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

Autor:	Its, Alexander R., Miyahara, Kenta, Yattselev, Maxim L.
Rok vydání:	2024
Předmět:	Nonlinear Sciences - Exactly Solvable and Integrable Systems Mathematical Physics Mathematics - Classical Analysis and ODEs
Druh dokumentu:	Working Paper
Popis:	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.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2410.22440 Zobrazit plný text záznamu View this record from Arxiv