Symmetries of the Kadomstev-Petviashvili Hierarchy

TL;DR

This paper explores the algebraic symmetries of the KP hierarchy, linking infinite-dimensional Lie algebras with point symmetries of its equations, and computes these symmetries across the hierarchy.

Contribution

It establishes a connection between the $ ext{\widehat{\Sl}}(\infty)$ algebra and Kac-Moody-Virasoro symmetries, and calculates point symmetries for all KP hierarchy equations.

Findings

Identified the relation between $ ext{\widehat{\Sl}}(\infty)$ algebra and Kac-Moody-Virasoro symmetries.

Calculated point symmetries for all equations in the KP hierarchy.

Enhanced understanding of the symmetry structure of the KP hierarchy.

Abstract

The relation between the $\widehat{\Sl}(\infty)$ algebra of flows commuting with the KP hierarchy and the Kac-Moody-Virasoro Lie point symmetries of individual equations is established. This is used to calculate the point symmetries for all equations in the hierarchy.