Painlevé-III Monodromy Maps Under the 𝐷₆ → 𝐷₈ Confluence and Applications to the Large-Parameter Asymptotics of Rational Solutions

The third Painlevé equation in its generic form, often referred to as Painlevé-III(𝐷₆), is given by d²𝑢/d𝑥² = 1/𝑢(d𝑢/d𝑥)² − 1/𝑥 d𝑢/d𝑥 + (α𝑢² + β)/𝑥 + 4𝑢³ − 4/𝑢, α, β ∈ ℂ. Starting from a generic initial solution 𝑢₀(𝑥) corresponding to parameters α, β, denoted as the triple (𝑢₀(𝑥), α, β), we apply an...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2024
Main Authors: Barhoumi, Ahmad, Lisovyy, Oleg, Miller, Peter D., Prokhorov, Andrei
Format: Article
Language:English
Published: Інститут математики НАН України 2024
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/212104
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Painlevé-III Monodromy Maps Under the 𝐷₆ → 𝐷₈ Confluence and Applications to the Large-Parameter Asymptotics of Rational Solutions. Ahmad Barhoumi, Oleg Lisovyy, Peter D. Miller and Andrei Prokhorov. SIGMA 20 (2024), 019, 77 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine