论文标题
椭圆形渐近表示超越
Elliptic asymptotic representation of the fifth Painlevé transcendents
论文作者
论文摘要
对于第五次Parelevé超然，Jacobi $ \ Mathrm {sn} $ - 函数的渐近表示形式沿着无穷大点附近的通用方向呈现在类似奶酪的带中。其椭圆形的主要部分取决于单个整合常数，该常数是相位移位，并通过单构型数据进行参数，用于相关的异构膜变形。此外，在某个假设下，错误术语也由显式渐近公式表示，其前术语是根据$ \ m m i \ m m mathrm {sn} $ - 函数和$ \ vartheta $ function编写的，并包含另一个集成常数。本文包含对早期版本中Stokes图和相关结果的更正。
For the fifth Painlevé transcendents an asymptotic representation by the Jacobi $\mathrm{sn}$-function is presented in cheese-like strips along generic directions near the point at infinity. Its elliptic main part depends on a single integration constant, which is the phase shift and is parametrised by monodromy data for the associated isomonodromy deformation. In addition, under a certain supposition, the error term is also expressed by an explicit asymptotic formula, whose leading term is written in terms of integrals of the $\mathrm{sn}$-function and the $\vartheta$-function, and contains the other integration constant. This paper contains corrections of the Stokes graph and of the related results in the early version.
