Casorati Determinant Solutions for the Discrete Painlev\'e III Equation
solv-int
2009-10-28 v1 High Energy Physics - Theory
Exactly Solvable and Integrable Systems
Abstract
The discrete Painlev\'e III equation is investigated based on the bilinear formalism. It is shown that it admits the solutions expressed by the Casorati determinant whose entries are given by the discrete Bessel function. Moreover, based on the observation that these discrete Bessel functions are transformed to the -Bessel functions by a simple variable transformation, we present a -difference analogue of the Painlev\'e III equation.
Cite
@article{arxiv.solv-int/9412004,
title = {Casorati Determinant Solutions for the Discrete Painlev\'e III Equation},
author = {Kenji Kajiwara and Yasuhiro Ohta and Junkichi Satsuma},
journal= {arXiv preprint arXiv:solv-int/9412004},
year = {2009}
}
Comments
16 pages in LaTeX