On Schlesinger Transformations for Higher Order Painleve Equations

Abstract

In this thesis, we studied the Schlesinger transformations solutions of the first three members of the Jimbo-Miwa second and fourth 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 these members of Jimbo-Miwa second and fourth Painlev´e hierarchies