New revival phenomena for linear integro–differential equations

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

Research output: Contribution to journalArticlepeer-review

Abstract

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
JournalStudies in Applied Mathematics
Early online date31 May 2021
DOIs
Publication statusE-pub ahead of print - 31 May 2021

Keywords

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

ASJC Scopus subject areas

  • Applied Mathematics

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