On the algebraic solutions of the Painleve-III (D7) equation

The D7 degeneration of the Painleve-III equation has solutions that are rational functions of \(x^{1/3}\) for certain parameter values. We apply the isomonodromy method to obtain a Riemann-Hilbert representation of these solutions. We demonstrate the utility of this representation by analyzing rigor...

Ausführliche Beschreibung

Gespeichert in:

Bibliographische Detailangaben
Veröffentlicht in:	arXiv.org 2022-02
Hauptverfasser:	Buckingham, Robert J, Miller, Peter D
Format:	Artikel
Sprache:	eng
Schlagworte:	Degeneration Mathematical analysis Mathematics - Classical Analysis and ODEs Mathematics - Mathematical Physics Parameters Physics - Exactly Solvable and Integrable Systems Physics - Mathematical Physics Rational functions Representations
Online-Zugang:	Volltext
Tags:	Tag hinzufügen Keine Tags, Fügen Sie den ersten Tag hinzu!

Beschreibung
Zusammenfassung:	The D7 degeneration of the Painleve-III equation has solutions that are rational functions of \(x^{1/3}\) for certain parameter values. We apply the isomonodromy method to obtain a Riemann-Hilbert representation of these solutions. We demonstrate the utility of this representation by analyzing rigorously the behavior of the solutions in the large parameter limit.
ISSN:	2331-8422
DOI:	10.48550/arxiv.2202.04217