KdV solves BKP

TL;DR

This paper demonstrates that solutions to the KdV hierarchy can be transformed into solutions of the BKP hierarchy through a straightforward rescaling of variables.

Contribution

It establishes a direct link between KdV and BKP hierarchies, showing that KdV tau-functions also solve BKP after rescaling.

Findings

Any KdV tau-function solves BKP after rescaling

Rescaling of times connects KdV and BKP hierarchies

Simplifies understanding of hierarchy relationships

Abstract

In this note, we prove that any tau-function of the KdV hierarchy also solves the BKP hierarchy after a simple rescaling of times.