A method of linearization for Painlevé equations: Painlevé IV, V (Q1105745)
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scientific article; zbMATH DE number 4059839
| Language | Label | Description | Also known as |
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| English | A method of linearization for Painlevé equations: Painlevé IV, V |
scientific article; zbMATH DE number 4059839 |
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A method of linearization for Painlevé equations: Painlevé IV, V (English)
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1988
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A method to linearize the initial value problem of the Painlevé equations IV, V is given. The procedure involves formulating a Riemann- Hilbert boundary value problem on intersecting lines for the inverse monodromy problem. This boundary value problem is reduced to a sequence of standard problems on single lines in a certain range of parameter space. Schlesinger transformations allow one to completely cover the parameter space. Special solutions are constructed from special cases of the Riemann problem as well.
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Riemann-Hilbert boundary value problem
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inverse monodromy problem
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Schlesinger transformations
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