Darboux transformations for differential operators on the superline

TL;DR

This paper provides a comprehensive description of Darboux transformations for differential operators on the superline, demonstrating their factorization into elementary transformations, and extends similar results to operators on the ordinary line.

Contribution

It introduces a complete characterization of Darboux transformations on the superline and proves their factorization into elementary transformations, generalizing known results.

Findings

Every Darboux transformation on the superline factorizes into elementary transformations.

Similar factorization results hold for operators on the ordinary line.

The paper offers a full description of Darboux transformations for arbitrary differential operators.

Abstract

We give a full description of Darboux transformations of any order for arbitrary (nondegenerate) differential operators on the superline. We show that every Darboux transformation of such operators factorizes into elementary Darboux transformations of order one. Similar statement holds for operators on the ordinary line.