Painlevé-III Monodromy Maps Under the ₆ → ₈ Confluence and Applications to the Large-Parameter Asymptotics of Rational Solutions

• 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
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Painlevé-III Monodromy Maps Under the ₆ → ₈ 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(₆), is given by d²/d² = 1/(d/d)² − 1/ d/d + (α² + β)/ + 4³ − 4/, α, β ∈ ℂ. Starting from a generic initial solution ₀() corresponding to parameters α, β, denoted as the triple (₀(), α, β), we apply an explicit Bäcklun...