A dynamical systems approach to the fourth Painlevé equation. (13th March 2019)

• Record Type: Journal Article
• Authors: Schiff, Jeremy; Twiton, Michael
• Is Part Of: Journal of physics. Volume 52:Number 14(2019)
• Publication Date: 2019-03-13
• Subjects: Painlevé equations -- dynamical systems -- fixed points; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/ab0752
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We use methods from dynamical systems to study the fourth Painlevé equation . Our starting point is the symmetric form of, to which the Poincaré 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 .