Exactly solvable models in atomic and molecular physics

We construct integrable generalized models in a systematic way exploring different representations of the gl(N)$\mathit{gl}(N)$ algebra. The models 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 models is given through the analytical Bethe ansatz method. We further extend these results to the case of the superalgebra gl(M|N)$\mathit{gl}(M|N)$, providing in this way models which also include fermions.