On the structure of Hamiltonian operators in field theory

DOI10.1016/0393-0440(86)90022-7zbMath0611.58051OpenAlexW2044049203MaRDI QIDQ1087207

A. M. Astashov, Alexandre M. Vinogradov

Publication date: 1986

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0393-0440(86)90022-7

zbMATH Keywords

symplectic structureHamiltonian operatorsDarboux's lemmaPoisson bracket structure

Mathematics Subject Classification ID

Applications of global differential geometry to the sciences (53C80) Applications of PDEs on manifolds (58J90) Classical field theories (70Sxx)

Related Items (12)

Classification results and the Darboux theorem for low-order Hamiltonian operators ⋮ Boundary values as Hamiltonian variables. I. New Poisson brackets ⋮ Boundary values as Hamiltonian variables. II. Graded structures ⋮ Projective-geometric aspects of bi-Hamiltonian structures of KdV type ⋮ On classification of Poisson vertex algebras ⋮ Geometry of jet spaces and integrable systems ⋮ Computing with Hamiltonian operators ⋮ Deformations of Poisson structures by closed 3-forms ⋮ Canonical Hamiltonian representation of the Krichever--Novikov equation ⋮ Symmetries and conservation laws of partial differential equations: Basic notions and results ⋮ Projective-geometric aspects of homogeneous third-order Hamiltonian operators ⋮ Variational Operators, Symplectic Operators, and the Cohomology of Scalar Evolution Equations

Cites Work

• The local structure of Poisson manifolds
• The \({\mathcal C}\)-spectral sequence, Lagrangian formalism, and conservation laws. II: The nonlinear theory
• Algebraic aspects of nonlinear differential equations
• Modifying Lax equations and the second Hamiltonian structure
• Geometry of nonlinear differential equations
• WHAT IS THE HAMILTONIAN FORMALISM?
• NON-LINEAR EQUATIONS OF KORTEWEG-DE VRIES TYPE, FINITE-ZONE LINEAR OPERATORS, AND ABELIAN VARIETIES
• LOCAL LIE ALGEBRAS
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