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arXiv · 2410.22440

The non-linear steepest descent approach to the singular asymptotics of the sinh-Gordon reduction of the Painlev\'e III equation

Alexander R. Its·Kenta Miyahara·Maxim L. Yattselev
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Abstract

Motivated by the simplest case of tt*-Toda equations, we study the large and small $x$ asymptotics for $x>0$ of real solutions of the sinh-Godron Painlev\'e III($D_6$) equation. These solutions are parametrized through the monodromy data of the corresponding Riemann-Hilbert problem. This unified approach provides connection formulae between the behavior at the origin and infinity of the considered solutions.

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Alexander R. Its, Kenta Miyahara, Maxim L. Yattselev. 2024-10-29. The non-linear steepest descent approach to the singular asymptotics of the sinh-Gordon reduction of the Painlev\'e III equation. https://arxiv.org/abs/2410.22440

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