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nlin.SI2026
Transition asymptotics for the real solutions of the sinh-Gordon Painlevé III equation
Kenta Miyahara, Maxim L. Yattselev
We consider solutions of the sinh-Gordon Painlevé III equation \[ u_{xx} + \frac{1}{x} u_x = \sinh u \] that are real on . They are parametrized by the monodromy parame…
nlin.SI2024
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 asymptotics for of real solutions of the sinh-Godron Painlevé III() equation. Thes…