Rational Solutions of Painlevé V from Hankel Determinants and the Asymptotics of Their Pole Locations

• Veröffentlicht in: Symmetry, Integrability and Geometry: Methods and Applications
• Datum: 2025
• Hauptverfasser: Balogoun, Malik, Bertola, Marco
• Format: Artikel
• Sprache: Englisch
• Veröffentlicht: Інститут математики НАН України 2025
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/214185
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: Rational Solutions of Painlevé V from Hankel Determinants and the Asymptotics of Their Pole Locations. Malik Balogoun and Marco Bertola. SIGMA 21 (2025), 097, 50 pages

In this paper, we analyze the asymptotic behaviour of the poles of certain rational solutions of the fifth Painlevé equation. These solutions are constructed by relating the corresponding tau function to a Hankel determinant of a certain sequence of moments. This approach was also used by one of the...