Abstract

A constructive method is proposed for the solution of the Riemann–Hilbert problem which is realized in the case of five singular points. The basic components of this method are the logarithmization of the product of matrix functions and the determination of the parameters of a related differential equation of Fuchsian type. The proposed method allows us to solve several related problems, namely, to factorize the piecewise constant matrix functions, to find partial indices and to explicitly solve the vector-matrix boundary value problem with the above piecewise constant matrix function as a coefficient.

中文翻译：

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具有五个奇异点的 $${2\times 2}$$ Fuchsian 系统的构建

摘要

提出了一种求解黎曼-希尔伯特问题的构造方法，该问题是在五个奇异点的情况下实现的。该方法的基本组成部分是矩阵函数乘积的对数化和 Fuchsian 型相关微分方程参数的确定。所提出的方法使我们能够解决几个相关问题，即对分段常数矩阵函数进行因式分解，找到部分索引以及以上述分段常数矩阵函数为系数显式求解向量-矩阵边界值问题。