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

References in corpus (3)

• Quantum and classical integrable sine-Gordon model with defect
• A multisymplectic approach to defects in integrable classical field theory
• Multisymplectic approach to integrable defects in the sine-Gordon model