Fractal solutions of dispersive partial differential equations on the torus

M. B. Erdoğan, G. Shakan

Research output: Contribution to journalArticle

Abstract

We use exponential sums to study the fractal dimension of the graphs of solutions to linear dispersive PDE. Our techniques apply to Schrödinger, Airy, Boussinesq, the fractional Schrödinger, and the gravity and gravity–capillary water wave equations. We also discuss applications to certain nonlinear dispersive equations. In particular, we obtain bounds for the dimension of the graph of the solution to cubic nonlinear Schrödinger and Korteweg–de Vries equations along oblique lines in space–time.

Original languageEnglish (US)
Article number11
JournalSelecta Mathematica, New Series
Volume25
Issue number1
DOIs
StatePublished - Mar 1 2019

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

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