$ \mathcal{N}=1 $ super sinh-Gordon model in the half line: breather solutions

Abstract

We examine the N=1 super sinh-Gordon (SShG) model restricted into the half line through a reduction from the defect SShG model. The B\"acklund transformations are employed to generate one-, two- and three-soliton solutions as well as a class of breathers solution for this model. The parameters of such classical solutions are shown to satisfy some contraints in order to preserve both integrability and supersymmetry properties of the original bulk theory. Additionally, previous results are recovered when performing the purely bosonic limit.