Linearization And Solutions Of The Discrete Painlev\'e-III Equation
solv-int
2009-10-22 v1 Exactly Solvable and Integrable Systems
Abstract
We present particular solutions of the discrete Painlev\'e III (d-P) equation of rational and special function (Bessel) type. These solutions allow us to establish a close parallel between this discrete equation and its continuous counterpart. Moreover, we propose an alternate form for d-P and confirm its integrability by explicitly deriving its Lax pair.
Cite
@article{arxiv.solv-int/9310003,
title = {Linearization And Solutions Of The Discrete Painlev\'e-III Equation},
author = {B. Grammaticos and F. W. Nijhoff and V. Papageorgiou and A. Ramani},
journal= {arXiv preprint arXiv:solv-int/9310003},
year = {2009}
}