The generalized nonlinear Schrödinger hierarchy, its integrable coupling system and their bi-Hamiltonian structure

DOI10.1016/J.PHYSLETA.2007.08.078zbMath1220.37051OpenAlexW2095177545MaRDI QIDQ637674

Juan-Miguel Gracia

Publication date: 6 September 2011

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2007.08.078

zbMATH Keywords

Lie algebrabi-Hamiltonian structureintegrable coupling

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Loop groups and related constructions, group-theoretic treatment (22E67) Applications of Lie groups to the sciences; explicit representations (22E70) Groups and algebras in quantum theory and relations with integrable systems (81R12)

Related Items (3)

The quasi-AKNS and quasi-\(s o(3)\) type AKNS hierarchies as well as a gallery of simple Lie algebras contained in \(s l(3; \mathbb{C})\) ⋮ The two generalized AKNS hierarchies and their Hamiltonian structures ⋮ SOME EXPANDING SEMI-DIRECT SUMS OF LIE ALGEBRA $\bar{G}$ AND ITS APPLICATION

Cites Work

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• Semi-direct sums of Lie algebras and continuous integrable couplings
• A generalized Boite-Pempinelli-Tu (BPT) hierarchy and its bi-Hamiltonian structure
• Hamiltonian structure of the integrable coupling of the Jaulent-Miodek hierarchy
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• A new loop algebra and a corresponding integrable hierarchy, as well as its integrable coupling

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