Integrable Hamiltonian systems related to the polynomial eigenvalue problem

DOI10.1063/1.528987zbMath0850.70174OpenAlexW2018881089MaRDI QIDQ3971955

Yunbo Zeng, Yi-Shen Li

Publication date: 25 June 1992

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

Full work available at URL: https://doi.org/10.1063/1.528987

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (10)

Families of quasi-bi-Hamiltonian systems and separability ⋮ The general scheme for higher-order decompositions of zero-curvature equations associated with \(\widetilde {sl}(2)\) ⋮ A hierarchy of nonlinear evolution equations and finite-dimensional involutive systems ⋮ An involutive system and integrable C. Neumann system associated with the modified Korteweg–de Vries hierarchy ⋮ The generalized Neumann hierarchy associated with the energy dependent Schrödinger equation ⋮ Binary symmetry constraints of N-wave interaction equations in 1+1 and 2+1 dimensions ⋮ Families of dynamical r-matrices and Jacobi inversion problem for nonlinear evolution equations ⋮ Restarted generalized Krylov subspace methods for solving large-scale polynomial eigenvalue problems ⋮ Do symmetry constraints nonlinearize spectral problems into Hamiltonian systems? ⋮ Model-order reduction of large-scalekth-order linear dynamical systems via akth-order Arnoldi method

Cites Work

• An approach to the integrability of Hamiltonian systems obtained by reduction
• The constraints of potentials and the finite-dimensional integrable systems
• Schrödinger spectral problems with energy–dependent potentials as sources of nonlinear Hamiltonian evolution equations
• On the use of isospectral eigenvalue problems for obtaining hereditary symmetries for Hamiltonian systems
• Rational and elliptic solutions of the korteweg-de vries equation and a related many-body problem

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