Matrix Painlevé II equations

We use the Painlevé–Kovalevskaya test to find three matrix versions of the Painlevé II equation. We interpret all these equations as group-invariant reductions of integrable matrix evolution equations, which allows constructing isomonodromic Lax pairs for them.

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Bibliographic Details
Published in:Theoretical and mathematical physics 2021-05, Vol.207 (2), p.560-571
Main Authors: Adler, V. E., Sokolov, V. V.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Applications of Mathematics
Mathematical analysis
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary:We use the Painlevé–Kovalevskaya test to find three matrix versions of the Painlevé II equation. We interpret all these equations as group-invariant reductions of integrable matrix evolution equations, which allows constructing isomonodromic Lax pairs for them.
ISSN:0040-5779
1573-9333
DOI:10.1134/S0040577921050020