The partition function of the extended $r$-reduced Kadomtsev-Petviashvili hierarchy

TL;DR

This paper derives a specific solution for the extended r-reduced KP hierarchy using a generalized string equation, extending previous results from the r=2 case to arbitrary r≥2.

Contribution

It generalizes Buryak's recent solutions of the extended open KdV hierarchy to the extended r-reduced KP hierarchy for all r≥2.

Findings

Derived a particular solution for the extended r-reduced KP hierarchy.

Extended the solution framework from r=2 to arbitrary r≥2.

Connected the solution to a generalized string equation.

Abstract

We derive a particular solution of the extended $r$-reduced KP hierarchy, which is specified by a generalized string equation. The work is a generalization to arbitrary $r\geq 2$ of Buryak's recent results of a solution to the extended open KdV hierarchy which corresponds to $r=2$.