Using the Painlevé-Kovalevskaya test, we find several new matrix generalizations of the Painlevé-4 equation. Some limiting transitions reduces them to known matrix Painlevé -2 equations.
We study non-abelian systems of Painlevé 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 Painlevé systems. This allows us to construct an isomonodromic Lax pair for each of them.
Using the Painlevé–Kovalevskaya test, we find several polynomial matrix systems, which can be regarded as non-commutative generalisations of the Painlevé-4 equation. For these systems isomonodromic Lax pairs are presented. Limiting transitions that reduce them to known matrix Painlevé-2 equations are found.
For all non-equivalent matrix systems of Painlevé-4 type found by authors in [4], isomonodromic Lax pairs are presented. Limiting transitions from these systems to matrix Painlevé-2 equations are found.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.