Dispersion of discontinuous periodic waves

Gong Chen, Peter J. Olver

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

The dynamic evolution of linearly dispersive waves on periodic domains with discontinuous initial profiles is shown to depend remarkedly upon the asymptotics of the dispersion relation at large wavenumbers. Asymptotically linear or sublinear dispersion relations produce slowly changing waves, while those with polynomial growth exhibit dispersive quantization, a.k.a. the Talbot effect, being (approximately) quantized at rational times, but a nondifferentiable fractal at irrational times. Numerical experiments suggest that such effects persist into the nonlinear regime, for both integrable and nonintegrable systems. Implications for the successful modelling of wave phenomena on bounded domains and numerical challenges are discussed.

Original languageEnglish (US)
Article number20120407
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume469
Issue number2149
DOIs
StatePublished - Jan 8 2013

Keywords

  • Dispersion
  • Fractal
  • Splitting method
  • Talbot effect
  • Wave

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