  As is well-known, there exists a four parameter family of local interactions
in 1D. We interpret these parameters as coupling constants of delta-type
interactions which include different kinds of momentum dependent terms, and we
determine all cases leading to many-body systems of distinguishable particles
which are exactly solvable by the coordinate Bethe Ansatz. We find two such
families of systems, one with two independent coupling constants deforming the
well-known delta interaction model to non-identical particles, and the other
with a particular one-parameter combination of the delta- and (so-called)
delta-prime interaction. We also find that the model of non-identical particles
gives rise to a somewhat unusual solution of the Yang-Baxter relations. For the
other model we write down explicit formulas for all eigenfunctions.
