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http://hdl.handle.net/20.500.12358/21401
TitleOn Cauchy Problems for Higher Order Painleve' Equations
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Abstract

A rigorous methodology for studying the initial value problems associated with certain integrable nonlinear ordinary differential equations was introduced by Fokas and Zhou, and was used to investigate Painlev´e second and fourth Painlev´e equations. The same methodology has been applied to the other Painlev´e equations and to the second member of a fourth Painlev´e hierarchy. We studied the application of this methodology to the second members of fourth and second Painlev´e hierarchies. We show that the Cauchy problems for these equations admit, in general, global solutions, meromorphic in x. Furthermore, for special relations among the monodromy data, the associated Riemann-Hilbert problems can be reduced to a set of scalar Riemann-Hilbert problems. By solving these RiemannHilbert problems, we obtain special solutions of the second members of fourth and second Painlev´e hierarchies which can be written in terms of special functions.

Authors
Baltayyan, Basema A.
Supervisors
Sakka, Ayman H.
Elshamy, Sevjan
Typeرسالة ماجستير
Date2013
LanguageEnglish
Publisherالجامعة الإسلامية - غزة
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  • PhD and MSc Theses- Faculty of Science [445]
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The institutional repository of the Islamic University of Gaza was established as part of the ROMOR project that has been co-funded with support from the European Commission under the ERASMUS + European programme. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

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The institutional repository of the Islamic University of Gaza was established as part of the ROMOR project that has been co-funded with support from the European Commission under the ERASMUS + European programme. This publication reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.

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