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Localized vortices with a semi-integer charge in nonlinear dynamical lattices.

P G Kevrekidis1, Boris A Malomed, A R Bishop

  • 1Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, MS B262, Los Alamos, New Mexico 87545, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 22, 2002
PubMed
Summary

Researchers discovered stable half-integer topological charge (S=1/2) vortex solitons in 2D discrete nonlinear Schrödinger (DNLS) models. These fractional vortices are stable oscillating solutions, unlike in continuum models.

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Area of Science:

  • Nonlinear dynamics
  • Soliton theory
  • Condensed matter physics

Background:

  • Topological charge in vortexlike configurations is typically integer and conserved.
  • Continuum models of the nonlinear Schrödinger equation do not support fractional topological charges.

Purpose of the Study:

  • To investigate the existence and stability of fractional topological charge vortices in 2D discrete nonlinear Schrödinger (DNLS) models.
  • To compare the behavior of discrete vortices with their continuum counterparts and previously reported quantum lattice findings.

Main Methods:

  • Analysis of stationary solutions to the 2D DNLS equation.
  • Linear stability analysis of the vortex solutions.
  • Direct numerical simulations of the full 2D DNLS model.

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Main Results:

  • Demonstrated the existence of stable S=1/2 vortex solitons in the 2D DNLS model, which are absent in the continuum version.
  • Confirmed the stability of S=1/2 vortices through simulations, showing them as stable oscillating solutions.
  • Identified distinct S=1 discrete vortices, more energetic and less stable than S=1/2 vortices, and found 1D analogs of S=1/2 vortices.

Conclusions:

  • Discrete nonlinear lattices can support stable fractional topological charge vortices (S=1/2), challenging assumptions based on continuum models.
  • The stability and behavior of discrete vortices differ significantly from continuum models and quantum lattice predictions.
  • Fractional vortices in 1D and 2D DNLS models exhibit unique properties, including stable oscillating soliton behavior.