On The Hamiltonian Structures and The Reductions of The KP Hierarchy

TL;DR

This paper reviews the Hamiltonian structures of the classical KP hierarchy, showing their reduction to the NLS system, and discusses related free field realizations within integrable models.

Contribution

It introduces a new perspective on the Hamiltonian structures of the KP hierarchy and their reduction to the NLS system, connecting free field realizations to integrable models.

Findings

Hamiltonian structures of the KP hierarchy are related to free field realizations.

The KP hierarchy can be reduced to the NLS system.

The reduction provides insights into the integrable structure of these systems.

Abstract

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. (Talk given by D.A.D. at the NSERC-CAP Workshop on Quantum Groups, Integrable Models and Statistical Systems, Kingston, Canada July 13-17 1992.)