New Revival Phenomena for Linear Integro-Differential Equations

3 Oct 2020 · Lyonell Boulton, Peter J. Olver, Beatrice Pelloni, David A. Smith ·

We present and analyse 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 quantised cusped solutions at rational times. We give an analytic description of this phenomenon, and present illustrative numerical simulations.

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New Revival Phenomena for Linear Integro-Differential Equations

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