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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)