KP constraints from reduced multi-component hierarchies

The (m-vector) k-constrained Kadomtsev-Petviashvili (KP) hierarchy is shown to be a "pseudo"-reduction of the (m+1)-component KP hierarchy. To facilit ate the implementation of this reduction on the level of the solutions, the typical multi-component KP solutions are mapped onto solutions of a Toda m olecule-type equation from which (Wronskian and Grammian) solutions for the constrained KP hierarchy follow. The reduction of the associated linear sy stems is discussed and its importance for the choice of bilinear representa tion of the reduced systems is explained. (C) 1999 American Institute of Ph ysics. [S0022-2488(99)01310-9].