Multicomponent integrable wave equations I. Darboux-Dressing Transformation

The Darboux-Dressing Transformations are applied to the Lax pair associated to systems of coupled nonlinear wave equations in the case of boundary values which are appropriate to both bright and dark soliton solutions. The general formalism is set up and the relevant equations are explicitly solved. Several instances of multicomponent wave equations of applicative interest, such as vector nonlinear Schroedinger-type equations and three resonant wave equations are considered.