Bessel function type solutions of the ultradiscrete Painlevé III equation with parity variables

The discrete Painlevé III equation ( dP III ) possesses a class of special solutions with determinantal structure whose entries are written by the q -difference Bessel function. In this paper, an ultradiscrete analogue of the q -Bessel function is constructed by ultradiscretization with parity varia...

Full description

Saved in:
Bibliographic Details
Published in:Japan journal of industrial and applied mathematics 2017-08, Vol.34 (2), p.343-372
Main Author: Isojima, Shin
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computational Mathematics and Numerical Analysis
Mathematics
Mathematics and Statistics
Original Paper
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 discrete Painlevé III equation ( dP III ) possesses a class of special solutions with determinantal structure whose entries are written by the q -difference Bessel function. In this paper, an ultradiscrete analogue of the q -Bessel function is constructed by ultradiscretization with parity variables (p-ultradiscretization). Based on this result, special solutions for the p-ultradiscrete Painlevé III equation are derived from those of dP III . The ultradiscrete solutions capture oscillating behaviour of the (differential) Painlevé III equation.
ISSN:0916-7005
1868-937X
DOI:10.1007/s13160-017-0250-3