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 facilitate the implementation of this reduction on the level of the solutions, the typical multi-component KP solutions are mapped onto solutions of a Toda molecule-type equation from which (Wronskian and Grammian) solutions for the constrained KP hierarchy follow. The reduction of the associated linear systems is discussed and its importance for the choice of bilinear representation of the reduced systems is explained. (C) 1999 American Institute of Physics. [S0022-2488(99)01310-9].