Working in the context of hyperbolic reaction–diffusion–acoustic theory, we present a detailed study of singular surface shock phenomena under two hyperbolic versions of the Fisher–KPP equation, both of which are based on flux laws originally used to describe the phenomenon of second-sound. Employing both analytical and numerical methods, we investigate the propagation, evolution, and qualitative behavior of density shocks, i.e., propagating surfaces across which the density exhibits a jump, under the two models considered. In the process, we identify a class of wave equations with the property that members of the class all exhibit the same shock structure, evolution, and velocity. Lastly, possible follow-on investigations are proposed and applications to other areas of continuum physics are noted.

在双曲反应-扩散-声学理论的背景下，我们对Fisher-KPP方程的两个双曲形式下的奇异表面冲击现象进行了详细研究，这两个都是基于最初用于描述第二个现象的通量定律。 -声音。在分析的两个模型下，我们采用分析和数值方法，研究了密度激波的传播，演化和定性行为，即密度在其上传播的传播表面。在此过程中，我们识别出一类波动方程，其性质是所有波动方程的成员都具有相同的激波结构，演化和速度。最后，提出了可能的后续研究，并指出了在连续谱物理其他领域的应用。