

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