BIMSA > BIMSA Integrable Systems Seminar Different approaches for constructing non-abelian Painlevé equations
Different approaches for constructing non-abelian Painlevé equations
Organizers
Nicolai Reshetikhin , Ivan Sechin , Andrey Tsiganov
Speaker
Irina Bobrova
Time
Friday, February 24, 2023 5:00 PM - 6:30 PM
Venue
A6-101
Abstract
The famous Painlevé equations play a significant role in modern mathematical physics. The interest in their non-commutative extensions was motivated by the needs of modern quantum physics as well as by natural attempts of mathematicians to extend ‘’classical’’ structures to the non-commutative case. In this talk we will consider several approaches that are useful for detecting non-commutative analogs of the Painlevé equations. Namely, the matrix Painlevé-Kovalevskaya test, integrable non-abelian auxiliary autonomous systems, and infinite non-commutative Toda equations. All of these methods allow us to find a finite list of non-abelian candidates for such analogs. To provide their integrability, one can present an isomonodromic Lax pair. This talk is based on a series of papers joint with Vladimir Sokolov and on arXiv:2205.05107 joint with Vladimir Retakh, Vladimir Rubtsov, and George Sharygin (publ. in J. Phys. A: Math. Theor.).