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arXiv · 2206.10580

Non-abelian Painlev\'e systems with generalized Okamoto integral

Irina Bobrova·Vladimir Sokolov
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Abstract

We study non-abelian systems of Painlev\'e type. To derive them, we introduce an auxiliary autonomous system with the frozen independent variable and postulate its integrability in the sense of the existence of a non-abelian first integral that generalizes the Okamoto Hamiltonian. All non-abelian P6-P2-systems with such integrals are found. A coalescence limiting scheme is constructed for these non-abelian Painlev\'e systems. This allows us to construct an isomonodromic Lax pair for each of them.

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Irina Bobrova, Vladimir Sokolov. 2022-06-21. Non-abelian Painlev\'e systems with generalized Okamoto integral. https://doi.org/10.1090/conm%2F789%2F15839

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