Solitons from dressing in an algebraic approach to the constrained KP hierarchy

The algebraic matrix hierarchy approach based on affine Lie sl(n) algebras leads to a variety of 1 + 1 soliton equations. By varying the rank of the u nderlying sl(n) algebra as well as its gradation in the affine setting, one encompasses the set of the soliton equations of the constrained KP hierarc hy. The soliton solutions are then obtained as elements of the orbits of the dr essing transformations constructed in terms of representations of the verte x operators of the affine sl(n) algebras realized in the unconventional gra dations. Such soliton solutions exhibit non-trivial dependence on the KdV ( odd) time flows and KP (odd and even) time Bows which distinguishes them Fr om the conventional structure of the Darboux-Backlund-Wronskian solutions o f the constrained KP hierarchy.