A Constructive Proof for the Umemura Polynomials of the Third Painlevé Equation

• Опубліковано в: : Symmetry, Integrability and Geometry: Methods and Applications
• Дата: 2023
• Автори: Clarkson, Peter A., Law, Chun-Kong, Lin, Chia-Hua
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут математики НАН України 2023
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/212004
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: A Constructive Proof for the Umemura Polynomials of the Third Painlevé Equation. Peter A. Clarkson, Chun-Kong Law and Chia-Hua Lin. SIGMA 19 (2023), 080, 20 pages

We are concerned with the Umemura polynomials associated with rational solutions of the third Painlevé equation. We extend Taneda's method, which was developed for the Yablonskii-Vorob'ev polynomials associated with the second Painlevé equation, to give an algebraic proof that the rational...