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

We provide a geometric transformation on null curves in the anti-de Sitter $3$-space (AdS) which induces the Bäcklund 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.