Recursion Operator and B\"acklund Transformation for Super mKdV Hierarchy

TL;DR

This paper develops a recursion operator and B"acklund transformations for the supersymmetric mKdV hierarchy, revealing new algebraic structures and integrability properties within the affine  sl(2,1) algebra.

Contribution

It introduces a novel recursion operator and constructs B"acklund transformations for the super mKdV hierarchy within an affine algebra framework.

Findings

Recursion operator relates consecutive flows in the hierarchy.

B"acklund transformations are constructed via gauge transformations.

Hierarchy is embedded in an affine  sl(2,1) algebra.

Abstract

In this paper we consider the ${\cal N}=1$ supersymmetric mKdV hierarchy composed of positive odd flows embedded within an affine $\hat sl(2,1)$ algebra. Its B\"acklund transformations are constructed in terms of a gauge transformation preserving the zero curvature representation. The recursion operator relating consecutive flows is derived and shown to relate their B\"acklund transformations.