A scalar Riemann–Hilbert problem on the torus: applications to the KdV equation
Analysis and Mathematical Physics(2022)
摘要
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.
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关键词
Riemann–Hilbert problem,KdV equation,Jacobi theta functions
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