Finite-dimensional integrable systems related to the n-wave interaction equations

DOI10.1063/1.1385565zbMath1005.37040OpenAlexW2026808241MaRDI QIDQ2774983

Qi-Yan Shi

Publication date: 26 February 2002

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

Full work available at URL: https://doi.org/10.1063/1.1385565

zbMATH Keywords

Hamiltonian systemLax pairsLax representationsadjoint Lax pairscomplete Liouville integrabilitygeneralized Zakharov-Shabat eigenvalue problem

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Cites Work

• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• The constraints of potentials and the finite-dimensional integrable systems
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• Restricted flows of the AKNS hierarchy
• How to construct finite-dimensional bi-Hamiltonian systems from soliton equations: Jacobi integrable potentials
• Relation between the Kadometsev–Petviashvili equation and the confocal involutive system
• From the special 2 + 1 Toda lattice to the Kadomtsev-Petviashvili equation
• C Neumann and Bargmann systems associated with the coupled KdV soliton hierarchy

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