Different linearizations of non-abelian second Painlev\'e systems and related monodromy surfaces
Exactly Solvable and Integrable Systems
2023-10-10 v2 Classical Analysis and ODEs
Abstract
In this paper, we discuss a connection between different linearizations for non-abelian analogs of the second Painlev\'e equation. For each of the analogs, we listed the pairs of the Harnard-Tracy-Widom (HTW), Flaschka-Newell (FN), and Jimbo-Miwa (JM) types. A method for establishing the HTW-JM correspondence is suggested. For one of the non-abelian analogs, we derive the corresponding non-abelian generalizations of the monodromy surfaces related to the FN- and JM-type linearizations. A natural Poisson structure associated with these monodromy surfaces is also discussed.
Keywords
Cite
@article{arxiv.2302.10694,
title = {Different linearizations of non-abelian second Painlev\'e systems and related monodromy surfaces},
author = {Irina Bobrova},
journal= {arXiv preprint arXiv:2302.10694},
year = {2023}
}
Comments
Some typos were fixed. A setting in the Introduction has been rewritten. A dedication was added