New Liouville integrable noncanonical Hamiltonian systems from the AKNS spectral problem

DOI10.1063/1.1478802zbMath1059.37048OpenAlexW2020505933MaRDI QIDQ4832650

Wen-Xiu Ma, Maciej Błaszak

Publication date: 14 December 2004

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

Full work available at URL: https://doi.org/10.1063/1.1478802

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) Poisson manifolds; Poisson groupoids and algebroids (53D17) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

Related Items (4)

The Second mKdV Equation and Its Hereditary Symmetry and Hamiltonian Structure ⋮ A hierarchy of nonlinear differential-difference equations and a new Bargmann type integrable system ⋮ A new \(4\times 4\) AKNS spectral problem and its associated integrable decomposition of the AKNS equation ⋮ Hierarchies, integrable decompositions and conservation laws of Geng equation

Cites Work

• Do symmetry constraints nonlinearize spectral problems into Hamiltonian systems?
• Binary nonlinearization of AKNS spectral problem under higher-order symmetry constraints.
• The Hamiltonian structure and new finite-dimensional integrable system associated with Harry-Dym type equations
• 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 soliton hierarchies: coupled KdV and Harry Dym case
• Restricted flows of the AKNS hierarchy
• How to construct finite-dimensional bi-Hamiltonian systems from soliton equations: Jacobi integrable potentials
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• The algebraic structure of zero curvature representations and application to coupled KdV systems
• Miura map and Bi-Hamiltonian formulation for restricted flows of the KdV hierarchy
• New Finite-Dimensional Integrable Systems by Symmetry Constraint of the KdV Equations
• A new method to introduce additional separated variables for high-order binary constrained flows
• Separation of variables for soliton equations via their binary constrained flows

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