由相关随机游动导出的离散Burgers方程的一种变形及其超离散化
A variant of the discrete Burgers equation derived from the correlated random walk and its ultradiscretization
摘要：
本文证明了离散Burgers方程的一个变形可以通过Cole-Hopf变换得到一个对应于相关随机游动的广义离散扩散方程，它也被称为是著名的随机游动的推广。通过应用超离散化技术，我们得到了广义超离散扩散方程，超离散Cole-Hopf变换和超离散Burgers方程的一个变形.此外，我们表明，由此产生的超离散Burgers方程产生元胞自动机，它可以被解释为一个交通流模型。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
