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

2013/03/14 by Kohei Iwaki, Iwaki, Kohei
Mathematics · Physics and Astronomy · #34M40 #34M55 #34M60 #Advanced Differential Equations and Dynamical Systems #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #math-ph #math.CA #math.MP #msc:34M40 #msc:34M55 #msc:34M60

paper · pdf · doi:10.48550/arxiv.1303.3603

44 pages, many figures

arxiv created 2013/03/14 · openalex publication_date 2013/03/14 · arxiv updated 2013/03/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

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