Bäcklund Transformations for First and Second Painlevé Hierarchies

Abstract

We give Bäcklund transformations for first and second Painlevé hierarchies. These Bäcklund transformations are generalization of known Bäcklund transformations of the first and second Painlevé equations and they relate the considered hierarchies to new hierarchies of Painlevé-type equations.

Keywords

• Painlevé hierarchies
• Bäcklund transformations