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Moving embedded lattice solitons.

B A Malomed1, J Fujioka, A Espinosa-Cerón

  • 1Department of Interdisciplinary Studies, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel.

Chaos (Woodbury, N.Y.)
|April 8, 2006
PubMed
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Researchers discovered stable, moving embedded lattice solitons (ELS) in a novel discrete system. These solitons can move at any speed and withstand collisions, with potential applications in Bose-Einstein condensates.

Area of Science:

  • Nonlinear physics
  • Condensed matter physics
  • Soliton theory

Background:

  • Previous work proved the existence of embedded lattice solitons (ELS) in discrete systems.
  • Explicit solutions for unstable isolated ELS were found for a higher-order nonlinear Schrödinger equation.

Purpose of the Study:

  • To investigate the existence of continuous families of ELS.
  • To determine if ELS can be stable and mobile.
  • To understand ELS interactions.

Main Methods:

  • Introduced a novel discrete equation (modified Korteweg-de Vries type with next-nearest-neighbor couplings).
  • Derived exact solutions for a two-parameter continuous family of ELS.
  • Employed numerical simulations to verify stability and collision dynamics.

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Main Results:

  • Demonstrated a two-parameter continuous family of exact ELS.
  • Confirmed that these ELS can move with arbitrary velocities.
  • Numerical simulations showed ELS are completely stable and robust against collisions, with collisions resulting only in positional shifts.

Conclusions:

  • The novel discrete system supports stable, mobile, and collision-resilient ELS.
  • These findings address key questions regarding the nature and behavior of ELS.
  • The model has potential applications in describing Bose-Einstein condensates with specific interactions in optical lattices.