Multidimensional solitons in a low-dimensional periodic potential (9 pages)

By B. Baizakov, Boris A. Malomed, M. Salerno. 2003

142 citations recorded by the source corpus.

Using the variational approximation and direct simulations in real and imaginary time, we find stable two-dimensional (2D) and 3D solitons in the self-attractive Gross-Pitaevskii equation (GPE) with a potential which is uniform in one direction (z) and periodic in the others (however, the quasi-1D potentials cannot stabilize 3D solitons). The family of solitons includes single- and multiple-peaked ones. The results apply to Bose-Einstein condensates (BEC's) in optical lattices (OL's) and to spatial or spatiotemporal solitons in layered optical media. This is the first prediction of mobile 2D and 3D solitons in BEC's, as they keep mobility along z. Head-on collisions of in-phase solitons lead to their fusion into a collapsing pulse. Slow collisions between two multiple-peaked solitons whose main peaks are separated by an intermediate channel end up with their fusion into one single-peaked soliton in the middle channel, {approx_equal}1/3 of the original number of atoms being shed off. Stable localized states in the self-repulsive GPE with the low-dimensional OL combined with a parabolic trap are found too. Two such pulses in one channel perform recurrent elastic collisions, periodically featuring sharp interference patterns in the strong-overlap state.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f858dca437384dfa8ca34c64731b0dfe2a315544

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

(INVITED) Vortex solitons: Old results and new perspectives (2019, methodology): “, U = U (x, y), may be sufficient to support stable 3D solitons [165–167].”
Light propagation and localization in modulated photonic lattices and waveguides (2011, background): “Discreteness in photonic lattices can provide an additional stabilization mechanism, and indeed stable continuous–discrete solitons were found in nonlinear waveguide arrays [137,8] and optical fiber bundles [142,143].”
Solitons in nonlinear lattices (2010, background): “Finally, it is worthy to note that, as shown by Baizakov, Malomed, and Salerno (2004), a reduced quasi-1D linear-lattice potential, which depends on one coordinate only, is sufficient for the full stabilization of 2D solitons.”