Defects in the supersymmetric mKdV hierarchy via Backlund transformations

TL;DR

This paper explores the integrability of the supersymmetric mKdV hierarchy with defects by constructing super B"acklund transformations using two methods, and introduces type I defects while analyzing conserved quantities.

Contribution

It develops a general super B"acklund transformation framework for the supersymmetric mKdV hierarchy using defect matrices and superspace formalism, and applies it to introduce and analyze defects.

Findings

Super B"acklund transformations are constructed for the hierarchy.

Explicit B"acklund equations are derived for specific flows.

Type I defects are introduced and integrability is analyzed.

Abstract

The integrability of the ${\cal N}=1$ supersymmetric modified Korteweg de-Vries (smKdV) hierarchy in the presence of defects is investigated through the construction of its super B\"acklund transformation. The construction of such transformation is performed by using essentially two methods: the B\"acklund-defect matrix approach and the superfield approach. Firstly, we employ the defect matrix associated to the hierarchy which turns out to be the same for the supersymmetric sinh-Gordon (sshG) model. The method is general for all flows and as an example we derive explicitly the B\"acklund equations in components for the first few flows of the hierarchy, namely $t_3$ and $t_5$. Secondly, the supersymmetric extension of the B\"acklund transformation in the superspace formalism is constructed for those flows. Finally, this super B\"acklund transformation is employed to introduce type I defects for the supersymmetric mKdV hierarchy. Further integrability aspects by considering modified conserved quantities are derived from the defect matrix.