This article is cited in 14 papers

Matrix Painlevé II equations

V. E. Adler^a, V. V. Sokolov<sup>ab

a</sup> Landau Institute for Theoretical Physics, RAS, Chernogolovka, Moscow Oblast, Russia
^b Federal University of ABC, Santo André, Sao Paulo, Brazil

Abstract: 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.

Keywords: Painlevé equation, Lax representation, symmetric reduction.

Received: 10.12.2020
Revised: 11.01.2021

DOI: 10.4213/tmf10027

 English version: Theoretical and Mathematical Physics, 2021, 207:2, 560–571

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