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.
| Original language | English |
|---|---|
| Pages (from-to) | 5439-5450 |
| Number of pages | 12 |
| Journal | Journal of Physics A: Mathematical and General |
| Volume | 31 |
| Issue number | 24 |
| DOIs | |
| Publication status | Published - 1998 Jun 19 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)