Advances in Difference Equations
Volume 2007 (2007), Article ID 96752, 15 pages
An Ultradiscrete Matrix Version of the Fourth Painlevé Equation
School of Mathematics and Statistics F07, The University of Sydney, Sydney NSW 2006, Australia
Received 27 February 2007; Accepted 1 May 2007
Academic Editor: Kilkothur Munirathinam Tamizhmani
Copyright © 2007 Chris M. Field and Chris M. Ormerod. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper is concerned with the matrix generalization of ultradiscrete systems.
Specifically, we establish a matrix generalization of the ultradiscrete fourth Painlevé
equation (ud-). Well-defined multicomponent systems that permit ultradiscretization are obtained
using an approach that relies on a group defined by constraints imposed by the requirement of
a consistent evolution of the systems.
The ultradiscrete limit of these systems yields coupled multicomponent ultradiscrete systems
ud-. The dynamics, irreducibility, and integrability of the matrix-valued ultradiscrete
systems are studied.