Two-dimensional Burgers cellular automaton

Katsuhiro Nishinari*, Junta Matsukidaira, Daisuke Takahashi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


In this paper, a two-dimensional cellular automaton (CA) associated with a two-dimensional Burgers equation is presented. The 2D Burgers equation is an integrable generalization of the wellknown Burgers equation, and is transformed into a 2D diffusion equation by the Cole-Hopf transformation. The CA is derived from the 2D Burgers equation by using the ultradiscrete method, which can transform dependent variables into discrete ones. Some exact solutions of the CA. such as shock wave solutions, are studied in detail. The CA is considered as a pairing model of particles that move to different directions.

Original languageEnglish
Pages (from-to)2267-2272
Number of pages6
Journaljournal of the physical society of japan
Issue number8
Publication statusPublished - 2001 Aug


  • Burgers equation
  • Cellular automaton
  • Integrable
  • Particle model
  • Shock wave
  • Ultradiscrete method

ASJC Scopus subject areas

  • Physics and Astronomy(all)


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