New revival phenomena for linear integro–differential equations

Lyonell Boulton, Peter J. Olver, Beatrice Pelloni, David A. Smith

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
JournalStudies in Applied Mathematics
StateAccepted/In press - 2021

Bibliographical note

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  • dispersive quantization
  • dynamical systems
  • partial differential equations
  • periodic boundary value problem
  • Talbot effect


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