Supersymmetric and Deformed Harry Dym hierarchies

TL;DR

This paper discusses the supersymmetrization of the Harry Dym hierarchy and introduces a new deformed hierarchy with two parameters, which is integrable and encompasses known systems in certain limits.

Contribution

It presents the first supersymmetric extension of the Harry Dym hierarchy and constructs a novel deformed hierarchy with arbitrary parameters that generalizes existing integrable systems.

Findings

The deformed hierarchy is integrable for all parameter values.

Various known integrable systems are recovered in specific parameter limits.

Supersymmetric extension broadens the applicability of the Harry Dym hierarchy.

Abstract

In this talk, we describe our recent results on the supersymmetrization of the Harry Dym hierarchy as well as a newly constructed deformed Harry Dym hierarchy which is integrable with two arbitrary parameters. In various limits of these parameters, the deformed hierarchy reduces to various known integrable systems.