Beam stabilization in the two-dimensional nonlinear Schrodinger equation with an attractive potential by beam splitting and radiation

B.J. leMesurier, Peter Leth Christiansen, Yuri Borisovich Gaididei, Jens Juul Rasmussen

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Abstract

The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrodinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrodinger equation in the critical dimension 2 and can lead to a stable oscillating beam. This is observed to involve a splitting of the beam into an inner part that is oscillatory and of subcritical power and an outer dispersing part. An analysis is given in terms of the rate competition between the linear and nonlinear focusing effects, radiation losses, and known stable periodic behavior of certain solutions in the presence of attractive potentials.
Original languageEnglish
JournalPhysical Review E
Volume70
Issue number4
Pages (from-to)046614 (7 pages)
ISSN2470-0045
DOIs
Publication statusPublished - 2004

Bibliographical note

Copyright (2004) American Physical Society.

Keywords

  • COLLAPSE
  • BOSE-GAS
  • CRITICAL DIMENSION
  • DYNAMICS
  • DISPERSION

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