Classification of Hamiltonian non-abelian Painlevé type systems

Abstract

All Hamiltonian non-abelian Painlevé systems of ${\mathrm{P}}_1-{\mathrm{P}}_6$ type with constant coefficients are found. For ${\mathrm{P}}_1-{\mathrm{P}}_5$ systems, we replace an appropriate inessential constant parameter with a non-abelian constant. To prove the integrability of new ${\mathrm{P}}_3^{\prime }$ and ${\mathrm{P}}_5$ systems thus obtained, we find isomonodromic Lax pairs for them.

Some typos were fixed

References in corpus (1)

• On matrix Painlevé-4 equations. Part 2: Isomonodromic Lax pairs

Cited by in corpus (1)

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