Аннотация:
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.
\RBibitem{DubKap18}
\by Boris~Dubrovin, Andrei~Kapaev
\paper A Riemann--Hilbert Approach to the Heun Equation
\jour SIGMA
\yr 2018
\vol 14
\papernumber 093
\totalpages 24
\mathnet{http://mi.mathnet.ru/sigma1392}
\crossref{https://doi.org/10.3842/SIGMA.2018.093}
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Эта публикация цитируется в следующих 7 статьяx:
Shoko Sasaki, Shun Takagi, Kouichi Takemura, Contemporary Mathematics, 782, Recent Trends in Formal and Analytic Solutions of Diff. Equations, 2023, 119
Nalini Joshi, Pieter Roffelsen, “On the Monodromy Manifold of q-Painlevé VI and Its Riemann–Hilbert Problem”, Commun. Math. Phys., 404:1 (2023), 97
Stoyanova Ts., “Stokes Matrices of a Reducible Double Confluent Heun Equation Via Monodromy Matrices of a Reducible General Huen Equation With Symmetric Finite Singularities”, J. Dyn. Control Syst., 28:1 (2022), 207–245
Mikhail Bershtein, Pavlo Gavrylenko, Alba Grassi, “Quantum Spectral Problems and Isomonodromic Deformations”, Commun. Math. Phys., 393:1 (2022), 347
O. Lisovyy, A. Naidiuk, “Accessory parameters in confluent Heun equations and classical irregular conformal blocks”, Lett. Math. Phys., 111:6 (2021), 137
Xia J., Xu Sh.-X., Zhao Yu.-Q., “Isomonodromy Sets of Accessory Parameters For Heun Class Equations”, Stud. Appl. Math., 146:4 (2021), 901–952
B. C. da Cunha, J. P. Cavalcante, “Confluent conformal blocks and the teukolsky master equation”, Phys. Rev. D, 102:10 (2020), 105013
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