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 language | English (US) |
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Pages (from-to) | 1209-1239 |
Number of pages | 31 |
Journal | Studies in Applied Mathematics |
Volume | 147 |
Issue number | 4 |
DOIs | |
State | Published - Nov 2021 |
Bibliographical note
Funding Information:The authors gratefully acknowledge support from Yale‐NUS College workshop Grant IG18‐CW003, which funded all of them to attend a week‐long workshop where the results presented here were first discovered and discussed.
Publisher Copyright:
© 2021 Wiley Periodicals LLC.
Keywords
- Talbot effect
- dispersive quantization
- dynamical systems
- partial differential equations
- periodic boundary value problem