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Symmetry, Integrability and Geometry: Methods and Applications, 2018, Volume 14, 093, 24 pp.
DOI: https://doi.org/10.3842/SIGMA.2018.093 (Mi sigma1392) 		 
This article is cited in 7 scientific papers (total in 7 papers)

A Riemann–Hilbert Approach to the Heun Equation

Boris Dubrovina, Andrei Kapaevb

a SISSA, Via Bonomea 265, 34136, Trieste, Italy
b Deceased
Full-text PDF (570 kB) Citations (7)
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DOI: https://doi.org/10.3842/SIGMA.2018.093
Abstract: 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.
Keywords: Heun polynomials; Riemann–Hilbert problem; Painlevé equations.
Funding agency Grant number
Saint Petersburg State University 11.38.215.2014
Acknowledgments A.K. was supported by the project SPbGU 11.38.215.2014.
Received: February 7, 2018; in final form August 15, 2018; Published online September 7, 2018
Bibliographic databases:
Document Type: Article
MSC: 34M03; 34M05; 34M35; 34M55; 57M50
Language: English
Citation: Boris Dubrovin, Andrei Kapaev, “A Riemann–Hilbert Approach to the Heun Equation”, SIGMA, 14 (2018), 093, 24 pp.
Citation in format AMSBIB
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\paper A Riemann--Hilbert Approach to the Heun Equation
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    • This publication is cited in the following 7 articles:
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    		Symmetry, Integrability and Geometry: Methods and Applications
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