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.