Dispersive quantization

Peter J. Olver

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


The evolution, through linear dispersion, of piecewise constant periodic initial data leads to surprising quantized structures at rational times, and fractal, nondifferentiable profiles at irrational times. Similar phenomena have been observed in optics and quantum mechanics, and lead to intriguing connections with exponential sums arising in number theory. Ramifications of these observations for numerics and nonlinear dispersion are proposed as open problems.

Original languageEnglish (US)
Pages (from-to)599-610
Number of pages12
JournalAmerican Mathematical Monthly
Issue number7
StatePublished - Aug 2010


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