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Discrete surface solitons in two dimensions.

H Susanto1, P G Kevrekidis, B A Malomed

  • 1Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 7, 2007
PubMed
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Investigating 2D lattices with edges reveals that surfaces expand soliton stability and create orientation-dependent dipole behavior. Lattice solitons near edges exhibit unique properties, with some unstable patterns transforming into ordinary solitons.

Area of Science:

  • Nonlinear physics
  • Condensed matter physics
  • Optical lattices

Background:

  • Localized modes in two-dimensional (2D) lattices are crucial for understanding wave phenomena.
  • The presence of an edge or surface significantly alters the behavior of these modes compared to uniform lattices.

Purpose of the Study:

  • To investigate fundamental localized modes in 2D lattices with an edge.
  • To analyze the impact of the edge on the stability and properties of different types of solitons.

Main Methods:

  • Analytical calculations to derive theoretical predictions.
  • Numerical simulations to verify theoretical findings and explore complex behaviors.

Main Results:

  • The edge expands the stability region for fundamental solitons and introduces anisotropy for dipoles.

Related Experiment Videos

  • Lattice vortex solitons are destabilized near the edge.
  • A novel horseshoe-shaped soliton, unstable in uniform lattices, is supported by the edge and can transform into ordinary solitons.

    • Conclusions:

    • Edges play a critical role in modifying the dynamics and stability of localized modes in 2D lattices.
    • The edge environment enables the existence and transformation of specific soliton structures, like the horseshoe soliton.