# Darboux transformation and soliton solutions of the semi-discrete massive Thirring model

## TL;DR

This paper derives a Darboux transformation for the semi-discrete massive Thirring model, enabling explicit soliton solutions that mirror those of the continuous model, advancing understanding of discrete integrable systems.

## Contribution

It introduces a one-fold Darboux transformation for the semi-discrete massive Thirring model and constructs explicit soliton solutions on various backgrounds.

## Key findings

- Discrete solitons share properties with continuous model solitons
- Exact soliton solutions are obtained on zero and nonzero backgrounds
- Transformation bridges solutions between discrete and continuous models

## Abstract

A one-fold Darboux transformation between solutions of the semi-discrete massive Thirring model is derived using the Lax pair and dressing methods. This transformation is used to find the exact expressions for soliton solutions on zero and nonzero backgrounds. It is shown that the discrete solitons have the same properties as solitons of the continuous massive Thirring model.