New Revival Phenomena for Linear Integro-Differential Equations
Analysis of PDEs
2020-10-06 v1 Mathematical Physics
math.MP
Abstract
We present and analyse 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 quantised cusped solutions at rational times. We give an analytic description of this phenomenon, and present illustrative numerical simulations.
Keywords
Cite
@article{arxiv.2010.01320,
title = {New Revival Phenomena for Linear Integro-Differential Equations},
author = {Lyonell Boulton and Peter J. Olver and Beatrice Pelloni and David A. Smith},
journal= {arXiv preprint arXiv:2010.01320},
year = {2020}
}