环面上的一个标量黎曼-希尔伯特问题：对KdV方程的应用
A scalar Riemann-Hilbert problem on the torus: applications to the KdV equation.
作者信息
Piorkowski Mateusz, Teschl Gerald
机构信息
Department of Mathematics, KU Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium.
Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria.
出版信息
Anal Math Phys. 2022;12(5):112. doi: 10.1007/s13324-022-00715-4. Epub 2022 Aug 22.
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.
我们更深入地研究与Korteweg-de Vries方程的单间隙解相关的黎曼-希尔伯特问题。为了获得更多见解，我们将其重新表述为环面上的标量黎曼-希尔伯特问题。这使我们能够根据雅可比θ函数演绎地推导出模型向量值和奇异矩阵值解。我们将我们的结果与最近文献中获得的结果进行比较。
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