A construction of Multidimensional Dubrovin-Novikov Brackets

DOI10.1080/14029251.2019.1591716zbMath1462.37078arXiv1806.10382OpenAlexW2811364850MaRDI QIDQ5197842

Ian A. B. Strachan

Publication date: 20 September 2019

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

Full work available at URL: https://arxiv.org/abs/1806.10382

zbMATH Keywords

integrable systemsHamiltonian structures

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 infinite-dimensional Lie algebras and other algebraic structures (37K30) General theory of infinite-dimensional Hamiltonian and Lagrangian systems, Hamiltonian and Lagrangian structures, symmetries, conservation laws (37K06)

Related Items (1)

Bi-Hamiltonian systems in \((2+1)\) and higher dimensions defined by Novikov algebras

Cites Work

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• The classification of nonsingular multidimensional Dubrovin-Novikov brackets
• Dubrovin-Novikov type Poisson brackets (DN-brackets)
• Hamiltonian operators and algebraic structures related to them
• Novikov-Poisson algebras
• Classification of Novikov algebras
• Hamiltonian operators of Dubrovin-Novikov type in 2D
• On deformations of multidimensional Poisson brackets of hydrodynamic type
• The classification of Novikov algebras in low dimensions
• The classification of Novikov algebras in low dimensions: invariant bilinear forms
• Degenerate first-order Hamiltonian operators of hydrodynamic type in 2D

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