Browsing by Subject "Painleve equations--Numerical solutions."

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    The solvability of PVI equation and second-order second-degree Painleve type equations
    (1998) Sakka, Ayman
    A 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.
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    Unified approach to transformations of Painleve equations
    (1993) Chahardehi, Ali Reza Modaressi
    In this thesis, we iind the explicit form of some transformations associated with the second, third, fourth and fifth Painleve equations. These transformations are obtained by using the Schlesinger transformations associated with the linear system of equations of Painleve eciuations.The application of such transformations enables us to generate the new solutions of the given Painleve equation with different values of parameters, from the known solutions.