N=1 super sinh-Gordon model in the half line: Breather solutions

TL;DR

This paper studies the N=1 super sinh-Gordon model on a half-line, deriving breather and soliton solutions using Bäcklund transformations while ensuring the model's integrability and supersymmetry are preserved.

Contribution

It introduces a method to generate explicit soliton and breather solutions for the half-line super sinh-Gordon model, maintaining key symmetries and extending previous bosonic results.

Findings

Derived explicit breather solutions for the half-line model

Established parameter constraints for preserving integrability and supersymmetry

Recovered previous bosonic results in the appropriate limit

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.