Connection problem for the tau-function of the Sine-Gordon reduction of Painlevé-III equation via the Riemann-Hilbert approach

Abstract

We evaluate explicitly, in terms of the Cauchy data, the constant pre-factor in the large $x$ asymptotics of the Painlevé III tau-function. Our result proves the conjectural formula for this pre-factor obtained recently by O. Lisovyy, Y. Tykhyy, and the first co-author with the help of the recently discovered connection of the Painlevé tau-functions with the Virasoro conformal blocks. Our approach does not use this connection, and it is based on the Riemann-Hilbert method.

21 pages, 2 figures

References in corpus (2)

• Painlevé VI connection problem and monodromy of c=1 conformal blocks
• Connection problem for the sine-Gordon/Painlevé III tau function and irregular conformal blocks

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