On matrix Painlevé-4 equations
Abstract
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.
- Publication:
-
Nonlinearity
- Pub Date:
- December 2022
- DOI:
- arXiv:
- arXiv:2110.12159
- Bibcode:
- 2022Nonli..35.6528B
- Keywords:
-
- matrix ODEs;
- Painlevé-Kovalevskaya test;
- Painlevé equations;
- isomonodromic Lax pairs;
- 34M55;
- 46L55;
- 34M56;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Mathematical Physics
- E-Print:
- doi:10.1088/1361-6544/ac9bc2