A Riemann-Hilbert approach to the Heun equation

DOI10.3842/SIGMA.2018.093zbMath1404.34100arXiv1809.02311OpenAlexW2890061625WikidataQ129277663 ScholiaQ129277663MaRDI QIDQ1792497

Andrei A. Kapaev, B. A. Dubrovin

Publication date: 12 October 2018

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1809.02311

zbMATH Keywords

Heun polynomialsRiemann-Hilbert problemPainlevé equationsHeun equation

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) General geometric structures on low-dimensional manifolds (57M50) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Entire and meromorphic solutions to ordinary differential equations in the complex domain (34M05) Linear ordinary differential equations and systems in the complex domain (34M03)

Related Items (5)

𝑞-Heun equation and initial-value space of 𝑞-Painlevé equation ⋮ Quantum spectral problems and isomonodromic deformations ⋮ On the monodromy manifold of \(q\)-Painlevé VI and its Riemann-Hilbert problem ⋮ Accessory parameters in confluent Heun equations and classical irregular conformal blocks ⋮ Stokes matrices of a reducible double confluent Heun equation via monodromy matrices of a reducible general Heun equation with symmetric finite singularities

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