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Discrete vortex solitons.

B A Malomed1, P G Kevrekidis

  • 1Department of Interdisciplinary Studies, Faculty of Engineering, Tel Aviv University, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 11, 2001
PubMed
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Vortex solitons in discrete 2D nonlinear Schrödinger equations can conserve vorticity. S=1 solitons are stable below a critical coupling, while higher vorticity solitons and S=0 solitons exhibit instability. Stable bound states of S=1 and S=0 solitons are possible.

Area of Science:

  • Nonlinear optics
  • Condensed matter physics
  • Mathematical physics

Background:

  • Discrete nonlinear Schrödinger equation models

Purpose of the Study:

  • Investigate localized states, specifically vortex solitons, in the discrete 2D nonlinear Schrödinger equation.
  • Analyze the stability and dynamics of these solitons, particularly focusing on vorticity conservation.

Main Methods:

  • Linear stability analysis
  • Direct numerical simulations

Main Results:

  • Identified stable vortex solitons with integer vorticity S=1 below a critical intersite coupling C((1))(cr).
  • Observed instability in S=1 solitons for C > C((1))(cr), leading to splitting and symmetry breaking.

Related Experiment Videos

  • Found that usual (S=0) solitons become unstable at C > C((0))(cr) via a different mechanism.
  • Constructed higher-energy S=1 solitons centered between lattice sites.
  • Determined that S=2 vortex solitons are always unstable.
  • Demonstrated the formation of stable bound states between S=1 and S=0 solitons.

    • Conclusions:

    • Vorticity can act as a dynamical invariant for solitons in this system, despite the lack of conserved angular momentum in the lattice.
    • The stability of vortex solitons is critically dependent on the intersite coupling and vorticity.
    • Complex dynamics, including splitting, decay, and bound state formation, are observed.