Darboux Transformations for Supersymmetric Korteweg - de Vries Equations

TL;DR

This paper develops Darboux transformations for supersymmetric KdV equations, establishing supersymmetric analogs of classical transformations and deriving Bäcklund transformations for specific supersymmetric KdV systems.

Contribution

It introduces supersymmetric Darboux and Darboux-Levi transformations for supersymmetric KdV spectral problems, expanding the mathematical tools for supersymmetric integrable systems.

Findings

Established supersymmetric Darboux transformations for MRM sKdV and MR sKdV.

Derived several Bäcklund transformations for these supersymmetric systems.

Extended classical transformation techniques to supersymmetric integrable models.

Abstract

\hspace{.2in}We consider the Darboux type transformations for the spectral problems of supersymmetric KdV systems. The supersymmetric analogies of Darboux and Darboux-Levi transformations are established for the spectral problems of Manin-Radul-Mathieu sKdV and Manin-Radul sKdV. Several B\"acklund transformations are derived for the MRM sKdV and MR sKdV systems.