Nonlinear bi-Hamiltonian dynamical systems: current Lie algebraic approach

DOI10.1016/S0034-4877(01)80031-8zbMath0986.37064OpenAlexW2091793807MaRDI QIDQ5942392

Andrzej Szum

Publication date: 29 August 2001

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0034-4877(01)80031-8

zbMATH Keywords

Camassa-Holm equationhierarchiesLie algebraic approach

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) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

Cites Work

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• Infinite dimensional Lie algebras. An introduction
• Symplectic structures, their Bäcklund transformations and hereditary symmetries
• Acoustic scattering and the extended Korteweg-de Vries hierarchy
• Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation
• A simple model of the integrable Hamiltonian equation
• Multi-peakons and a theorem of Stieltjes
• Algebraic structure of the gradient-holonomic algorithm for Lax integrable nonlinear dynamical systems. I
• Adler–Kostant–Symes construction, bi-Hamiltonian manifolds, and KdV equations
• An integrable shallow water equation with peaked solitons
• Zero curvature formulations of dual hierarchies
• Foundations of Quantum Mechanics
• Generalized Hamiltonian Dynamics

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