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

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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)
Pages (from-to)	1209-1239
Number of pages	31
Journal	Studies in Applied Mathematics
Volume	147
Issue number	4
DOIs	https://doi.org/10.1111/sapm.12397
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

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title = "New revival phenomena for linear integro–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.",

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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.",

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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 - Talbot effect

KW - dispersive quantization

KW - dynamical systems

KW - partial differential equations

KW - periodic boundary value problem

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JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

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ER -

New revival phenomena for linear integro–differential equations

Abstract

Bibliographical note

Keywords

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