• Corpus ID: 235490272

# A scalar Riemann-Hilbert problem on the torus: Applications to the KdV equation

```@inproceedings{Piorkowski2021ASR,
title={A scalar Riemann-Hilbert problem on the torus: Applications to the KdV equation},
author={Mateusz Piorkowski and Gerald Teschl},
year={2021}
}```
• Published 21 June 2021
• Mathematics
We take a closer look at the Riemann–Hilbert problem associated to one-gap solutions of the Korteweg–de Vries equation. To gain more insight, we reformulate it as a scalar Riemann–Hilbert problem on the torus. This enables us to derive deductively the model vector-valued and singular matrixvalued solutions in terms of Jacobi theta functions. We compare our results with those obtained in recent literature.

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