Two-dimensional Burgers Cellular Automaton
Exactly Solvable and Integrable Systems
2009-11-07 v1 Adaptation and Self-Organizing Systems
Abstract
A two-dimensional cellular automaton(CA) associated with a two-dimensional Burgers equation is presented. The 2D Burgers equation is an integrable generalization of the well-known Burgers equation, and is transformed into a 2D diffusion equation by the Cole-Hopf transformation. The CA is derived from the 2D Burgers equation by using the ultradiscrete method, which can transform dependent variables into discrete ones. Some exact solutions of the CA, such as shock wave solutions, are studied in detail.
Keywords
Cite
@article{arxiv.nlin/0102027,
title = {Two-dimensional Burgers Cellular Automaton},
author = {K. Nishinari and J. Matsukidaira and D. Takahashi},
journal= {arXiv preprint arXiv:nlin/0102027},
year = {2009}
}
Comments
Latex2.09, 17 pages including 7 figures