On the properties of Bäcklund transformations on Painleväé 6th equations (Journal of Applied Science and Engineering A, 2023)
In his series of papers Okamoto give detailed explanation of Painlevé equations of types 2-6. On the other hand Kajiwara et.al described Bäcklund transformations for these types of Painlevé equations. Later, Bobenko and Eitner found that Painlevé equations of types 6 and 5 give rise Bonnet surfaces and vise-versa. In this research we study properties of Bäcklund transformations of 6th Painlevé equations P6 and determine explicit formula of such transformations which give a new Bonnet surfaces.