Recursion Operator and Bäcklund Transformation for Super mKdV Hierarchy

Abstract

In this paper we consider the $\mathcal{N}=1$ supersymmetric mKdV hierarchy composed of positive odd flows embedded within an affine $\hat{s}l(2,1)$ algebra. Its Bäcklund 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 Bäcklund transformations.

17 pages. Version accepted for publication in the Proceedings of the X International Symposium Quantum Theory and Symmetries and XII International Worshop Lie Theory and Its Applications in Physics