The Borel transform of the WKB solution to the Pearcey system

We study the system of partial differential equations which characterizes the Pearcey integral from the viewpoint of the exact WKB analysis. It is shown that the Borel transform of the WKB solutions to the system can be written as a linear combination of the branches of an algebraic function of degree $4$. Moreover, some connection formulas for the system are given.