Negative Flows of the KP-Hierarchy

TL;DR

This paper develops a Grassmannian-like framework for the potential KP-hierarchy that incorporates negative flows, extending the tau-function concept and comparing with existing results by notable researchers.

Contribution

It introduces a novel Grassmannian formulation for the potential KP-hierarchy that includes negative flows, broadening the theoretical understanding of integrable systems.

Findings

Generalized tau-function to include negative flows

Established connections with Hirota, Satsuma, and Bogoyavlenskii's work

Provided a new perspective on the structure of the KP-hierarchy

Abstract

We construct a Grassmannian-like formulation for the potential KP-hierarchy including additional ``negative'' flows. Our approach will generalize the notion of a tau-function to include negative flows. We compare the resulting hierarchy with results by Hirota, Satsuma and Bogoyavlenskii.