Darboux' theorem for Hamiltonian differential operators

DOI10.1016/0022-0396(88)90036-8zbMath0651.47036OpenAlexW2074808032MaRDI QIDQ1106452

Peter J. Olver

Publication date: 1988

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(88)90036-8

zbMATH Keywords

constant coefficient formfirst order Hamiltonian differential operator

Mathematics Subject Classification ID

General theory of ordinary differential operators (47E05) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items

Symplectic integration of Hamiltonian wave equations, Classification results and the Darboux theorem for low-order Hamiltonian operators, Compatibility conditions for Hamiltonian pairs, Local symplectic operators and structures related to them, The variational bicomplex for hyperbolic second-order scalar partial differential equations in the plane, On Hamiltonian formulations of the \(\mathcal{C}_1(m, a, b)\) equations, Liouville correspondences between multicomponent integrable hierarchies, Miura-reciprocal transformations and localizable Poisson pencils, On classification of Poisson vertex algebras, A new 3-component Degasperis-Procesi hierarchy, Computing with Hamiltonian operators, \(K(m,n)\) equations with fifth order symmetries and their integrability, Behaviors of \(N = 1\) supersymmetric Euler derivatives and Hamiltonian operators under general superconformal transformations, Homogeneous Hamiltonian operators and the theory of coverings, Compactons, Variational Operators, Symplectic Operators, and the Cohomology of Scalar Evolution Equations, Multi-Hamiltonian structure of the Born–Infeld equation, Differential geometric Poisson bivectors in one space variable, Structure-preserving reduced basis methods for Poisson systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On integrable systems with higher order corrections
• Hamiltonian operators and algebraic structures related to them
• Symmetry groups and group invariant solutions of partial differential equations
• Symplectic manifolds and their Lagrangian submanifolds
• Nonlinear stability of fluid and plasma equilibria
• Hamiltonian perturbation theory in noncanonical coordinates
• Hamiltonian perturbation theory and water waves
• Dirac’s theory of constraints in field theory and the canonical form of Hamiltonian differential operators
• On the Hamiltonian structure of evolution equations
• A simple model of the integrable Hamiltonian equation
• On the Analogy Between Classical and Quantum Mechanics