A Lax integrable hierarchy, \(N\)-Hamiltonian structure, \(r\)-matrix, finite-dimensional Liouville integrable involutive systems, and involutive solutions.

DOI10.1016/S0960-0779(01)00150-3zbMath1067.37105OpenAlexW1971848445MaRDI QIDQ1610082

Zhenya Yan, Hong-Qing Zhang

Publication date: 18 August 2002

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

Full work available at URL: https://doi.org/10.1016/s0960-0779(01)00150-3

zbMATH Keywords

conservation lawseigenvalue problemsymmetriesnonlinear Schrödinger equationsnonlinearizationLenard operators

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)

Related Items (1)

Two types of hierarchies of evolution equations associated with the extended Kaup-Newell spectral problem with an arbitrary smooth function.

Cites Work

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• Nonlinearization of the Lax system for AKNS hierarchy
• Index of a singular point of a vector field, the Petrovskii-Oleinik inequality, and mixed Hodge structures
• The Modified Korteweg-de Vries Equation
• Theta functions and non-linear equations
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• The inverse scattering transform: Semi-infinite interval
• A simple model of the integrable Hamiltonian equation
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• A coupled AKNS–Kaup–Newell soliton hierarchy
• The finite-band solution of the Jaulent–Miodek equation
• Method for Solving the Korteweg-deVries Equation
• The deduction of the Lax representation for constrained flows from the adjoint representation
• Families of dynamical r-matrices and Jacobi inversion problem for nonlinear evolution equations

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