A dynamical systems approach to the fourth Painlevé equation

Jeremy Schiff, Michael Twiton

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We use methods from dynamical systems to study the fourth Painleve equation P IV . Our starting point is the symmetric form of P IV , to which the Poincare compactification is applied. The motion on the sphere at infinity can be completely characterized. There are fourteen fixed points, which are classified into three different types. Generic orbits of the full system are curves from one of four asymptotically unstable points to one of four asymptotically stable points, with the set of allowed transitions depending on the values of the parameters. This allows us to give a qualitative description of a generic real solution of P IV .

Original languageEnglish
Article number145201
JournalJournal of Physics A: Mathematical and Theoretical
Volume52
Issue number14
DOIs
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© 2019 IOP Publishing Ltd.

Keywords

  • Painleve equations
  • dynamical systems
  • fixed points

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