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

Katsuhiro Nishinari, Daisuke Takahashi

研究成果: Article

94 引用 (Scopus)

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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.

元の言語English
ページ(範囲)5439-5450
ページ数12
ジャーナルJournal of Physics A: Mathematical and General
31
発行部数24
DOI
出版物ステータスPublished - 1998 6 19

ASJC Scopus subject areas

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

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