Inspired by recent results on the effect of integrable boundary conditions on
the bulk behavior of an integrable system, and in particular on the behavior of
an existing defect we systematically formulate the Lax pairs in the
simultaneous presence of integrable boundaries and defects. The respective
sewing conditions as well as the relevant equations of motion on the defect
point are accordingly extracted. We consider a specific prototype i.e. the
vector non-linear Schr\"{o}dinger (NLS) model to exemplify our construction.
This model displays a highly non-trivial behavior and allows the existence of
two distinct types of boundary conditions based on the reflection algebra or
the twisted Yangian.Comment: 19 pages, Latex. A few comments and clarifications added. Version to
appear in J. Phys.
