Loop Algebra Symmetries and Commuting Flows for the Kadomtsev-Petviashvili Hierarchy

TL;DR

This paper explores the connection between loop algebra symmetries and commuting flows in the KP hierarchy, establishing the relationship with Kac-Moody-Virasoro symmetries and identifying local symmetries.

Contribution

It demonstrates the link between $\, ext{ extasciigrave}\hat ext{ extasciigrave}\gl(\infty)$ symmetry and Kac-Moody-Virasoro symmetries in the KP hierarchy, showing local symmetries are unique.

Findings

$\, ext{ extasciigrave}\hat ext{ extasciigrave}\gl(\infty)$ symmetry relates to commuting flows

Kac-Moody-Virasoro symmetries are the only local symmetries

Establishes the structure of symmetries in the KP hierarchy

Abstract

The relation between the $\widehat\gl(\infty)$ symmetry of the Kadomtsev-Petviashvili hierarchy and the Kac-Moody-Virasoro Lie point symmetries of the individual equations is established. The Lie point symmetries are shown to be the only local ones.