Reductions of N-wave interactions related to low-rank simple Lie   algebras. I: Z_2- reductions
  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. 
V. S. Gerdjikov (Institute for Nuclear Research and Nuclear Energy,   Sofia, Bulgaria), G. G. Grahovski (Institute for Nucle...