New revival phenomena for linear integro–differential equations

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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
Pages (from-to)1209-1239
Number of pages31
JournalStudies in Applied Mathematics
Issue number4
Early online date31 May 2021
Publication statusPublished - Nov 2021


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

ASJC Scopus subject areas

  • Applied Mathematics


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