Different linearizations of non-abelian second Painlevé systems and related monodromy surfaces

Abstract

In this paper, we discuss a connection between different linearizations for non-abelian analogs of the second Painlevé 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.

Some typos were fixed. A setting in the Introduction has been rewritten. A dedication was added

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