On the Hamiltonian Structures and the Reductions of the KP Hierarchy

D.A. Depireux and Jeremy Schiff

Invited talk given by D.A.Depireux at the NSERC-CAP Workshop Quantum Groups, Integrable Models and Statistical Systems, Kingston, Ontario (July 1992). Published in workshop proceedings (Plenum 1993).

Recent work on a free field realization of the Hamiltonian structures of the classical KP hierarchy and of its flows is reviewed. It is shown that it corresponds to a reduction of KP to the NLS system.