An ultradiscrete matrix version of the fourth Painleve equation
Exactly Solvable and Integrable Systems
2007-05-23 v2 Cellular Automata and Lattice Gases
Abstract
We establish a matrix generalization of the ultradiscrete fourth Painlev\'e equation (ud-PIV). 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 that generalize ud-PIV. The dynamics, irreducibility, and integrability of the matrix valued ultradiscrete systems are studied.
Keywords
Cite
@article{arxiv.nlin/0610041,
title = {An ultradiscrete matrix version of the fourth Painleve equation},
author = {Chris M. Field and Chris M. Ormerod},
journal= {arXiv preprint arXiv:nlin/0610041},
year = {2007}
}
Comments
12 pages, 12 figures, Latex2e, Submitted to J. Phys. A, corrections made