On the solvability of the Painleve VI equation
Date
1995
Authors
Mugan, U.
Sakka, A.
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Abstract
A rigorous method was introduced by Fokas and Zhou (1992) for studying the Riemann-Hilbert problem associated with the Painleve II and IV equations. The same methodology has been applied to the Painleve I, III and V equations. In this paper, we will apply the same methodology to the Painleve VI equation. We will show that the Cauchy problem for the Painleve VI equation admits, in general, a global meromorphic solution in t. Furthermore, the special solution which can be written in terms of a hypergeometric function is obtained via solving the special case of the Riemann-Hilbert problem.
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Journal of Physics A: Mathematical and General
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Institute of Physics Publishing Ltd.
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English
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Article