ANALYTICAL PROPERTIES OF ULTRADISCRETE BURGERS-EQUATION AND RULE-184 CELLULAR-AUTOMATON

In this paper, we propose an ultradiscrete Burgers equation of which a ll the variables are discrete. The equation is derived from a discrete Burgers equation under an ultradiscrete limit and reduces to an ultra discrete diffusion equation through the Cole-Hopf transformation. More over, it becomes a cellular automaton (CA) under appropriate condition s and is identical to rule-184 CA in a specific case. We show shock wa ve solutions and asymptotic behaviours of the CA exactly via the diffu sion equation. Finally, we propose a particle model expressed by the C A and discuss a mean flux of particles.