Painlevé-III monodromy maps under the \(D_6 \rightarrow D_8\) confluence and applications to the large-parameter asymptotics of rational solutions. (English) Zbl 1536.34083
In [V. I. Gromak, Differ. Uravn. 9, 2082–2083 (1973; Zbl 0275.34002)], a transformation of a solution of Painlevé III equation with parameters \((\alpha,\beta)\) to a solution of Painlevé III equation with parameters \((\alpha+4,\beta+4)\) was found. In the paper under review a limit of sequence of these transformations is investigated. It is proved that the limit is a solution of a Painlevé III (\(D_8\)) equation.
Reviewer: Dmitry Artamonov (Moskva)
MSC:
| 34M55 | Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies |
| 34E05 | Asymptotic expansions of solutions to ordinary differential equations |
| 34M50 | Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain |
| 34M56 | Isomonodromic deformations for ordinary differential equations in the complex domain |
| 33E17 | Painlevé-type functions |
Keywords:
Painlevé-III equation; Riemann-Hilbert analysis; Umemura polynomials; large-parameter asymptoticsCitations:
Zbl 0275.34002References:
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