Points of constancy of the periodic linearized Korteweg–deVries equation

Peter J. Olver, Efstratios Tsatis

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We investigate the points of constancy in the piecewise constant solution profiles of the periodic linearized Korteweg–deVries equation with step function initial data at rational times. The solution formulae are given by certain Weyl sums, and we employ number theoretic techniques, including Kummer sums, in our analysis. These results constitute an initial attempt to understand the complementary phenomenon of ‘fractalization’ at irrational times.

Original languageEnglish (US)
Article number0160
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume474
Issue number2217
DOIs
StatePublished - Sep 1 2018

Keywords

  • Dispersive quantization
  • Kummer sum
  • Linearized Korteweg–deVries equation
  • Point of constancy
  • Weyl sum

Fingerprint Dive into the research topics of 'Points of constancy of the periodic linearized Korteweg–deVries equation'. Together they form a unique fingerprint.

Cite this