The discrete and continuous Painlevé VI hierarchy and the Garnier systems (Q2744543)
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scientific article; zbMATH DE number 1649129
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The discrete and continuous Painlevé VI hierarchy and the Garnier systems |
scientific article; zbMATH DE number 1649129 |
Statements
The discrete and continuous Painlevé VI hierarchy and the Garnier systems (English)
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14 August 2002
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KdV hierarchy
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constrained lattice system
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Garnier systems
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Painlevé VI equation
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ordinary difference equation
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partial difference equation
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The authors study the connection between multidimensional systems associated with higher-order generalizations of the Painlevé VI equation and the ordinary difference equation described by the higher-dimensional lattice system of the Korteweg-de Vries family. The basic constructions in both discrete and continuous cases are outlined and e.g. the reduction of a partial difference equation to a coupled system is presented in details. The connection with Garnier systems is also considered.
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