Geodesic
Matrix Painlev\'e II equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 2, pp. 188-201

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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. 
@article{TMF_2021_207_2_a1,
     author = {V. E. Adler and V. V. Sokolov},
     title = {Matrix {Painlev\'e} {II} equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {188--201},
     publisher = {mathdoc},
     volume = {207},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_207_2_a1/}
}
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V. E. Adler; V. V. Sokolov. Matrix Painlev\'e II equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 2, pp. 188-201. http://geodesic.mathdoc.fr/item/TMF_2021_207_2_a1/