Construction of variable mass sine-Gordon and other novel inhomogeneous quantum integrable models

The inhomogeneity of the media or the external forces usually destroy the i ntegrability of a system. We propose a systematic construction of a class o f 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 Ablopiitz-Ladik model etc.