On Schlesinger Transformtions For Third Painleve Hierarchy

Abstract

The main objective of this thesis is to study the Schlesinger transformations of first, second and third members of third Painlev´e hierarchy. We have calculated Schlesinger transformations for these equations, which transform a solution of the given equation to another solution of the same equation but with a different values of the parameters. Using Schlesinger transformations, we obtained the corresponding Backlund transformations for each of the considered equations. Finally, we discussed some special solutions of the second member of third Painlev´e hierarchy.