  The inhomogeneity of the media or the external forces usually destroy the
integrability of a system. We propose a systematic construction of a class of
quantum models, which retains their exact integrability inspite of their
explicit inhomogeneity. Such models include variable mass sine-Gordon model,
cylindrical NLS, spin chains with impurity, inhomogeneous Toda chain, the
Ablowitz-Ladik model etc.
