Classical \(r\)-matrices and the four-wave interaction equation

DOI10.1016/S0960-0779(97)00087-8zbMath0933.37067OpenAlexW2027361162WikidataQ127872539 ScholiaQ127872539MaRDI QIDQ1963180

Yanyan Li

Publication date: 24 January 2000

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0960-0779(97)00087-8

zbMATH Keywords

bi-HamiltonianKlein-Gordonzero-curvature equationfour-wave interaction equation

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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• What is a classical r-matrix?
• The homogeneous Heisenberg subalgebra and equations of AKNS type
• Banach-Lie groups and integrable systems
• Lax Pairs for Four-Wave Interaction Systems
• Dressing transformations and Poisson group actions

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