On matrix Painlev\'e-4 equations. Part 2: Isomonodromic Lax pairs

TL;DR

This paper presents isomonodromic Lax pairs for all non-equivalent matrix Painlevé-4 systems identified previously and explores their limiting transitions to matrix Painlevé-2 equations.

Contribution

It provides explicit isomonodromic Lax pairs for matrix Painlevé-4 systems and analyzes their connections to matrix Painlevé-2 equations, advancing the understanding of these integrable systems.

Findings

Explicit Lax pairs for all non-equivalent matrix Painlevé-4 systems

Limiting transitions to matrix Painlevé-2 equations

Enhanced understanding of matrix Painlevé equations' structure

Abstract

For all non-equivalent matrix systems of Painlev\'e-4 type found by authors in arXiv:2107.11680, isomonodromic Lax pairs are presented. Limiting transitions from these systems to matrix Painlev\'e-2 equations are found.