We show several basic properties concerning the relation between the Stokes geometry (i.e., configuration of Stokes curves and turning points) of a higher order Painlevé equation with a large… (More)

For a higher order linear ordinary differential operator P , its Stokes curve bifurcates in general when it hits another turning point of P . This phenomenon is most neatly understandable by taking… (More)

In our earlier paper ([AKT1]), by interpreting the formal transformation to the Airy equation near a simple turning point as the symbol of a microdifferential operator, we derived the Voros… (More)

The principal aim of this paper is to form a basis for the exact WKB analysis of a Schrödinger equation (0.1) d 2 dx 2 − η 2 Q(x, η) ψ = 0 (η : a large parameter) with one simple turning point and… (More)

equations (cf. [AKT1]), the exact WKB analysis provides us with a powerful tool for studying global behavior of solutions of linear ordinary di erential equations. To generalize such an analysis to… (More)

Using two concrete examples, we discuss the multisummability of WKB solutions of singularly perturbed linear ordinary differential equations. Integral representations of solutions and a criterion for… (More)

We announce a generalization of the reduction theorem for 0parameter solutions of the traditional (i.e., second order) Painlevé equations with a large parameter to those of some higher order Painlevé… (More)

Exact WKB analysis for instanton-type solutions of the degenerate third Painlevé equation of type (D8) is discussed. Explicit connection formulas are obtained through computations of the monodromy… (More)