Darboux-Backlund transformations, dressing & impurities in multi-component NLS

Abstract

We consider the discrete and continuous vector non-linear Schrodinger (NLS) model. We focus on the case where space-like local discontinuities are present, and we are primarily interested in the time evolution on the defect point. This in turn yields the time part of a typical Darboux-Backlund transformation. Within this spirit we then explicitly work out the generic Backlund transformation and the dressing associated to both discrete and continuous spectrum, i.e. the Darboux transformation is expressed in the matrix and integral representation respectively.

30 pages, Latex. Typos corrected, version to appear in NBP

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Cited by in corpus (9)

• Non-commutative NLS-type hierarchies: dressing & solutions
• Partial differential systems with nonlocal nonlinearities: Generation and solutions
• Time-like boundary conditions in the NLS model
• Drinfel'd-Sokolov construction and exact solutions of vector modified KdV hierarchy
• Solitons: conservation laws & dressing methods
• Discretizations of the generalized AKNS scheme
• An algebraic approach to discrete time integrability
• Stochastic analysis & discrete quantum systems
• On refactorization problems and rational Lax matrices of quadrirational Yang-Baxter maps