On classification of non-abelian Painlevé type systems

Abstract

We find all non-abelian generalizations of ${\text{P}}_1-{\text{P}}_6$ Painlevé systems such that the corresponding autonomous system obtained by freezing the independent variable is integrable. All these systems have isomonodromic Lax representations.

References in corpus (8)

• Noncommutative Toda Chains, Hankel Quasideterminants And Painlev'e II Equation
• Painlevé type reductions for the non-Abelian Volterra lattices
• On matrix Painlevé II equations
• On the Linearization of the First and Second Painleve' Equations
• On matrix Painlevé-4 equations. Part 2: Isomonodromic Lax pairs
• On matrix Painlevé-4 equations. Part 1: Painlevé--Kovalevskaya test
• Non-commutative generalization of integrable quadratic ODE systems
• Non-Abelian Toda lattice and analogs of Painlevé III equation

Cited by in corpus (1)

• Different linearizations of non-abelian second Painlevé systems and related monodromy surfaces