Transformation properties of Painleve VI equation

Abstract

In this thesis, we studied the Schlesinger transformations of Painleve VI equation. We showed that Painleve VI equation admits Schlesinger transformations which relate a given solution of Paileve VI to solution of Painleve VI but with different values of the parameters. Using these transformations we obtained the corresponding Bäcklund transformations for Painleve VI. Also, we showed that the Schlesinger transformations and the corresponding Bäcklund transformations break down if and only if Painleve VI has certain one-parameter family of solutions.