Dispersive lamb systems

Peter J. Olver, Natalie E. Sheils

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

Under periodic boundary conditions, a one-dimensional dispersive medium driven by a Lamb oscillator exhibits a smooth response when the dispersion relation is asymptotically linear or superlinear at large wave numbers, but unusual fractal solution profiles emerge when the dispersion relation is asymptotically sublinear. Strikingly, this is exactly the opposite of the superlinear asymptotic regime required for fractalization and dispersive quantization, also known as the Talbot effect, of the unforced medium induced by discontinuous initial conditions.

Original languageEnglish (US)
Pages (from-to)239-254
Number of pages16
JournalJournal of Geometric Mechanics
Volume11
Issue number2
DOIs
StatePublished - Jun 2019

Bibliographical note

Publisher Copyright:
© American Institute of Mathematical Sciences

Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

Keywords

  • Dispersive quantization
  • Lamb system
  • Periodic boundary conditions
  • Talbot effect

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