On the simpleness of zeros of Stokes multipliers

A direct method to find Stokes multipliers in closed form for P1 and more general integrable systems

We introduce a new rigorous method, based on Borel summability and asymptotic constants of motion generalizing \cite{invent} and \cite{ode1}, to analyze singular behavior of nonlinear ODEs in a neighborhood of infinity and provide global information about their solutions. In equations with the Painlevé-Kowalevski (P-K) property (stating that movable singularities are not branched) it allows for solving connection problems. The analysis in carried in detail for P$_1$, $y"=6y^2+z$, for which we find the Stokes multipliers in closed form and global asymptotics for solutions having power-like beha…

高阶WKBJ理论中Stokes系数的自同构

Automorphisms of Stokes multipliers in higher-order WKBJ theory

研究高阶Stokes现象中Stokes系数的自同构框架，通过参数Alien算术和晚期晚期项展开解释，应用于Swallowtail问题，揭示高阶Stokes线交点处自同构变化的机制。

On Stokes Matrices in terms of Connection Coefficients

The classical problem of computing a complete system of Stokes multipliers of a linear system of ODEs of rank one in terms of some connection coefficients of an associated hypergeometric system of ODEs, is solved with no genericness assumptions on the residue matrix at zero, by an extension of the method of [3].

线性微分方程中单级一阶奇点处Stokes乘子的严格数值计算

Rigorous numerical computation of the Stokes multipliers for linear differential equations with single level one

本文提出了一种高效算法用于计算线性微分方程在单级一阶奇点处的Stokes乘子，支持高精度计算并提供严格误差界。

Resurgent Deformations for an Ordinary Differential Equation of Order 2

We consider in the complex field the differential equation $\displaystyle \frac{d^2}{d x^2} Φ(x) = \frac{P_m(x,\a)}{x^2}Φ(x)$, where $P_m$ is a monic polynomial function of order $m$ with coefficients $\a=(a_1, ..., a_m)$. We investigate the asymptotic, resurgent, properties of the solutions at infinity, focusing in particular on the analytic dependence on $\a$ of the Stokes-Sibuya multipliers. Taking into account the non trivial monodromy at the origin, we derive a set of functional equations for the Stokes-Sibuya multipliers. We show how these functional relations can be used to compute the …

Rigorous Results in Existence and Selection of Saffman-Taylor Fingers by Kinetic Undercooling

The selection of Saffman-Taylor fingers by surface tension has been extensively investigated. In this paper we are concerned with the existence and selection of steadily translating symmetric finger solutions in a Hele-Shaw cell by small but non-zero kinetic undercooling ($ε^2 $). We rigorously conclude that for relative finger width $λ$ near one half, symmetric finger solutions exist in the asymptotic limit of undercooling $ε^2 ~\rightarrow ~0$ if the Stokes multiplier for a relatively simple nonlinear differential equation is zero. This Stokes multiplier $S$ depends on the parameter $α\equiv…