The non-linear steepest descent approach to the singular asymptotics of the sinh-Gordon reduction of the Painlevé III equation
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| Format: | Preprint |
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2024
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| _version_ | 1866914997139931136 |
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| author | Its, Alexander R. Miyahara, Kenta Yattselev, Maxim L. |
| author_facet | Its, Alexander R. Miyahara, Kenta Yattselev, Maxim L. |
| contents | 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. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22440 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The non-linear steepest descent approach to the singular asymptotics of the sinh-Gordon reduction of the Painlevé III equation Its, Alexander R. Miyahara, Kenta Yattselev, Maxim L. Exactly Solvable and Integrable Systems Mathematical Physics Classical Analysis and ODEs 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. 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. |
| title | The non-linear steepest descent approach to the singular asymptotics of the sinh-Gordon reduction of the Painlevé III equation |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2410.22440 |