Discretization effects in the nonlinear Schrödinger equation

Gadi Fibich, Boaz Ilan

Research output: Contribution to journalArticlepeer-review

Abstract

We show that discretization effects in finite-difference simulations of blowup solutions of the nonlinear Schrödinger equation (NLS) initially accelerate self focusing but later arrest the collapse, resulting instead in focusing-defocusing oscillations. The modified equation of the semi-discrete NLS, which is the NLS with high-order anisotropic dispersion, captures the arrest of collapse but not the subsequent oscillations. Discretization effects in perturbed NLS equations are also discussed.

Original languageEnglish
Pages (from-to)63-75
Number of pages13
JournalApplied Numerical Mathematics
Volume44
Issue number1-2
DOIs
StatePublished - Jan 2003

Keywords

  • Beam collapse
  • Blowup
  • Modified equation
  • Self focusing
  • Singularity formation

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