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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Veröffentlicht in:	Theoretical and mathematical physics 2021-05, Vol.207 (2), p.560-571
Hauptverfasser:	Adler, V. E., Sokolov, V. V.
Format:	Artikel
Sprache:	eng
Schlagworte:	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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Beschreibung
Zusammenfassung:	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