A variant of the discrete Burgers equation derived from the correlated random walk and its ultradiscretization

In this paper, we show that a variant of the discrete Burgers equation can be obtained through the Cole--Hopf transformation to a generalized discrete diffusion equation corresponding to the correlated random walk, which is also known as a generalization of the well known random walk. By applying th...

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Bibliographic Details
Published inarXiv.org
Main Authors Fukuda, Akiko, Segawa, Etsuo, Watanabe, Sennosuke
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 05.11.2021
Subjects
Burgers equation
Cellular automata
Linear equations
Random walk
Traffic flow
Traffic models
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Summary:In this paper, we show that a variant of the discrete Burgers equation can be obtained through the Cole--Hopf transformation to a generalized discrete diffusion equation corresponding to the correlated random walk, which is also known as a generalization of the well known random walk. By applying the technique called ultradiscretization, we obtain the generalized ultradiscrete diffusion equation, the ultradiscrete Cole--Hopf transformation and a variant of the ultradiscrete Burgers equation. Moreover, we show that the resulting ultradiscrete Burgers equation yields cellular automata which can be interpreted as a traffic flow model.
ISSN:2331-8422