Bobrova I., Sokolov V. Matrix Painlevé equations (abstract)

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Speakers: Irina Bobrova and Vladimir Sokolov

Title: Matrix Painlevé equations

Abstract:
The interest in the non-commutative extensions of various integrable systems was motivated by needs of modern quantum psychics as well as by a natural attempts of mathematicians to extend various "classical" structures to non-commutative case.

The Painlevé equations satisfy the Painlevé-Kovalevskaya test and possess isomonodromic Lax pairs. We generalize the test to find matrix Painlevé equations and propose a non-abelinization procedure of known Lax pairs for searching Lax representations for these matrix systems.

The talk is based on the following recent papers: arXiv:2012.05639 (V. Adler, V. Sokolov) and arXiv:2107.11680, arXiv:2110.12159 (I. Bobrova, V. Sokolov).


Event: Diffieties, Cohomological Physics, and Other Animals, 13-17 December 2021, Moscow.
Alexandre Vinogradov Memorial Conference.