N-wave interactions related to simple Lie algebras. Z_2- reductions and   soliton solutions
  The reductions of the integrable N-wave type equations solvable by the inverse scattering method with the generalized Zakharov-Shabat systems L and related to some simple Lie algebra g are analyzed. The Zakharov- Shabat dressing method is extended to the case when g is an orthogonal algebra. Several types of one soliton solutions of the corresponding N- wave equations and their reductions are studied. We show that to each soliton solution one can relate a (semi-)simple subalgebra of g. We illustrate our results by 4-wave equations related to so(5) which find applications in Stockes-anti-Stockes wave generation. 
V. S. Gerdjikov (Institute for Nuclear Research and Nuclear Energy,   Sofia, Bulgaria), G. G. Grahovski (Institute for Nucle...