Trans-Series Asymptotics of Solutions to the Degenerate Painlevé III Equation: A Case Study

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2025
• ISSN: 1815-0659
• Main Author: Vartanian, Arthur
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2025
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/214097
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Trans-Series Asymptotics of Solutions to the Degenerate Painlevé III Equation: A Case Study. Arthur Vartanian. SIGMA 21 (2025), 067, 135 pages

A one-parameter family of trans-series asymptotics as τ → ±∞ and τ → ±i∞ for solutions of the degenerate Painlevé III equation (DP3E), ′′(τ) = (′(τ))²/(τ) − ′(τ)/τ + 1/τ(−8ε(u(τ))² + 2) + ²/(τ), where ε ∈ {±1}, ∈ ℂ, and ∈ ℝ∖{0}, are parametrised in terms of the monodromy data of an associated firs...