A description of Lax type integrable dynamical systems via the Marsden-Weinstein reduction method

DOI10.1016/j.cnsns.2013.01.010zbMath1310.53072OpenAlexW1987110920MaRDI QIDQ2513463

Yarema A. Prykarpatsky

Publication date: 28 January 2015

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2013.01.010

zbMATH Keywords

Lax type integrabilityPoissonian structurecurrent loop-group symmetryMarsden-Weinstein reduction methodR-matrix structure

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Momentum maps; symplectic reduction (53D20) Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics (70H33)

Cites Work

• What is a classical r-matrix?
• Reduction of Hamiltonian systems, affine Lie algebras and Lax equations
• Generating equation for \(r\)-matrices related to dynamical systems of Calogero type.
• Reduction technique for matrix nonlinear evolution equations solvable by the spectral transform
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