Discretization effects in the nonlinear Schrödinger equation

Gadi Fibich*, Boaz Ilan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


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
Issue number1-2
StatePublished - Jan 2003


FundersFunder number
United States-Israel Binational Science Foundation


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


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