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New revival phenomena for linear integro–differential equations
Author(s) -
Boulton Lyonell,
Olver Peter J.,
Pelloni Beatrice,
Smith David A.
Publication year - 2021
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/sapm.12397
Subject(s) - phenomenon , mathematics , convolution (computer science) , mathematical analysis , differential equation , partial differential equation , integro differential equation , physics , computer science , first order partial differential equation , quantum mechanics , machine learning , artificial neural network
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.