On the constrained KP hierarchy

TL;DR

This paper explains how constrained KP hierarchies are related to symmetries of the KP hierarchy, showing that additional symmetries enable reduction to constrained KP from the KP hierarchy.

Contribution

It provides a symmetry-based explanation for constrained hierarchies, connecting them with the symmetries of the KP hierarchy.

Findings

Ordinary symmetries reduce KP to KdV hierarchies.

Additional symmetries enable reduction from KP to constrained KP.

Link between symmetries and hierarchy reductions established.

Abstract

An explanation for the so-called constrained hierarhies is presented by linking them with the symmetries of the KP hierarchy. While the existence of ordinary symmetries (belonging to the hierarchy) allows one to reduce the KP hierarchy to the KdV hierarchies, the existence of additional symmetries allows to reduce KP to the constrained KP.