Binary Nonlinearization of AKNS Spectral Problem under Higher-Order Symmetry Constraints

1998/08/20 by Yishen Li, Wen-Xiu Ma, Wen‐Xiu Ma +2
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Electron Spin Resonance Studies #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Quantum chaos and dynamical systems #nlin.SI #solv-int

paper · pdf · doi:10.48550/arxiv.solv-int/9808010

16 pages, latex, to appear in Chaos, Solitons and Fractals

arxiv created 1998/08/20 · openalex publication_date 1998/08/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Binary nonlinearization of AKNS spectral problem is extended to the cases of higher-order symmetry constraints. The Hamiltonian structures, Lax representations, r-matrices and integrals of motion in involution are explicitly proposed for the resulting constrained systems in the cases of the first four orders. The obtained integrals of motion are proved to be functionally independent and thus the constrained systems are completely integrable in the Liouville sense.

Related

• Non-symmetry constraints of the AKNS system yielding integrable Hamiltonian systems
• The Theory of Binary Nonlinearization and Its Applications to Soliton Equations
• Binary Nonlinearization of Lax Pairs
• Binary nonlinearization for the Dirac systems
• Symmetries for the Ablowitz-Ladik hierarchy: II. Integrable discrete nonlinear Schrödinger equation and discrete AKNS hierarchy