Hamilton Operators and Related Integrable Differential Algebraic Novikov–Leibniz Type Structures

DOI10.1007/978-3-319-63594-1_10zbMath1402.35018OpenAlexW2786011436MaRDI QIDQ4556837

Anatoliy K. Prykarpatsky

Publication date: 28 November 2018

Published in: Trends in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-319-63594-1_10

zbMATH Keywords

integrabilityPoisson bracketsNovikov algebraRiemann type hydrodynamic hierarchydifferential algebrasRiemann algebraloop-algebraright Leibniz algebra

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Invariance and symmetry properties for PDEs on manifolds (58J70) Initial value problems for nonlinear higher-order PDEs (35G25) Geometric theory, characteristics, transformations in context of PDEs (35A30) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Overdetermined systems of PDEs with variable coefficients (35N10) Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds (58J72)

Cites Work

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• A simple way of making a Hamiltonian system into a bi-Hamiltonian one
• Hamiltonian operators and algebraic structures related to them
• Differential-algebraic and bi-Hamiltonian integrability analysis of the Riemann hierarchy revisited
• Novikov Algebras and a Classification of Multicomponent Camassa-Holm Equations
• Quadratic Poisson brackets compatible with an algebra structure

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