Article
Anal. Math. Phys. 12, 112 (2022) [DOI: 10.1007/s13324-022-00715-4]

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

Mateusz Piorkowski and Gerald Teschl

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.

MSC2000: Primary 35Q15, 35Q53; Secondary 30F10, 33E05
Keywords: Riemann-Hilbert problem, KdV equation, Jacobi theta functions

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