The generalized Zakharov-Shabat system and the soliton perturbations

DOI10.1007/BF01016144zbMath0850.35108MaRDI QIDQ1918825

Vladimir S. Gerdjikov

Publication date: 21 July 1996

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

inverse scattering methodmatrix nonlinear Schrödinger equationsoliton perturbationsgeneralized Zakharov-Shabat systemmatrix \(n\)-wave equations

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Soliton equations (35Q51)

Related Items (4)

Multicomponent NLS-type equations on symmetric spaces and their reductions ⋮ Drinfel'd-Sokolov construction and exact solutions of vector modified KdV hierarchy ⋮ Noncommutative integrability and recursion operators ⋮ The generalised Zakharov–Shabat system and the gauge group action

Cites Work

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• On the spectral theory of the integro-differential operator Lambda generating nonlinear evolution equations
• Bäcklund transformations for nonlinear sigma models with values in Riemannian symmetric spaces
• On the complete integrability of completely integrable systems
• Nonlinear Schrödinger equations and simple Lie algebras
• Gauge covariant theory of the generating operator. I
• Generalised Fourier transforms for the soliton equations. Gauge-covariant formulation
• C-integrable nonlinear partial differentiation equations. I
• Expansions over the 'squared' solutions and the inhomogeneous nonlinear Schrodinger equation

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