On Stokes phenomena for the alternate discrete PI equation
On Stokes phenomena for the alternate discrete PI equation
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交替离散 PI 方程的斯托克斯现象
DOI：
10.1007/978-3-319-52842-7_10
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Nalini Joshi and Yoshitsugu Takei
中科院分区：
文献类型：
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作者：
Nalini Joshi and Yoshitsugu Takei
交替离散PI方程（或alt-dPI）通过Bäcklund变换从连续第二Painlevé方程（PII）产生。在这篇公告论文中，我们考虑斯托克斯现象（alt-dPI）从精确的WKB分析的观点。在构造了（alt-dPI）的跨级数解并定义了其Stokes几何之后，我们得到了描述（alt-dPI）的跨级数解在其Stokes曲线上的Stokes现象的显式连接公式.推导是基于与（PII）和（alt-dPI）相关的Lax对的斯托克斯乘子的计算。详细的证明和计算将在我们即将发表的论文中讨论。
The alternate discrete PI equation (or alt-dPI) arises from the continuous second Painlevé equation (PII) through Bäcklund transformations. In this announcement paper we consider Stokes phenomena for (alt-dPI) from the viewpoint of exact WKB analysis. After constructing transseries solutions and defining the Stokes geometry of (alt-dPI), we derive explicit connection formulas that describe Stokes phenomena for transseries solutions of (alt-dPI) on its Stokes curves. The derivation is based on the computation of Stokes multipliers of the Lax pair associated with (PII) and (alt-dPI). The detailed proof and computations will be discussed in our forthcoming paper.