Automorphisms of Stokes multipliers in higher-order WKBJ theory
Abstract
We consider the Stokes phenomenon and higher-order Stokes phenomenon (HOSP) of formal asymptotic transseries arising in the WKBJ analysis of linear differential equations and integral problems. We introduce a framework of automorphisms that act on the Stokes constants of the divergent expansion, explained via late-late-term expansions and parametric Alien calculus, to capture this phenomenon. Our method is applied to a paradigmatic example: we obtain the full Stokes line structure and automorphisms for the Swallowtail problem from catastrophe theory, which contains four WKBJ components. We demonstrate that, in a system with four or more WKBJ components, the automorphism associated with the HOSP can itself change value across another higher-order Stokes line, which occurs when different higher-order Stokes lines intersect. We then argue that no additional special behaviour emerges for transseries with five or more WKBJ components.
Cite
@article{arxiv.2603.13332,
title = {Automorphisms of Stokes multipliers in higher-order WKBJ theory},
author = {Josh Shelton and Samuel Crew and Christopher J. Lustri},
journal= {arXiv preprint arXiv:2603.13332},
year = {2026}
}