Uniformization and transcendence of solutions for the first and second Painlevé hierarchies
The first and second Painlevé equation hierarchies are considered. Relations between them are given. Bäcklund transformations for second Painlevé equations of higher order are presented. Some rational solutions to these equations are obtained. The indices for the first and second Painlevé equations of fourth order are found. These equations are shown to pass the Painlevé test. Lax pairs for the first and second Painlevé equations of higher order are given. The transcendence of the solutions to the first Painlevé hierarchy is discussed.
first and second Painlevé equations of fourth order
scientific article; zbMATH DE number 1411890
scientific article