Gerdjikov V.S.Kostov N.A.Valchev T.I.2024-07-102024-07-102024-07-102024-07-102007-01-011815-065910.3842/SIGMA.2007.039SCOPUS_ID:84889235929https://rlib.uctm.edu/handle/123456789/295We consider N-wave type equations related to the orthogonal algebras obtained from the generic ones via additional reductions. The first Z2-reduction is the canonical one. We impose a second Z2-reduction and consider also the combined action of both reductions. For all three types of N-wave equations we construct the soliton solutions by appropriately modifying the Zakharov-Shabat dressing method. We also briefly discuss the different types of one-soliton solutions. Especially rich are the types of one-soliton solutions in the case when both reductions are applied. This is due to the fact that we have two different configurations of eigenvalues for the Lax operator L: doublets, which consist of pairs of purely imaginary eigenvalues, and quadruplets. Such situation is analogous to the one encountered in the sine-Gordon case, which allows two types of solitons: kinks and breathers. A new physical system, describing Stokes-anti Stokes Raman scattering is obtained. It is represented by a 4-wave equation related to the B2algebra with a canonical Z2reduction.enArticle