Asymptotic analysis of instanton-type solutions

在这项研究中，我们从精确WKB分析的角度研究了大参数微分方程解的全局性质。主要有三个结果。首先，我们构造了属于第一个Painleve层次的方程的指数渐近（瞬时型）解，即一般形式解。其次，根据高斯方程的参数对高斯方程Stokes曲线的拓扑类型进行了分类。第三，定义并计算了大参数高斯方程Voros系数的显式形式，得到了它们的Borel和。我们得到了描述WKB解的参数Stokes现象的公式。

In this research, we have investigated the global properties of solutions to differential equations with a large parameter from the view point of the exact WKB analysis. There are three main results. Firstly, we have constructed the exponential-asymptotic (instanton-type) solutions, namely general formal solutions, to the equations which belong to the first Painleve hierarchies. Secondly, we have classified the topological types of the Stokes curves of the Gauss equation in terms of the parameters of the equation. Thirdly we have defined and computed explicit forms of the Voros coefficients of Gauss equation with a large parameter and obtained the Borel sums go them. We have obtained the formulas that describe parametric Stokes phenomena of WKB solutions.