The two generalized AKNS hierarchies and their Hamiltonian structures

DOI10.1016/J.CNSNS.2008.11.006zbMath1221.37129OpenAlexW2084588500WikidataQ56431443 ScholiaQ56431443MaRDI QIDQ717958

Hui Chang, Baiying He

Publication date: 23 September 2011

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2008.11.006

zbMATH Keywords

Lie algebraHamiltonian structuretri-trace identityintegrable equation hierarchy

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

Related Items (1)

The quasi-AKNS and quasi-\(s o(3)\) type AKNS hierarchies as well as a gallery of simple Lie algebras contained in \(s l(3; \mathbb{C})\)

Cites Work

• Two unified formulae
• The generalized nonlinear Schrödinger hierarchy, its integrable coupling system and their bi-Hamiltonian structure
• Semi-direct sums of Lie algebras and continuous integrable couplings
• A generalized AKNS hierarchy and its bi-Hamiltonian structures
• Hamiltonian structure of the integrable coupling of the Jaulent-Miodek hierarchy
• A type of loop algebra and the associated loop algebras
• New integrable couplings and Hamiltonian structure of the KN hierarchy and the DLW hierarchy
• Three New Integrable Hierarchies of Equations
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• Induced Lie Algebras of a Six-Dimensional Matrix Lie Algebra
• The quadratic-form identity for constructing the Hamiltonian structure of integrable systems

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