Voros coefficients of the third Painelv'e equation and parametric Stokes phenomena

TL;DR

This paper computes Voros coefficients for the third Painleve equation of type D6, analyzes parametric Stokes phenomena in transseries solutions, and derives connection formulas under Borel summability assumptions.

Contribution

It provides explicit Voros coefficients for the third Painleve D6 and D7 equations and explores the associated parametric Stokes phenomena with connection formulas.

Findings

Computed all Voros coefficients for Painleve D6 and D7 equations.

Analyzed parametric Stokes phenomena in formal transseries solutions.

Derived connection formulas under Borel summability assumptions.

Abstract

We compute all Voros coefficients of the third Painleve equation of the type D6 (in the sense of [OKSO]) and discuss the parametric Stokes phenomena occurring to formal transseries solutions. We derive connection formulas for parametric Stokes phenomena under an assumption for Borel summability of transseries solutions. Furthermore, we also compute the Voros coefficient of the degenerate third Painleve equation of the type D7 in Appendix D.