Geometric Transformations on Null Curves in the Anti-de Sitter 3-Space

TL;DR

This paper introduces a geometric transformation on null curves in anti-de Sitter 3-space that induces the Bäcklund transformation for the KdV equation and satisfies a permutability property.

Contribution

It presents a novel geometric transformation on null curves in AdS3 that connects to integrable systems and demonstrates its permutability theorem.

Findings

Transformation induces Bäcklund transformation for KdV

Satisfies a permutability theorem

Implementation shown for constant bending null curves

Abstract

We provide a geometric transformation on null curves in the anti-de Sitter 3-space (AdS) which induces the B\"acklund transformation for the KdV equation. In addition, we show that this geometric transformation satisfies a suitable permutability theorem. We also illustrate how to implement it when the original null curve has constant bending.