Series expansions of painlevé transcendents near the point at infinity

Shun Shimomura

研究成果: Article査読

3 被引用数 (Scopus)

抄録

For the Painlevé equations (I) through (V) near the point at infinity we present several families of two-parameter solutions. Our solutions are expressed by asymptotic series with coefficients polynomial in exponential terms, and also by convergent power series in exponential terms with coefficients expanded into asymptotic series. Both expressions are valid without a restriction on integration constants. We propose a direct method to derive asymptotic solutions, which is also applicable to more general nonlinear equations. As applications of our results, for general solutions of the third and the fifth Painlevé equations, we give estimates for the number of a-points including poles in given sectors.

本文言語English
ページ(範囲)277-319
ページ数43
ジャーナルFunkcialaj Ekvacioj
58
2
DOI
出版ステータスPublished - 2015 8 13

ASJC Scopus subject areas

  • 分析
  • 代数と数論
  • 幾何学とトポロジー

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