A finite-dimensional integrable system and the r-matrix method

DOI10.1063/1.533232zbMath0985.37062OpenAlexW2088566417MaRDI QIDQ2737924

Qi-Yan Shi, Si-Ming Zhu

Publication date: 30 August 2001

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

Full work available at URL: https://doi.org/10.1063/1.533232

zbMATH Keywords

Lax representation\(r\)-matrixsoliton hierarchynonlinearizationAKNS 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) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

Related Items

Binary symmetry constraints of N-wave interaction equations in 1+1 and 2+1 dimensions ⋮ Binary nonlinearization of spectral problems of the perturbation AKNS systems.

Cites Work

• What is a classical r-matrix?
• Nonlinearization of the \(3\times 3\) matrix eigenvalue problem related to coupled nonlinear Schrödinger equations
• The Hamiltonian structure and new finite-dimensional integrable system associated with Harry-Dym type equations
• A finite-dimensional integrable system associated with the three-wave interaction equations
• New Finite-Dimensional Integrable Systems by Symmetry Constraint of the KdV Equations
• The deduction of the Lax representation for constrained flows from the adjoint representation
• A new integrable symplectic map associated with lattice soliton equations
• C Neumann and Bargmann systems associated with the coupled KdV soliton hierarchy