Matrix Painlevé II equations
Abstract
We use the Painlevé-Kovalevskaya test to find three matrix versions of the Painlevé II equation. We interpret all these equations as group-invariant reductions of integrable matrix evolution equations, which allows constructing isomonodromic Lax pairs for them.
- Publication:
-
Theoretical and Mathematical Physics
- Pub Date:
- May 2021
- DOI:
- 10.1134/S0040577921050020
- arXiv:
- arXiv:2012.05639
- Bibcode:
- 2021TMP...207..560A
- Keywords:
-
- Painlevé equation;
- Lax representation;
- symmetric reduction;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- Mathematical Physics
- E-Print:
- 13 pages