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

Shun Shimomura

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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.

Original languageEnglish
Article numberS09
Pages (from-to)12153-12165
Number of pages13
JournalJournal of Physics A: Mathematical and General
Issue number39
Publication statusPublished - 2006 Sep 29


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)

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