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