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arXiv · 2104.14009

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

Akiko Fukuda·Etsuo Segawa·Sennosuke Watanabe
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Abstract

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.

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Akiko Fukuda, Etsuo Segawa, Sennosuke Watanabe. 2021-04-28. A variant of the discrete Burgers equation derived from the correlated random walk and its ultradiscretization. https://arxiv.org/abs/2104.14009

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