Asymptotics of Discrete Painlevé V transcendents via the Riemann–Hilbert Approach
Asymptotics of Discrete Painlevé V transcendents via the Riemann–Hilbert Approach
复制标题
通过黎曼-希尔伯特方法的离散 Painlevé V 超越数的渐近
DOI：
10.1111/j.1467-9590.2012.00573.x
复制
发表时间：
2013
影响因子：
2.7
通讯作者：
Y.
中科院分区：
文献类型：
--
作者：
Shusheng Xu;Y.
We study a system of discrete Painlevé V equations via the Riemann–Hilbert approach. We begin with an isomonodromy problem for dPV, which admits a discrete Riemann–Hilbert problem formulation. The asymptotics of the discrete Riemann–Hilbert problem is derived via the nonlinear steepest descent method of Deift and Zhou. In the analysis, a parametrix is constructed in terms of specific Painlevé V transcendents. As a result, the asymptotics of the dPV transcendents are represented in terms of the PV transcendents. In the special case, our result confirms a conjecture of Borodin, that the difference Schlesinger equations converge to the differential Schlesinger equations at the solution level.
影响因子：
2.4
作者：
H. Sakai
通讯作者：
H. Sakai