Two-dimensional Burgers cellular automaton

Katsuhiro Nishinari; Junta Matsukidaira; Daisuke Takahashi

doi:10.1143/JPSJ.70.2267

Two-dimensional Burgers cellular automaton

Katsuhiro Nishinari^*, Junta Matsukidaira, Daisuke Takahashi

^*Corresponding author for this work

School of Fundamental Science and Engineering

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	2267-2272
Number of pages	6
Journal	journal of the physical society of japan
Volume	70
Issue number	8
DOIs	https://doi.org/10.1143/JPSJ.70.2267
Publication status	Published - 2001 Aug

Keywords

Burgers equation
Cellular automaton
Integrable
Particle model
Shock wave
Ultradiscrete method

ASJC Scopus subject areas

Physics and Astronomy(all)

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10.1143/JPSJ.70.2267

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AB - 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.

KW - Burgers equation

KW - Cellular automaton

KW - Integrable

KW - Particle model

KW - Shock wave

KW - Ultradiscrete method

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Two-dimensional Burgers cellular automaton

Abstract

Keywords

ASJC Scopus subject areas

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