The classification of nonsingular multidimensional Dubrovin-Novikov brackets

DOI10.1007/s10688-008-0004-8zbMath1180.37088arXivmath/0611785OpenAlexW1971204397MaRDI QIDQ1002790

Oleg I. Mokhov

Publication date: 26 February 2009

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0611785

zbMATH Keywords

Dubrovin-Novikov bracketmultidimensional Poisson bracket of hydrodynamic type

Mathematics Subject Classification ID

Related Items (17)

First Order Hamiltonian Operators of Differential-Geometric Type in 2D ⋮ Higher-order dispersive deformations of multidimensional Poisson brackets of hydrodynamic type ⋮ On compatible diagonal metrics ⋮ Pencils of compatible metrics and integrable systems ⋮ Dispersive deformations of Hamiltonian systems of hydrodynamic type in \(2+1\) dimensions ⋮ New integrable (\(3+1\))-dimensional systems and contact geometry ⋮ Hamiltonian systems of hydrodynamic type in \(2+1\) dimensions ⋮ The multi-dimensional Hamiltonian structures in the Whitham method ⋮ Poisson cohomology of scalar multidimensional Dubrovin-Novikov brackets ⋮ Hamiltonian operators of Dubrovin-Novikov type in 2D ⋮ Normal forms of dispersive scalar Poisson brackets with two independent variables ⋮ A construction of Multidimensional Dubrovin-Novikov Brackets ⋮ Bi-Hamiltonian systems in \((2+1)\) and higher dimensions defined by Novikov algebras ⋮ On the canonical forms of the multi-dimensional averaged Poisson brackets ⋮ Form-invariant Poisson brackets of hydrodynamic type with several spatial variables ⋮ On deformations of multidimensional Poisson brackets of hydrodynamic type ⋮ Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2 + 1 dimensions

Cites Work

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• Dubrovin-Novikov type Poisson brackets (DN-brackets)
• Integrability of the equations for nonsingular pairs of compatible flat metrics
• Compatible flat metrics
• On the integrability of \((2+1)\)-dimensional quasilinear systems
• Compatible Poisson brackets of hydrodynamic type
• Flat pencils of metrics and integrable reductions of Lamé's equations
• Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory
• A simple model of the integrable Hamiltonian equation
• Symplectic and Poisson structures on loop spaces of smooth manifolds, and integrable systems
• Compatible and almost compatible pseudo-Riemannian metrics

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