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