The generalized non-linear Schrodinger model on the interval

Abstract

The generalized (1+1)-D non-linear Schrodinger (NLS) theory with particular integrable boundary conditions is considered. More precisely, two distinct types of boundary conditions, known as soliton preserving (SP) and soliton non-preserving (SNP), are implemented into the classical $g{l}_N$ NLS model. Based on this choice of boundaries the relevant conserved quantities are computed and the corresponding equations of motion are derived. A suitable quantum lattice version of the boundary generalized NLS model is also investigated. The first non-trivial local integral of motion is explicitly computed, and the spectrum and Bethe Ansatz equations are derived for the soliton non-preserving boundary conditions.

33 pages, Latex. Minor misprints corrected

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• Defects in the discrete non-linear Schrodinger model
• Boundary Lax pairs for the $A_n^{(1)}$ Toda field theories
• Systematic classical continuum limits of integrable spin chains and emerging novel dualities
• Non-commutative NLS-type hierarchies: dressing & solutions
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• Classical impurities associated to high rank algebras
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