Hydrodynamic chains and the classification of their Poisson brackets

DOI10.1063/1.2399086zbMath1112.37062arXivnlin/0603056OpenAlexW3102336311MaRDI QIDQ3442148

Maxim P. Pavlov

Publication date: 16 May 2007

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

Full work available at URL: https://arxiv.org/abs/nlin/0603056

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53)

Related Items (2)

Automated symbolic calculations in nonequilibrium thermodynamics ⋮ Differential geometry of hydrodynamic Vlasov equations

Cites Work

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• Benney's long waves equations: Hamiltonian formalism
• The Liouville canonical form for compatible nonlocal Poisson brackets of hydrodynamic type and integrable hierarchies
• Relationships between differential substitutions and Hamiltonian structures of the Korteweg-de Vries equation
• Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
• Classification of integrable Hamiltonian hydrodynamic chains associated with Kupershmidt’s brackets
• The characterization of two-component (2+1)-dimensional integrable systems of hydrodynamic type
• ClassicalR-matrix theory of dispersionless systems: II. (2   1) dimension theory
• THE GEOMETRY OF HAMILTONIAN SYSTEMS OF HYDRODYNAMIC TYPE. THE GENERALIZED HODOGRAPH METHOD
• Reciprocal transformations of Hamiltonian operators of hydrodynamic type: Nonlocal Hamiltonian formalism for linearly degenerate systems
• Some Properties of Long Nonlinear Waves
• On the local systems Hamiltonian in the weakly non-local Poisson brackets

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