A Riemann-Hilbert Approach to the Heun Equation

Symmetry Integrability and Geometry-Methods and Applications

article

Boris Dubrovin¹  Andrei Kapaev² 

[1] SISSA;Deceased

关键词: Heun polynomials;    Riemann–Hilbert problem;    Painlev´e equations;   

DOI  :  10.3842/SIGMA.2018.093

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown