A FOUR-BY-FOUR MATRIX EIGENVALUE PROBLEM, RELATED HIERARCHY OF LAX INTEGRABLE EQUATIONS AND THEIR HAMILTONIAN STRUCTURES

DOI10.1142/S0217979208048735zbMath1200.37065MaRDI QIDQ3607484

Weili Cao, Xi-Xiang Xu, Hong-Xiang Yang

Publication date: 2 March 2009

Published in: International Journal of Modern Physics B (Search for Journal in Brave)

zbMATH Keywords

Hamiltonian structureLiouville integrabilityLax pairgeneralized trace identityMatrix eigenvalue problem

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Soliton equations (35Q51)

Related Items (3)

Hamiltonian and super-Hamiltonian systems of a hierarchy of soliton equations ⋮ A HIERARCHY OF HAMILTONIAN EQUATIONS ASSOCIATED WITH THE MODIFIED JAULENT–MIODEK HIERARCHY ⋮ Hamiltonian and super-Hamiltonian extensions related to Broer-Kaup-Kupershmidt system

Cites Work

• Integrable theory of the perturbation equations.
• Hamiltonian methods in the theory of solitons. Transl. from the Russian by A. G. Reyman
• Semi-direct sums of Lie algebras and continuous integrable couplings
• Enlarging spectral problems to construct integrable couplings of soliton equations
• A generalized Wadati-Konno-Ichikawa hierarchy and new finite-dimensional integrable systems
• The bi-Hamiltonian structure of the perturbation equations of the KdV hierarchy.
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• A nonconfocal generator of involutive systems and three associated soliton hierarchies
• Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras
• New completely integrable Neumann systems related to the perturbation KdV hierarchy

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