A hierarchy of the Lax integrable system, its bi-Hamiltonian structure, finite-dimensional integrable system and involutive solution

DOI10.1016/S0960-0779(01)00045-5zbMath1028.37041MaRDI QIDQ1401030

Zhenya Yan

Publication date: 17 August 2003

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

zbMATH Keywords

zero-curvature representationhierarchyisospectral problembi-Hamiltonian structurescompletely integrable Hamiltonian systeminvolutive systemsLax integrable system

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) Integrable cases of motion in rigid body dynamics (70E40)

Related Items (1)

A new Lie algebra along with its induced Lie algebra and associated with applications

Cites Work

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• Index of a singular point of a vector field, the Petrovskii-Oleinik inequality, and mixed Hodge structures
• Completely integrable system related to a new hierarchy of isospectral evolution equations
• A hierarchy of generalized AKNS equations, N-Hamiltonian structures and finite-dimensional involutive systems and integrable systems
• The Modified Korteweg-de Vries Equation
• New Integrable Nonlinear Evolution Equations
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• 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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