# Darboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation

## TL;DR

This paper derives Darboux transformations for the discrete potential mKdV equation from the Hirota-Miwa equation, enabling the construction of exact solutions for this integrable system.

## Contribution

It introduces Darboux and binary Darboux transformations specifically for the discrete potential mKdV equation, derived via a 2-periodic reduction from the Hirota-Miwa equation.

## Key findings

- Derived Lax pairs from Hirota-Miwa equation
- Constructed Darboux transformations for the discrete potential mKdV
- Demonstrated how to generate exact solutions

## Abstract

The paper presents two results. First it is shown how the discrete potential modified KdV equation and its Lax pairs in matrix form arise from the Hirota-Miwa equation by a 2-periodic reduction. Then Darboux transformations and binary Darboux transformations are derived for the discrete potential modified KdV equation and it is shown how these may be used to construct exact solutions.