  A systematic approach to Liouville integrable defects is proposed, based on
an underlying Poisson algebraic structure. The non-linear Schrodinger model in
the presence of a single particle-like defect is investigated through this
algebraic approach. Local integrals of motions are constructed as well as the
time components of the corresponding Lax pairs. Continuity conditions imposed
upon the time components of the Lax pair to all orders give rise to sewing
conditions, which turn out to be compatible with the hierarchy of charges in
involution. Coincidence of our results with the continuum limit of the discrete
expressions obtained in earlier works further confirms our approach.
