Darboux–Bäcklund transformations, dressing and impurities in multi-component NLS

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Abstract

We consider the discrete and continuous vector non-linear Schrödinger (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–Bäcklund transformation. Within this spirit we then explicitly work out the generic Bäcklund 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.
Original languageEnglish
Pages (from-to)91–114
Number of pages24
JournalNuclear Physics B
Volume918
Early online date3 Mar 2017
DOIs
Publication statusPublished - May 2017

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