Numerical simulation of nonlinear dispersive quantization

Gong Chen, Peter J. Olver

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

When posed on a periodic domain in one space variable, linear dispersive evolution equations with integral polynomial dispersion relations exhibit strikingly different behaviors depending upon whether the time is rational or irrational relative to the length of the interval, thus producing the Talbot effect of dispersive quantization and fractalization. The goal here is to show that these remarkable phenomena extend to nonlinear dispersive evolution equations. We will present numerical simulations, based on operator splitting methods, of the nonlinear Schrödinger and Korteweg-deVries equations with step function initial data and periodic boundary conditions. For the integrable nonlinear Schrödinger equation, our observations have been rigorously confirmed in a recent paper of Erdoǧan and Tzirakis, [10].

Original languageEnglish
Pages (from-to)991-1008
Number of pages18
JournalDiscrete and Continuous Dynamical Systems
Volume34
Issue number3
DOIs
StatePublished - Mar 2014

Keywords

  • Dispersion
  • Fractal
  • Korteweg-deVries equation
  • Nonlinear schrodinger equation
  • Operator splitting scheme
  • Quantized
  • Talbot effect

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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