We study the occurrence of traveling wave solutions for a modified Burgers’ equation with diffusivity $D$ and a time delay $\tau$. Monotonic traveling waves with speed $c$ are shown to exist when $\tau c^2∕D\le e^{-1}$. Graphs are provided to help characterize the behavior of these solutions compared to those for the familiar Burgers’ equation without delay.

中文翻译：

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时滞Burgers方程的行波解

我们研究了具有扩散率的修正Burgers方程的行波解的出现 $d$ 和时间延迟 $\tau$。单调行波速度$C$ 显示存在的时间 $\tau C^2∕d\le {Ë}^{-\mathrm{1个}}$。与熟悉的Burgers方程相比，提供了图表来帮助表征这些解决方案的行为，而不会出现延迟。