  The relationship between the nonlinear Schrodinger hierarchy and the
parafermion and SL(2,R)/U(1) coset models, analogous to the relationship
between the KdV hierarchy and the minimal models, is explained. To do this I
first present an in depth study of a series of integrable hierarchies related
to NLS, and write down an action from which any of these hierarchies, and the
associated second Poisson bracket structures, can be obtained. In quantizing
the free part of this action we find many features in common with the bosonized
parafermion and SL(2,R)/U(1) models, and particularly it is clear that the
quantum NLS hamiltonians are conserved quantities in these models. The first
few quantum NLS hamiltonians are constructed.
