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In this paper, we discuss a connection between different linearizations fornon-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), andJimbo-Miwa (JM) types. A method for establishing the HTW-JM correspondence issuggested. For one of the non-abelian analogs, we derive the correspondingnon-abelian generalizations of the monodromy surfaces related to the FN- andJM-type linearizations. A natural Poisson structure associated with thesemonodromy surfaces is also discussed.

Different linearizations of non-abelian second Painlev\'e systems and related monodromy surfaces