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

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2024
• Hauptverfasser: Barhoumi, Ahmad, Lisovyy, Oleg, Miller, Peter D., Prokhorov, Andrei
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2024
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/212104
• 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

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...