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.
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页数：24
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