Non-Integrability of Some Higher-Order Painlevé Equations in the Sense of Liouville

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2015
• ISSN: 1815-0659
• Main Authors: Christov, O., Georgiev, G.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2015
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/147104
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Non-Integrability of Some Higher-Order Painlevé Equations in the Sense of Liouville / O. Christov, G. Georgiev // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 32 назв. — англ.

In this paper we study the equation
 w⁽⁴⁾=5w′′(w²−w′)+5w(w′)²−⁵+(λz+α)w+γ,
 which is one of the higher-order Painlevé equations (i.e., equations in the polynomial class having the Painlevé property). Like the classical Painlevé equations, this equation admits a Hamiltonian formulatio...