  We analyze a family of two-dimensional BCS Hamiltonians with general l-wave
pairing interactions, classifying the models in this family that are
Bethe-ansatz solvable in the finite-size regime. We show that these solutions
are characterized by nontrivial winding numbers, associated with topological
phases, in some part of the corresponding phase diagrams. By means of a
comparative study, we demonstrate benefits and limitations of the mean-field
approximation, which is the standard approach in the limit of a large number of
particles. The mean-field analysis also allows to extend part of the results
beyond integrability, clarifying the peculiarities associable with the
integrability itself.
