On Stieltjes relations, Painlevé-IV hierarchy and complex monodromy
On Stieltjes relations, Painlevé-IV hierarchy and complex monodromy
复制标题
关于 Stieltjes 关系、Painlevé-IV 等级制度和复杂单一性
DOI：
10.1088/0305-4470/34/16/318
复制
发表时间：
2000
期刊：
影响因子：
--
通讯作者：
A. P. Veselov
中科院分区：
文献类型：
--
作者：
A. P. Veselov
本文提出了第四类Painleve（PIV）超越量及其由缀饰链确定的高阶类似量的Stieltjes关系的推广。证明了如果某类有理函数满足这些关系，则它一定是某个高阶PIV方程的解。该方法是基于解释的Stieltjes关系的局部平凡的monodromy条件某些薛定谔方程在复杂的域。作为推论，利用PIV超越构造了一类新的平凡单值Schrodinger算子。
A generalization of the Stieltjes relations for the fourth Painleve (PIV) transcendents and their higher analogues determined by dressing chains is proposed. It is proven that if a rational function from a certain class satisfies these relations it must be a solution of some higher PIV equation. The approach is based on the interpretation of the Stieltjes relations as local trivial monodromy conditions for certain Schrodinger equations in the complex domain. As a corollary a new class of Schrodinger operators with trivial monodromy is constructed in terms of the PIV transcendents.