Download or read book Isomonodromic Deformation Methods for the Initial Value Problems of the Painleve Equations written by Tariq Mahmood Khan and published by . This book was released on 1989 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Painleve equations appeared in the theory of ordinary differential equations at the beginning of century, in connection with a classification problem the equations of the form: q''=F(q' , q,x) where F is rational in q', algebraic in q and locally analytic in x, whose solutions are free from movable critical points. This dissertation deals with the initial problems of some Painleve equations via monodromypreserving deformation methods. The dissertation divided into three chapters. Chapter 1 presents preliminary introduction an information about the forthcoming chapters. General theory about Painleve equations is discussed. A brief summary about the solutions of matrix linear differential equations, monodromy preserving deformationtheory and the Stokes phenomenon is given here. In chapter 2 and 3, respectivel the initial value problems of 2 nd and 4th Painleve equations are solved via isomonodromic deformation theory, Special solutions of these Painlave equations expressible in terms of the classical transcendental functions are obtained.