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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2024 |
| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2024
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212104 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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 |