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

Ognyan Christov, Georgi Georgiev

In this paper we study the equation $$w^{(4)}=5w"(w^2-w^{\prime })+5w(w^{\prime }{)}^2-w^5+(\lambda z+\alpha )w+\gamma ,$$ which is one of the higher-order Painlevé equations (i.e., equations in the…