English

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