Hamiltonian Systems

Event Information On some classes of non-abelian Painlevé equations
12:30 on Tuesday February 14, 2023
13:30 on Tuesday February 14, 2023
Irina Bobrova

National Research University - Higher School of Economics, Moscow, Russia

All famous Painlevé equations are Hamiltonian and can be written as a system of first-order ODEs. These systems are non-autonomous and, therefore, the Hamiltonians are not an integral of motions. Since well-known properties of integrable autonomous systems can be naturally generalised to the non-commutative case, it is convenient to consider auxiliary autonomous systems related to the Painlevé systems. Using this approach, we construct two classes of non-abelian Painlevé type systems that are closed under the limiting transition. To provide their integrability, one can present an isomonodromic Lax pair.

This talk is based on the papers arXiv:2206.10580, arXiv:2209.00258 joint with Vladimir Sokolov.

The talk will be via Zoom at: https://utoronto.zoom.us/j/99576627828

Passcode: 448487

https://arxiv.org/abs/2206.10580 and https://arxiv.org/abs/2209.00258