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arXiv · 2603.13332

Automorphisms of Stokes multipliers in higher-order WKBJ theory

Josh Shelton·Samuel Crew·Christopher J. Lustri
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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.

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BibTeXRIS

Josh Shelton, Samuel Crew, Christopher J. Lustri. 2026-03-05. Automorphisms of Stokes multipliers in higher-order WKBJ theory. https://arxiv.org/abs/2603.13332

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