An approach for generating enlarging integrable systems

DOI10.1016/j.physleta.2006.11.103zbMath1203.37114OpenAlexW2055163626MaRDI QIDQ620850

Yu-Feng Zhang, En-gui Fan

Publication date: 20 January 2011

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

Full work available at URL: https://doi.org/10.1016/j.physleta.2006.11.103

zbMATH Keywords

Lie algebraHamiltonian structureintegrable system

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)

Related Items (10)

Hamiltonian and super-Hamiltonian systems of a hierarchy of soliton equations ⋮ The quasi-AKNS and quasi-\(s o(3)\) type AKNS hierarchies as well as a gallery of simple Lie algebras contained in \(s l(3; \mathbb{C})\) ⋮ AN ALGEBRAIC STRUCTURE OF ZERO CURVATURE REPRESENTATIONS ASSOCIATED WITH COUPLED INTEGRABLE COUPLINGS AND APPLICATIONS TO τ-SYMMETRY ALGEBRAS ⋮ Integrable decomposition of a hierarchy of soliton equations and integrable coupling system by semidirect sums of Lie algebras ⋮ Hamiltonian and super-Hamiltonian extensions related to Broer-Kaup-Kupershmidt system ⋮ A new soliton hierarchy and its two extending integrable models ⋮ THE ALGEBRAIC STRUCTURE OF ZERO CURVATURE REPRESENTATIONS ASSOCIATED WITH INTEGRABLE COUPLINGS ⋮ SPECTRAL RADIUS ANALYSIS OF MATRICES AND THE ASSOCIATED WITH INTEGRABLE SYSTEMS ⋮ The algebraic structure of discrete zero curvature equations associated with integrable couplings and application to enlarged Volterra systems ⋮ A super-discrete variational identity and its application for constructing super-discrete Hamiltonian systems

Cites Work

• Integrable theory of the perturbation equations.
• A few expanding Lie algebras of the Lie algebra \(A_1\) and applications
• 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 coupled AKNS–Kaup–Newell soliton hierarchy
• A direct method for integrable couplings of TD hierarchy

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