Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2005-01-27
Phys. Rev. Lett. 94 (2005) 203901
Physics
Condensed Matter
Soft Condensed Matter
4 pages, 4 figures, submitted January 2005
Scientific paper
10.1103/PhysRevLett.94.203901
We construct a variety of novel localized states with distinct topological structures in the 3D discrete nonlinear Schr{\"{o}}dinger equation. The states can be created in Bose-Einstein condensates trapped in strong optical lattices, and crystals built of microresonators. These new structures, most of which have no counterparts in lower dimensions, range from purely real patterns of dipole, quadrupole and octupole types to vortex solutions, such as "diagonal" and "oblique" vortices, with axes oriented along the respective directions $(1,1,1)$ and $(1,1,0)$. Vortex "cubes" (stacks of two quasi-planar vortices with like or opposite polarities) and "diamonds" (discrete skyrmions formed by two vortices with orthogonal axes) are constructed too. We identify stability regions of these 3D solutions and compare them with their 2D counterparts, if any. An explanation for the stability/instability of most solutions is proposed. The evolution of unstable states is studied as well.
Carretero-González Ricardo
Frantzeskakis Dimitri J.
Kevrekidis Panagiotis G.
Malomed Boris A.
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