Surface Solitons in Three Dimensions

Details Surface Solitons in Three Dimensions Surface Solitons in Three Dimensions

2008-06-06

arxiv.org/abs/0806.1087v2

Phys. Rev. E 78 (2008) 036605

Nonlinear Sciences

Pattern Formation and Solitons

10 pages, 12 figures, submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.78.036605

We study localized modes on the surface of a three-dimensional dynamical lattice. The stability of these structures on the surface is investigated and compared to that in the bulk of the lattice. Typically, the surface makes the stability region larger, an extreme example of that being the three-site "horseshoe"-shaped structure, which is always unstable in the bulk, while at the surface it is stable near the anti-continuum limit. We also examine effects of the surface on lattice vortices. For the vortex placed parallel to the surface this increased stability region feature is also observed, while the vortex cannot exist in a state normal to the surface. More sophisticated localized dynamical structures, such as five-site horseshoes and pyramids, are also considered.

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