Self-focusing in the damped nonlinear Schrödinger equation

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Abstract

We analyze the effect of damping (absorption) on critical self-focusing. We identify a threshold value δth for the damping parameter δ such that when δ > δth damping arrests blowup. When δ < δth, the solution blows up at the same asymptotic rate as the undamped nonlinear Schrödinger equation.

Original languageEnglish
Pages (from-to)1680-1705
Number of pages26
JournalSIAM Journal on Applied Mathematics
Volume61
Issue number5
DOIs
StatePublished - 2001

Keywords

  • Absorption
  • Blowup
  • Collapse
  • Critical power
  • Damping
  • Modulation theory
  • Singularity

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