Nonlinear differential equations of second Painlevé type with the quasi-Painlevé property along a rectifiable curve

Shun Shimomura

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We present a class of nonlinear differential equations of second Painlevé type. These equations, with a single exception, admit the quasi-Painlevé property along a rectifiable curve, that is, for general solutions, every movable singularity defined by a rectifiable curve is at most an algebraic branch point. Moreover we discuss the global many-valuedness of their solutions. For the exceptional equation, by the method of successive approximation, we construct a general solution having a movable logarithmic branch point.

Original languageEnglish
Pages (from-to)581-595
Number of pages15
JournalTohoku Mathematical Journal
Volume60
Issue number4
DOIs
Publication statusPublished - 2008 Dec

Fingerprint

Branch Point
General Solution
Nonlinear Differential Equations
Curve
Successive Approximation
Exception
Logarithmic
Singularity
Class

Keywords

  • Hyperelliptic integral
  • Nonlinear differential equation
  • Painlevé equation
  • Quasi-painlevé property

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Nonlinear differential equations of second Painlevé type with the quasi-Painlevé property along a rectifiable curve. / Shimomura, Shun.

In: Tohoku Mathematical Journal, Vol. 60, No. 4, 12.2008, p. 581-595.

Research output: Contribution to journalArticle

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