A family of solutions of a higher order PVI equation near a regular singularity

Shun Shimomura

研究成果: Article査読

抄録

Restriction of the N-dimensional Garnier system to a complex line yields a system of second-order nonlinear differential equations, which may be regarded as a higher order version of the sixth Painlevé equation. Near a regular singularity of the system, we present a 2N-parameter family of solutions expanded into convergent series. These solutions are constructed by iteration, and their convergence is proved by using a kind of majorant series. For simplicity, we describe the proof in the case N ≤ 2.

本文言語English
論文番号S09
ページ(範囲)12153-12165
ページ数13
ジャーナルJournal of Physics A: Mathematical and General
39
39
DOI
出版ステータスPublished - 2006 9 29

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学
  • 物理学および天文学(全般)

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