Parametric Stokes phenomenon for the second Painlevé equation (Q2928381)

The second Painlevé equation NEWLINE\[NEWLINE(P_{II}):\quad d^2\lambda /dt^2=\eta ^2(2\lambda ^3+t\lambda +c)NEWLINE\]NEWLINE with a large parameter \(\eta >0\) is analyzed from the viewpoint of the exact WKB (Wentzel-Kramers-Brillouin) analysis. The aim is to investigate a new kind of Stokes phenomenon (namely, a parametric one) which occurs to transseries solutions of \((P_{II})\). The study uses the Voros coefficient for \((P_{II})\) which in turn allows to derive a connection formula for transseries solutions of \((P_{II})\). This formula can be obtained also by the method of isomonodromic deformations.