Discrete surface solitons in two dimensions
arXiv:nlin/0607063 · doi:10.1103/PhysRevE.75.056605
Abstract
We investigate fundamental localized modes in 2D lattices with an edge (surface). Interaction with the edge expands the stability area for ordinary solitons, and induces a difference between perpendicular and parallel dipoles; on the contrary, lattice vortices cannot exist too close to the border. Furthermore, we show analytically and numerically that the edge stabilizes a novel wave species, which is entirely unstable in the uniform lattice, namely, a "horseshoe" soliton, consisting of 3 sites. Unstable horseshoes transform themselves into a pair of ordinary solitons.
6 pages, 4 composite figures
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- Two-dimensional solitons at interfaces between binary superlattices and homogeneous lattices
- Soliton excitation in waveguide arrays with an effective intermediate dimensionality
- Generation of linear waves in the flow of Bose-Einstein condensate past an obstacle
- Soliton emission in amplifying optical lattice surfaces
- Surface solitons in two-dimensional quadratic photonic lattices
- Interface solitons in two-dimensional photonic lattices
- Chaotic Bloch oscillations in dissipative optical systems driven by a periodic train of coherent pulses
- Excitation of Wannier-Stark states in a chain of coupled optical resonators with linear gain and nonlinear losses
- LOcalized modes on an Ablowitz-Ladik nonlinear impurity