A scalar Riemann-Hilbert problem on the torus: Applications to the KdV equation
Analysis of PDEs
2021-06-22 v1
Abstract
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 matrix-valued solutions in terms of Jacobi theta functions. We compare our results with those obtained in recent literature.
Cite
@article{arxiv.2106.10948,
title = {A scalar Riemann-Hilbert problem on the torus: Applications to the KdV equation},
author = {Mateusz Piorkowski and Gerald Teschl},
journal= {arXiv preprint arXiv:2106.10948},
year = {2021}
}