Analytical properties of ultradiscrete Burgers equation and rule-184 cellular automaton
- 19 June 1998
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 31 (24), 5439-5450
- https://doi.org/10.1088/0305-4470/31/24/006
Abstract
In this paper, we propose an ultradiscrete Burgers equation of which all the variables are discrete. The equation is derived from a discrete Burgers equation under an ultradiscrete limit and reduces to an ultradiscrete diffusion equation through the Cole-Hopf transformation. Moreover, it becomes a cellular automaton (CA) under appropriate conditions and is identical to rule-184 CA in a specific case. We show shock wave solutions and asymptotic behaviours of the CA exactly via the diffusion equation. Finally, we propose a particle model expressed by the CA and discuss a mean flux of particles.Keywords
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