Painlevé-III monodromy maps under the \(D_6 \rightarrow D_8\) confluence and applications to the large-parameter asymptotics of rational solutions (Q6196825)
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scientific article; zbMATH DE number 7819250
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Painlevé-III monodromy maps under the \(D_6 \rightarrow D_8\) confluence and applications to the large-parameter asymptotics of rational solutions |
scientific article; zbMATH DE number 7819250 |
Statements
Painlevé-III monodromy maps under the \(D_6 \rightarrow D_8\) confluence and applications to the large-parameter asymptotics of rational solutions (English)
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15 March 2024
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In [\textit{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.
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Painlevé-III equation
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Riemann-Hilbert analysis
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Umemura polynomials
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large-parameter asymptotics
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