Unifying quantization for inhomogeneous integrable models

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.