  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 $gl_N$ 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.
