Non-abelian Painlev\'e systems with generalized Okamoto integral
Exactly Solvable and Integrable Systems
2023-10-10 v1 Classical Analysis and ODEs
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.
Cite
@article{arxiv.2206.10580,
title = {Non-abelian Painlev\'e systems with generalized Okamoto integral},
author = {Irina Bobrova and Vladimir Sokolov},
journal= {arXiv preprint arXiv:2206.10580},
year = {2023}
}