We construct integrable generalized mo
dels in a systematic way exploring different representations of the
gl(N) algebra. The mo
dels are then interpreted in the context of atomic and molecular physics, most of them related to different types of Bose–Einstein condensates. The spectrum of the mo
dels is given through the analytical Bethe ansatz method. We further extend these results to the case of the superalgebra
gl(M|N), providing in this way mo
dels which also include fermions.