Self-focusing with fourth-order dispersion

Gadi Fibich*, Boaz Ilan, George Papanicolaou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

178 Scopus citations


We analyze self-focusing and singularity formation in the nonlinear Schrödinger equation (NLS) with high-order dispersion iψt±Δqψ+|ψ| ψ = 0, in the isotropic mixed-dispersion NLS iψt + Δψ + εΔ2ψ + |ψ| ψ = 0, and in nonisotropic mixed-dispersion NLS equations which model propagation in fiber arrays.

Original languageEnglish
Pages (from-to)1437-1462
Number of pages26
JournalSIAM Journal on Applied Mathematics
Issue number4
StatePublished - Apr 2002


  • Blowup
  • Critical exponent
  • Critical power
  • Gagliardo-Nirenberg inequality
  • Optimal constants


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