The non-linear steepest descent approach to the singular asymptotics of the sinh-Gordon reduction of the Painlevé III equation

Alexander R. Its, Kenta Miyahara, Maxim L. Yattselev

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 Painlevé III($D_6$) equation. Thes…