A scalar Riemann–Hilbert problem on the torus: applications to the KdV equation

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 s...

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Autores principales: Piorkowski, Mateusz, Teschl, Gerald
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9395479/
https://www.ncbi.nlm.nih.gov/pubmed/36035310
http://dx.doi.org/10.1007/s13324-022-00715-4
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author Piorkowski, Mateusz
Teschl, Gerald
author_facet Piorkowski, Mateusz
Teschl, Gerald
author_sort Piorkowski, Mateusz
collection PubMed
description 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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spelling pubmed-93954792022-08-24 A scalar Riemann–Hilbert problem on the torus: applications to the KdV equation Piorkowski, Mateusz Teschl, Gerald Anal Math Phys Article 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. Springer International Publishing 2022-08-22 2022 /pmc/articles/PMC9395479/ /pubmed/36035310 http://dx.doi.org/10.1007/s13324-022-00715-4 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Piorkowski, Mateusz
Teschl, Gerald
A scalar Riemann–Hilbert problem on the torus: applications to the KdV equation
title A scalar Riemann–Hilbert problem on the torus: applications to the KdV equation
title_full A scalar Riemann–Hilbert problem on the torus: applications to the KdV equation
title_fullStr A scalar Riemann–Hilbert problem on the torus: applications to the KdV equation
title_full_unstemmed A scalar Riemann–Hilbert problem on the torus: applications to the KdV equation
title_short A scalar Riemann–Hilbert problem on the torus: applications to the KdV equation
title_sort scalar riemann–hilbert problem on the torus: applications to the kdv equation
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9395479/
https://www.ncbi.nlm.nih.gov/pubmed/36035310
http://dx.doi.org/10.1007/s13324-022-00715-4
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