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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
Summary
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.
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.
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