New revival phenomena for linear integro–differential equations

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

doi:10.1111/sapm.12397

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 journal › Article › peer-review

12 Citations (Scopus)

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
Pages (from-to)	1209-1239
Number of pages	31
Journal	Studies in Applied Mathematics
Volume	147
Issue number	4
Early online date	31 May 2021
DOIs	https://doi.org/10.1111/sapm.12397
Publication status	Published - Nov 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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10.1111/sapm.12397

Cite this

@article{95361666b3454ed2838ef7f23b442e04,

title = "New revival phenomena for linear integro{\textendash}differential equations",

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.",

keywords = "dispersive quantization, dynamical systems, partial differential equations, periodic boundary value problem, Talbot effect",

author = "Lyonell Boulton and Olver, \{Peter J.\} and Beatrice Pelloni and Smith, \{David A.\}",

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: {\textcopyright} 2021 Wiley Periodicals LLC.",

year = "2021",

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doi = "10.1111/sapm.12397",

language = "English",

volume = "147",

pages = "1209--1239",

journal = "Studies in Applied Mathematics",

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T1 - New revival phenomena for linear integro–differential equations

AU - Boulton, Lyonell

AU - Olver, Peter J.

AU - Pelloni, Beatrice

AU - Smith, David A.

N1 - 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.

PY - 2021/11

Y1 - 2021/11

N2 - 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.

AB - 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.

KW - dispersive quantization

KW - dynamical systems

KW - partial differential equations

KW - periodic boundary value problem

KW - Talbot effect

UR - https://www.scopus.com/pages/publications/85107150580

U2 - 10.1111/sapm.12397

DO - 10.1111/sapm.12397

M3 - Article

AN - SCOPUS:85107150580

SN - 0022-2526

VL - 147

SP - 1209

EP - 1239

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

IS - 4

ER -

New revival phenomena for linear integro–differential equations

Abstract

Keywords

ASJC Scopus subject areas

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