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Extended Discrete KP Hierarchy and its Reductions from a Geometric Viewpoint

Authors:	Svinin Andrei K.

Affiliation:	(1) Institute of System Dynamics and Control Theory, Siberian Branch of Russian Academy of Sciences, PO Box 1233, 664033 Irkutsk, Russia

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 S₀ⁿ 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 reduction s to l-field lattices.

Keywords:	discrete KP hierarchy invariant submanifold
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