We present and analyze a novel manifestation of the revival phenomenon for linear spatially periodic evolution equations , in the concrete case of three nonlocal equations that arise in water wave theory and are defined by convolution kernels. Revival in these cases is manifested in the form of dispersively quantized cusped solutions at rational times. We give an analytic description of this phenomenon, and present illustrative numerical simulations.

中文翻译：

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线性积分微分方程的新复兴现象

我们在水波理论中出现并由卷积核定义的三个非局部方程的具体情况下，提出并分析了线性空间周期演化方程的复兴现象的新表现形式。在这些情况下，复兴以有理时间的分散量子化尖峰解的形式表现出来。我们对这种现象进行了分析描述，并提供了说明性的数值模拟。