The compatibility of additional symmetry and gauge transformations for the constrained discrete Kadomtsev-Petviashvili hierarchy

TL;DR

This paper investigates how gauge transformations and additional symmetries interact within the constrained discrete KP hierarchy, showing they preserve the hierarchy's structure up to certain flow shifts.

Contribution

It demonstrates the compatibility between gauge transformations and additional symmetries in the constrained discrete KP hierarchy, preserving its form under specific conditions.

Findings

Gauge transformations preserve the form of additional symmetries.

Compatibility is maintained up to shifts in additional flows.

The hierarchy's structure remains intact under these transformations.

Abstract

In this paper, the compatibility between the gauge transformations and the additional symmetry of the constrained discrete Kadomtsev-Petviashvili hierarchy is given, which preserving the form of the additional symmetry of the cdKP hierarchy, up to shifting of the corresponding additional flows by ordinary time flows.