Abstract We review work of Jordan on a hyperbolic variant of the Fisher - KPP equation, where a shock solution is found and the amplitude is calculated exactly. The Jordan procedure is extended to a hyperbolic variant of the Chafee – Infante equation. Extension of Jordan’s ideas to a model for traffic flow are also mentioned. We also examine a diffusive susceptible - infected (SI) model, and generalizations of diffusive Lotka – Volterra equations, including a Lotka – Volterra – Bass competition model with diffusion. For all cases we show how a Jordan - Cattaneo wave may be analysed and we indicate how to find the wavespeeds and the amplitudes. Finally we present details of a fully nonlinear analysis of acceleration waves in a Cattaneo – Christov poroacoustic model.

中文翻译：

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Jordan – Cattaneo 波：可压缩流的模拟

摘要 我们回顾了 Jordan 在 Fisher-KPP 方程的双曲线变体上的工作，其中找到了激波解并精确计算了振幅。Jordan 过程扩展到 Chafee-Infante 方程的双曲线变体。还提到了 Jordan 的想法在交通流模型上的扩展。我们还研究了扩散易感 - 感染 (SI) 模型，以及扩散 Lotka - Volterra 方程的推广，包括具有扩散的 Lotka - Volterra - Bass 竞争模型。对于所有情况，我们展示了如何分析 Jordan - Cattaneo 波，并指出如何找到波速和振幅。最后，我们详细介绍了 Cattaneo-Christov 多孔声学模型中加速度波的完全非线性分析。