Painlevé denklemlerinin bäcklund dönüşümleri ve ayrık painlevé denklemleri

ABSTRACTü ´BACKLUND TRANSFORMATIONS OF PAINLEVEEQUATIONS AND DISCRETE EQUATIONS OF´PAINLEVE TYPEKürşad TosunusM.S. in MathematicsSupervisor: Assoc. Prof. Dr. Uğurhan Muğang gSeptember, 2004With the help of the Schlesinger transformations, we obtain the Bücklundatransformations of the classical continuous Painlev´ equations (PII-PVI). Theneusing these Bücklund transformations we derived the corresponding discrete equa-ations. The main idea in obtaining these equations is to eliminate y from theBücklund transformations, Ti and Tj , in such a way that Ti ◦ Tj = Tj ◦ Ti = I.aThen we obtain an algebraic relation between yi , y and yj . This algebraic relationcan be considered as as a discrete equation of the Painlev´ type.eKeywords: Painlev´ Equation, Bücklund Transformation, Schlesinger Transfor-e amation, Discrete Painlev´ Equations.eiii