Browsing by Subject "Painleve equations."
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Item Open Access Bâcklund transformations of Painleve equations and discrete equations of Painleve type(2004) Tosun, KürşadWith the help of the Schlesinger transformations, we obtain the B¨acklund transformations of the classical continuous Painlev´e equations (PII-PVI). Then using these B¨acklund transformations we derived the corresponding discrete equations. The main idea in obtaining these equations is to eliminate y 0 from the B¨acklund transformations, Ti and Tj , in such a way that Ti ◦ Tj = Tj ◦ Ti = I. Then we obtain an algebraic relation between yi , y and yj . This algebraic relation can be considered as as a discrete equation of the Painlev´e type.Item Open Access Painleve test and the Painleve equations hierarchies(2001) Jrad, FahdRecently there has been a considerable interest in obtaining higher order ordinary differential equations having the Painleve property. In this thesis, starting from the first, the second and the third Painleve transcendents polynomial and non-polynomial type higher order ordinary differential equations having the Painleve property have been obtained by using the singular point analysis.Item Open Access Partial differential equations possessing the Painleve property(1996) Jrad, Fahd111 this tli(\sis, a|)|)lying llie l^viiilovc tost (l(ivolo|)('.(l by VV(hss, 'labor ainl t biriK'vale (VV1X9) investigatc'd the Pa.inleve property of Ibirgers’ ty|)e of ('(piarioiis, KdV type of equations and the KP extc'iisions of th(' KdV i-yi)(' of ('i|na,tions. VVe showed that there a.rc^ iiiiinitely many e(|nations of t,h('S(' t-ypc's poss('ssing tlu^ Painleve propcn'ty and tims we elassiíi(MÍ tlnmi witJi res])ect to Pa.illlevé property.Item Open Access Schlesinger transformations of second discrete painleve equation(2004) Yurtseven, ÖzdenItem Open Access The solvability of PVI equation and second-order second-degree Painleve type equations(1998) Sakka, AymanA rigorous method was introduced by Fokas and Zhou for studying the Riernaiin-Hilhert problem associated with the Painleve II and IV. The same methodology has been applied to Painleve I, III and V. In this thesis, we applied the same methodology to the Painleve VI equation. VVe showed that The Cauchy problem for the Painleve VI equation admits in general global meromorphic solution in /. Furthermore, a. special solution which can lie written in terms of hypergeometric function is obtained via sob’ing the special case of the Riemann-Hilbert problem. Moreover, an algorithmic method introduced by Fokas and Ablowitz to investigate the transformation properties of Painleve equations and a generalization of it are used to obtain one-to-one correspondence between the Painleve equations and the second-ord(U‘ seconddegree equations of Painleve type.