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Mathematics > Classical Analysis and ODEs

arXiv:2211.00886 (math)
[Submitted on 2 Nov 2022 (v1), last revised 13 Mar 2023 (this version, v2)]

Title:Elliptic asymptotics for the complete third Painlevé transcendents

Authors:Shun Shimomura
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Abstract:For a general solution of the third Painlevé equation of complete type we show the Boutroux ansatz near the point at infinity. It admits an asymptotic representation in terms of the Jacobi sn-function in cheese-like strips along generic directions. The expression is derived by using isomonodromy deformation of a linear system governed by the third Painlevé equation of this type. In our calculation of the WKB analysis, the treated Stokes curve ranges on both upper and lower sheets of the two sheeted Riemann surface.
Comments: 38 pages. arXiv admin note: substantial text overlap with arXiv:2207.11495
Subjects: Classical Analysis and ODEs (math.CA)
MSC classes: 34M55, 34M56, 34M40, 34M60
Cite as: arXiv:2211.00886 [math.CA]
  (or arXiv:2211.00886v2 [math.CA] for this version)
  https://doi.org/10.48550/arXiv.2211.00886

Submission history

From: Shun Shimomura [view email]
[v1] Wed, 2 Nov 2022 05:13:18 UTC (493 KB)
[v2] Mon, 13 Mar 2023 05:20:40 UTC (498 KB)
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