  The analysis and the classification of all reductions for the nonlinear
evolution equations solvable by the inverse scattering method is an interesting
and still open problem. We show how the second order reductions of the N-wave
interactions related to low-rank simple Lie algebras g can be embedded also in
the Weyl group of g. This allows us to display along with the well known ones a
number of new types of integrable N-wave systems. Some of the reduced systems
find applications to nonlinear optics.
