Asymptotics of Discrete Painleve V transcendents via the RiemannHilbert Approach

作者：Xu, S X; Zhao, Y Q^*

来源：Studies in Applied Mathematics, 2013, 130(3): 201-231.

DOI：10.1111/j.1467-9590.2012.00573.x

We study a system of discrete Painleve V equations via the RiemannHilbert approach. We begin with an isomonodromy problem for dPV, which admits a discrete RiemannHilbert problem formulation. The asymptotics of the discrete RiemannHilbert problem is derived via the nonlinear steepest descent method of Deift and Zhou. In the analysis, a parametrix is constructed in terms of specific Painleve 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.

• 出版日期2013-4
• 单位中山大学