Extended discrete KP hierarchy and its reductions from a geometric viewpoint

Abstract

We interpret the recently suggested extended discrete KP (Toda lattice) hierarchy from a geometrical point of view. We show that the latter corresponds to the union of invariant submanifolds $S_0^n$ of the system which is a chain of infinitely many copies of Darboux-KP hierarchy, while the intersections $S_0^n\cap S_{l-1}^{ln-r}$ yields a number of reductions to $l$-field lattices.