Discrete mKdV equation via Darboux transformation

TL;DR

This paper presents a novel approach to deriving the discrete potential mKdV equation through a specific discrete motion of planar curves, enhancing understanding of integrable discrete systems.

Contribution

It introduces a new method using Darboux transformation to obtain the discrete potential mKdV equation from discrete geometric motions.

Findings

Derived the discrete potential mKdV equation from discrete planar curve motions

Established a connection between geometric motions and integrable systems

Provided a framework for generating solutions via Darboux transformation

Abstract

We introduce an efficient route to obtaining the discrete potential mKdV equation emerging from a particular discrete motion of discrete planar curves.