INTEGRABLE COUPLINGS OF MULTI-COMPONENT AKNS–KAUP–NEWELL EQUATIONS HIERARCHIES

DOI10.1142/S0217979210056815zbMath1218.37097MaRDI QIDQ3002064

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Publication date: 19 May 2011

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

zbMATH Keywords

integrable couplingsmulti-component matrix spectral problemAKNS-Kaup-Newell hierarchy

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) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

Cites Work

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• New simple method for obtaining integrable hierarchies of soliton equations with multicomponent potential functions
• Painlevé property and conservation laws of multi-component mKdV equations
• Adjoint symmetry constraints of multicomponent AKNS equations.
• The bi-Hamiltonian structure of the perturbation equations of the KdV hierarchy.
• Multi-component WKI equations and their conservation laws
• Integrable couplings of vector AKNS soliton equations
• The multicomponent generalized Kaup–Newell hierarchy and its multicomponent integrable couplings system with two arbitrary functions
• The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems
• A coupled AKNS–Kaup–Newell soliton hierarchy
• A new loop algebra and a corresponding integrable hierarchy, as well as its integrable coupling
• A powerful approach to generate new integrable systems
• A discrete variational identity on semi-direct sums of Lie algebras
• 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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