A Riemann-Hilbert Approach to the Heun Equation

We describe the close connection between the linear system for the sixth Painlevé equation and the general Heun equation, formulate the Riemann-Hilbert problem for the Heun functions, and show how, in the case of reducible monodromy, the Riemann-Hilbert formalism can be used to construct explicit po...

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Бібліографічні деталі
Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2018
Автори: Dubrovin, B., Kapaev, A.
Формат: Стаття
Мова:English
Опубліковано: Інститут математики НАН України 2018
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/209864
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:A Riemann-Hilbert Approach to the Heun Equation / B. Dubrovin, A. Kapaev // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 30 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-209864
record_format dspace
spelling Dubrovin, B.
Kapaev, A.
2025-11-27T18:03:20Z
2018
A Riemann-Hilbert Approach to the Heun Equation / B. Dubrovin, A. Kapaev // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 30 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 34M03; 34M05; 34M35; 34M55; 57M50
arXiv: 1809.02311
https://nasplib.isofts.kiev.ua/handle/123456789/209864
https://doi.org/10.3842/SIGMA.2018.093
We describe the close connection between the linear system for the sixth Painlevé equation and the general Heun equation, formulate the Riemann-Hilbert problem for the Heun functions, and show how, in the case of reducible monodromy, the Riemann-Hilbert formalism can be used to construct explicit polynomial solutions of the Heun equation.
A.K. was supported by the project SPbGU 11.38.215.2014. He also thanks the staff of SISSA, where this project originated. Many thanks to the anonymous referees for their suggestions towards improving the manuscript.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
A Riemann-Hilbert Approach to the Heun Equation
Article
published earlier
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
title A Riemann-Hilbert Approach to the Heun Equation
spellingShingle A Riemann-Hilbert Approach to the Heun Equation
Dubrovin, B.
Kapaev, A.
title_short A Riemann-Hilbert Approach to the Heun Equation
title_full A Riemann-Hilbert Approach to the Heun Equation
title_fullStr A Riemann-Hilbert Approach to the Heun Equation
title_full_unstemmed A Riemann-Hilbert Approach to the Heun Equation
title_sort riemann-hilbert approach to the heun equation
author Dubrovin, B.
Kapaev, A.
author_facet Dubrovin, B.
Kapaev, A.
publishDate 2018
language English
container_title Symmetry, Integrability and Geometry: Methods and Applications
publisher Інститут математики НАН України
format Article
description We describe the close connection between the linear system for the sixth Painlevé equation and the general Heun equation, formulate the Riemann-Hilbert problem for the Heun functions, and show how, in the case of reducible monodromy, the Riemann-Hilbert formalism can be used to construct explicit polynomial solutions of the Heun equation.
issn 1815-0659
url https://nasplib.isofts.kiev.ua/handle/123456789/209864
citation_txt A Riemann-Hilbert Approach to the Heun Equation / B. Dubrovin, A. Kapaev // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 30 назв. — англ.
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