TY - JOUR
T1 - Analytical properties of ultradiscrete Burgers equation and rule-184 cellular automaton
AU - Nishinari, Katsuhiro
AU - Takahashi, Daisuke
PY - 1998/6/19
Y1 - 1998/6/19
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0032546711&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0032546711&partnerID=8YFLogxK
U2 - 10.1088/0305-4470/31/24/006
DO - 10.1088/0305-4470/31/24/006
M3 - Article
AN - SCOPUS:0032546711
SN - 0305-4470
VL - 31
SP - 5439
EP - 5450
JO - Journal of Physics A: Mathematical and General
JF - Journal of Physics A: Mathematical and General
IS - 24
ER -