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

The D7 degeneration of the Painlevé-III equation has solutions that are rational functions of x1/3 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 t...

Full description

Saved in:
Bibliographic Details
Published in:Physica. D 2022-12, Vol.441, p.133493, Article 133493
Main Authors: Buckingham, R.J., Miller, P.D.
Format: Article
Language:English
Subjects:
Algebraic solutions
Isomonodromy method
Painlevé-III (D7) equation
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:The D7 degeneration of the Painlevé-III equation has solutions that are rational functions of x1/3 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. •The algebraic solutions of the degenerate D7 type Painlevé-III equation are studied.•A Riemann-Hilbert representation of these solutions is deduced by the isomonodromy method.•That representation is used to study the solutions in the large-parameter limit.
ISSN:0167-2789
1872-8022
DOI:10.1016/j.physd.2022.133493