On the dressing method for the generalised Zakharov-Shabat system

DOI10.1016/j.nuclphysb.2004.06.039zbMath1151.37325arXivmath-ph/0402031OpenAlexW2081195137MaRDI QIDQ874178

Rossen I. Ivanov

Publication date: 5 April 2007

Published in: Nuclear Physics. B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0402031

zbMATH Keywords

solitonsnonlinear evolution equationsinverse scattering method

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Groups and algebras in quantum theory and relations with integrable systems (81R12) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

Related Items (15)

On the \(N\)-wave equations and soliton interactions in two and three dimensions ⋮ Solutions of multi-component NLS models and spinor Bose-Einstein condensates ⋮ On the Caudrey-Beals-Coifman System and the Gauge Group Action ⋮ On integrable wave interactions and Lax pairs on symmetric spaces ⋮ Exact solutions of a two-dimensional nonlinear Schrödinger equation ⋮ Kulish-Sklyanin-type models: integrability and reductions ⋮ Dressing Method for the Degasperis-Procesi Equation ⋮ Nonlocal reductions of the multicomponent nonlinear Schrödinger equation on symmetric spaces ⋮ An integrable decomposition of a model of dynamics of spinor Bose-Einstein condensates ⋮ Application of the Riemann-Hilbert approach to the multicomponent AKNS integrable hierarchies ⋮ The \(N\)-wave equations with \(\mathcal{PT}\) symmetry ⋮ Fordy-Kulish model and spinor Bose-Einstein condensate ⋮ Riemann-Hilbert problems and soliton solutions for a multi-component cubic-quintic nonlinear Schrödinger equation ⋮ The generalised Zakharov–Shabat system and the gauge group action ⋮ NLS-type equations from quadratic pencil of Lax operators: negative flows

Cites Work

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• Generalised Fourier transforms for the soliton equations. Gauge-covariant formulation
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Bäcklund transformations and loop group actions
• Reductions ofN-wave interactions related to low-rank simple Lie algebras: I. ℤ₂-reductions

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