A subalgebra of Lie algebra A2 and its associated two types of loop algebras, as well as Hamiltonian structures of integrable hierarchy

DOI10.1063/1.3122667zbMath1187.37103OpenAlexW2063215901WikidataQ115333479 ScholiaQ115333479MaRDI QIDQ3565287

Huan He Dong

Publication date: 3 June 2010

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

Full work available at URL: https://doi.org/10.1063/1.3122667

zbMATH Keywords

isospectral problemloop algebrasnew Liouville integrable Hamiltonian hierarchysubalgebra of Lie algebra \(A_ 2\)

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Applications of Lie algebras and superalgebras to integrable systems (17B80) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

Related Items (4)

Darboux transformations for super-Schrödinger equation, super-Dirac equation and their exact solutions ⋮ Two super-integrable hierarchies and their super-Hamiltonian structures ⋮ New super integrable hierarchies associated with \(\operatorname{osp}(2|2)\) and \(\operatorname{spo}(2|2)\) and their applications ⋮ A hierarchy of discrete integrable coupling system with self-consistent sources

Cites Work

• Multi-component bi-Hamiltonian Dirac integrable equations
• Integrable theory of the perturbation equations.
• Semi-direct sums of Lie algebras and continuous integrable couplings
• A new loop algebra and the corresponding computing formula of constant \(\gamma \) in the quadratic-form identity, as well as the generalized Burgers hierarchy
• Integrable couplings of Botie-Pempinelli-Tu (BPT) hierarchy
• Integrable evolution systems based on Gerdjikov–Ivanov equations, bi-Hamiltonian structure, finite-dimensional integrable systems and N-fold Darboux transformation
• Integrable couplings of vector AKNS soliton equations
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• New Matrix Loop Algebra and Its Application
• A direct method for integrable couplings of TD hierarchy
• A powerful approach to generate new integrable systems
• An approach to generate superextensions of integrable systems
• Multi-component C-KdV Hierarchy of Soliton Equations and Its Multi-component Integrable Coupling System
• Hamiltonian and quasi-Hamiltonian structures associated with semi-direct sums of Lie algebras
• Virasoro symmetry algebra of Dirac soliton hierarchy
• A new completely integrable Liouville's system, its Lax representation and bi-Hamiltonian structure

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