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

Brenton John leMesurier, Peter Leth Christiansen, Yuri B. Gaididei, and Jens Juul Rasmussen
Phys. Rev. E 70, 046614 – Published 28 October 2004

Abstract

The effect of attractive linear potentials on self-focusing in-waves modeled by a nonlinear Schrödinger equation is considered. It is shown that the attractive potential can prevent both singular collapse and dispersion that are generic in the cubic Schrödinger 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.

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  • Received 14 August 2003

DOI:https://doi.org/10.1103/PhysRevE.70.046614

©2004 American Physical Society

Authors & Affiliations

Brenton John leMesurier*

  • Department of Mathematics, College of Charleston, Charleston, South Carolina 29424, USA

Peter Leth Christiansen

  • Informatics and Mathematical Modelling and Department of Physics, Technical University of Denmark, DK-2800 Kgs Lyngby, Denmark

Yuri B. Gaididei

  • Bogolyubov Institute for Theoretical Physics, 252 143 Kiev, Ukraine

Jens Juul Rasmussen

  • Department of Optics and Plasma Research, OPL-128, Risø National Laboratory, P.O. Box 49, DK-4000 Roskilde, Denmark

  • *Electronic address: lemesurierb@cofc.edu
  • Electronic address: plc@imm.dtu.dk
  • Electronic address: jens.juul.rasmussen@risoe.dk

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Issue

Vol. 70, Iss. 4 — October 2004

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