论文标题
PainlevéI和确切的WKB：两参数跨系列的Stokes现象
Painlevé I and exact WKB: Stokes phenomenon for two-parameter transseries
论文作者
论文摘要
一个多世纪以来，PainlevéI方程式在物理和数学中都发挥了重要作用。它的两参数解决方案家族以多种不同的方式进行了研究，但仍带来新的惊喜和发现。这些研究中的两个流行工具是使用确切的WKB方法的等异构粒细胞变形的理论，以及根据两参数跨系列的渐近描述。结合了两个思想流派的方法，并在Takei和合作者的工作之后，我们发现解决方案的完整，两参数连接公式在复杂的平面中跨越任意的Stokes。这些公式使我们能够研究整个跨系列解决方案家族的Stokes现象。特别是，我们恢复了Baldino，Schwick，Schiappa和Vega最近发现的Stokes数据的精确表达式，并将我们的连接公式与他们的连接公式进行了比较。我们还解释了将跨系参数选择与实际Painlevé过渡者相关的几个歧义，研究正式溶液的单肌，并为我们的结果提供了高精度的数值测试。
For more than a century, the Painlevé I equation has played an important role in both physics and mathematics. Its two-parameter family of solutions was studied in many different ways, yet still leads to new surprises and discoveries. Two popular tools in these studies are the theory of isomonodromic deformation that uses the exact WKB method, and the asymptotic description of transcendents in terms of two-parameter transseries. Combining methods from both schools of thought, and following work by Takei and collaborators, we find complete, two-parameter connection formulae for solutions when they cross arbitrary Stokes lines in the complex plane. These formulae allow us to study Stokes phenomenon for the full two-parameter family of transseries solutions. In particular, we recover the exact expressions for the Stokes data that were recently found by Baldino, Schwick, Schiappa and Vega and compare our connection formulae to theirs. We also explain several ambiguities in relating transseries parameter choices to actual Painlevé transcendents, study the monodromy of formal solutions, and provide high-precision numerical tests of our results.
