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 Riemann–Hilbert approach to the Heun equation / Dubrovin, Boris; Kapaev, Andrei. - In: SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS. - ISSN 1815-0659. - 14(2018), pp. 1-24. [10.3842/SIGMA.2018.093]

A Riemann–Hilbert approach to the Heun equation

Dubrovin, Boris
;
Kapaev, Andrei
2018

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.
14
1
24
093
https://doi.org/10.3842/SIGMA.2018.093
http://www.emis.de/journals/SIGMA/2018/093/sigma18-093.pdf
https://arxiv.org/abs/1809.02311
Dubrovin, Boris; Kapaev, Andrei
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11767/84232
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