Homogeneous Hamiltonian operators and the theory of coverings

DOI10.1016/j.difgeo.2020.101713OpenAlexW3120663005WikidataQ115354645 ScholiaQ115354645MaRDI QIDQ2022401

Pierandrea Vergallo, Raffaele Vitolo

Publication date: 29 April 2021

Published in: Differential Geometry and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2007.15294

zbMATH Keywords

Hamiltonian PDEintegrable systemscovering of PDEshomogeneous Hamiltonian operator

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions) (35R20) General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws (37K06)

Related Items (7)

Classification of degenerate non-homogeneous Hamiltonian operators ⋮ Projective geometry of homogeneous second-order Hamiltonian operators ⋮ Projective-geometric aspects of bi-Hamiltonian structures of KdV type ⋮ Hamiltonian systems of Jordan block type: Delta-functional reductions of the kinetic equation for soliton gas ⋮ WDVV equations and invariant bi-Hamiltonian formalism ⋮ Quasilinear systems of first order PDEs with nonlocal Hamiltonian structures ⋮ WDVV equations: symbolic computations of Hamiltonian operators

Cites Work

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• Geometry of jet spaces and integrable systems
• Projective-geometric aspects of homogeneous third-order Hamiltonian operators
• Oriented associativity equations and symmetry consistent conjugate curvilinear coordinate nets
• Nonlocal symmetries and the theory of coverings: An addendum to A. M. Vinogradov's 'Local Symmetries and Conservation Laws'
• A new conservation theorem
• Darboux' theorem for Hamiltonian differential operators
• Systems of conservation laws with third-order Hamiltonian structures
• Hamiltonian operators and \(\ell^*\)-coverings
• A Darboux theorem for Hamiltonian operators in the formal calculus of variations.
• Hamiltonian operators of Dubrovin-Novikov type in 2D
• On the bi-Hamiltonian geometry of WDVV equations
• On a class of third-order nonlocal Hamiltonian operators
• A geometric study of the dispersionless Boussinesq type equation
• Local symplectic operators and structures related to them
• A simple model of the integrable Hamiltonian equation
• Differential geometric Poisson bivectors in one space variable
• On third-order Poisson brackets of differential geometry
• Towards the Classification of Homogeneous Third-Order Hamiltonian Operators: Table 1.
• Bi-Hamiltonian structures of KdV type
• THE GEOMETRY OF HAMILTONIAN SYSTEMS OF HYDRODYNAMIC TYPE. THE GENERALIZED HODOGRAPH METHOD
• Bi-Hamiltonian structure of the oriented associativity equation
• On the local systems Hamiltonian in the weakly non-local Poisson brackets

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