The sinh-Gordon defect matrix generalized for n defects

TL;DR

This paper derives a general formula for the n-defect matrix in the sinh-Gordon model, enabling the generation of Bäcklund transformations for systems with multiple type-I defects via gauge transformations.

Contribution

It introduces a unified expression for the n-defect matrix in the sinh-Gordon model, extending the understanding of defect interactions and transformations.

Findings

Derived a general n-defect matrix expression

Generated Bäcklund transformations for n defects

Enhanced understanding of defect interactions in sinh-Gordon model

Abstract

In this paper we obtain a general expression for the n-defect matrix for the sinh-Gordon model. This in turn generate the general B\"acklund transformations (BT) for a system with $n$ type-I defects, through a gauge transformation.