A Riemann-Hilbert Approach to the Heun Equation

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dc.contributor.authorDubrovin, B.
dc.contributor.authorKapaev, A.
dc.date.accessioned2025-11-27T18:03:20Z
dc.date.issued2018
dc.description.abstractWe 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.
dc.description.sponsorshipA.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.
dc.identifier.citationA 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.
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2018.093
dc.identifier.issn1815-0659
dc.identifier.other2010 Mathematics Subject Classification: 34M03; 34M05; 34M35; 34M55; 57M50
dc.identifier.otherarXiv: 1809.02311
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/209864
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleA Riemann-Hilbert Approach to the Heun Equation
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2018, том 14, випуск за цей рік