  Integrable inhomogeneous versions of the models like NLS, Toda chain,
Ablowitz-Ladik model etc., though well known at the classical level, have never
been investigated for their possible quantum extensions. We propose a unifying
scheme for constructing and solving such quantum integrable inhomogeneous
models including a novel inhomogeneous sine-Gordon model, which avoids the
difficulty related to the customary non-isospectral flow by introducing the
inhomogeneities through some central elements of the underlying algebra.
