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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2018 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209864 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862575419801206784 |
|---|---|
| author | Dubrovin, B. Kapaev, A. |
| author_facet | Dubrovin, B. Kapaev, A. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-04T23:10:33Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-209864 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-04T23:10:33Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| 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 |
| spellingShingle | A Riemann-Hilbert Approach to the Heun Equation Dubrovin, B. Kapaev, A. |
| title | 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_short | A Riemann-Hilbert Approach to the Heun Equation |
| title_sort | riemann-hilbert approach to the heun equation |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209864 |
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