Supersymmetric Sawada-Kotera Equation: B\"{a}cklund-Darboux Transformations and Applications

TL;DR

This paper develops Darboux and Bäcklund transformations for the supersymmetric Sawada-Kotera equation, enabling solution generation and connecting discrete and continuous systems in supersymmetric integrable models.

Contribution

It introduces new transformations for the supersymmetric Sawada-Kotera equation and explores their applications to solution construction and semi-discrete systems.

Findings

Constructed Darboux and Bäcklund transformations for SSK

Derived nonlinear superposition formula for SSK

Connected semi-discrete systems to the continuum SKK equation

Abstract

In this paper, we construct a Darboux transformation and the related B\"acklund transformation for the supersymmetric Sawada-Kotera (SSK) equation. The associated nonlinear superposition formula is also worked out. We demonstrate that these are natural extensions of the similar results of the Sawada-Kotera equation and may be applied to produce the solutions of the SSK equation. Also, we present two semi-discrete systems and show that the continuum limit of one of them goes to the SKK equation.