A Riemann-Hilbert Approach to the Heun Equation

被引：5

作者：

Dubrovin, Boris ^{[1
]}

Kapaev, Andrei ^{[1
]}

机构：

[1] SISSA, Via Bonomea 265, I-34136 Trieste, Italy

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2018年 / 14卷

关键词：

Heun polynomials; Riemann-Hilbert problem; Painleve equations; ORDINARY DIFFERENTIAL-EQUATIONS; PAINLEVE; MONODROMY; TRANSCENDENTS; DEFORMATION;

D O I：

10.3842/SIGMA.2018.093

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We describe the close connection between the linear system for the sixth Painleve 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.

引用

页数：24

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