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

• Опубліковано в: : Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2024
• Автори: Barhoumi, Ahmad, Lisovyy, Oleg, Miller, Peter D., Prokhorov, Andrei
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут математики НАН України 2024
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/212104
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: 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...