Exact WKB analysis for instanton-type solutions of the degenerate third Painlevé equation of type $(D_8)$ is discussed. Explicit connection formulas are obtained through computations of the monodromy data of the underlying linear equations.
Hideaki Wakako. Yoshitsugu Takei. "Exact WKB analysis for the degenerate third Painlevé equation of type $(D_8)$." Proc. Japan Acad. Ser. A Math. Sci. 83 (5) 63 - 68, May 2007. https://doi.org/10.3792/pjaa.83.63