Automorphisms of Stokes multipliers in higher-order WKBJ theory
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866910052500111360 |
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| author | Shelton, Josh Crew, Samuel Lustri, Christopher J. |
| author_facet | Shelton, Josh Crew, Samuel Lustri, Christopher J. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_13332 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Automorphisms of Stokes multipliers in higher-order WKBJ theory Shelton, Josh Crew, Samuel Lustri, Christopher J. Classical Analysis and ODEs Mathematical Physics 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. |
| title | Automorphisms of Stokes multipliers in higher-order WKBJ theory |
| topic | Classical Analysis and ODEs Mathematical Physics |
| url | https://arxiv.org/abs/2603.13332 |