Singular solutions of the subcritical nonlinear Schrödinger equation

Gadi Fibich*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We show that the subcritical d-dimensional nonlinear Schrdinger equation iψt+Δψ+| ψ |ψ=0, where 1<σd<2, admits smooth solutions that become singular in L p for p*<p≤∞, where p *:=σd/σd-1. Since limσd→2- p*=2, these solutions can collapse at any 2<p≤∞, and in particular for p=2σ+2.

Original languageEnglish
Pages (from-to)1119-1122
Number of pages4
JournalPhysica D: Nonlinear Phenomena
Volume240
Issue number13
DOIs
StatePublished - 15 Jul 2011

Keywords

  • Nonlinear Schrdinger equation
  • Singularity
  • Subcritical

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