Analytical properties of ultradiscrete Burgers equation and rule-184 cellular automaton

Katsuhiro Nishinari*, Daisuke Takahashi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

108 Citations (Scopus)


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 languageEnglish
Pages (from-to)5439-5450
Number of pages12
JournalJournal of Physics A: Mathematical and General
Issue number24
Publication statusPublished - 1998 Jun 19

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy(all)


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