The Stokes phenomenon for some moment partial differential equations
S{\l}awomir Michalik, Bo\.zena Tkacz
TL;DR
This paper investigates the Stokes phenomenon in solutions to certain linear moment partial differential equations in two complex variables, utilizing summability, multisummability, and hyperfunction theories to analyze Stokes lines and solution behaviors.
Contribution
It introduces a comprehensive analysis of the Stokes phenomenon for moment PDEs with holomorphic Cauchy data, expanding understanding of solution structures and singularity behavior.
Findings
Description of Stokes and anti-Stokes lines
Characterization of jumps across Stokes lines
Construction of a maximal family of solutions
Abstract
We study the Stokes phenomenon for the solutions of general homogeneous linear moment partial differential equations with constant coefficients in two complex variables under condition that the Cauchy data are holomorphic on the complex plane but finitely many singular or branching points with the appropriate growth condition at the infinity. The main tools are the theory of summability and multisummability, and the theory of hyperfunctions. Using them we describe Stokes lines, anti-Stokes lines, jumps across Stokes lines, and a maximal family of solutions.
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