The sixth painlevé transcendents and the associated schlesinger equation

Shun Shimqmura

研究成果: Article

6 引用 (Scopus)

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For the Schlesinger equation associated with the sixth Painlevé equation (PVI) near the critical point, we present families of solutions expanded into convergent series with matrix coefficients. These families yield four basic solutions of (PVI) in Guzzetti's table describing the critical behaviours of the sixth Painleve transcendents; two of the basic solutions are of complex power type, and two are of logarithmic type. Consequently, the convergence of the logarithmic solutions is verified. Furthermore we obtain more information on these basic solutions as well as on inverse logarithmic solutions. For complex power solutions, examining related inverse oscillatory ones, we discuss sequences of zeros and poles, non-decaying exponential oscillation and the analytic continuation around the critical point, and show the spiral distribution of poles conjectured by Guzzetti.

元の言語English
ページ(範囲)417-463
ページ数47
ジャーナルPublications of the Research Institute for Mathematical Sciences
51
発行部数3
DOI
出版物ステータスPublished - 2015 8 28

ASJC Scopus subject areas

  • Mathematics(all)

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