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Condensed Matter > Soft Condensed Matter

arXiv:cond-mat/0306645 (cond-mat)
[Submitted on 25 Jun 2003]

Title:Multidimensional solitons in periodic potentials

Authors:B. B. Baizakov, B. A. Malomed, M. Salerno
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Abstract: The existence of stable solitons in two- and three-dimensional (2D and 3D) media governed by the self-focusing cubic nonlinear Schrödinger equation with a periodic potential is demonstrated by means of the variational approximation (VA) and in direct simulations. The potential stabilizes the solitons against collapse. Direct physical realizations are a Bose-Einstein condensate (BEC) trapped in an optical lattice, and a light beam in a bulk Kerr medium of a photonic-crystal type. In the 2D case, the creation of the soliton in a weak lattice potential is possible if the norm of the field (number of atoms in BEC, or optical power in the Kerr medium) exceeds a threshold value (which is smaller than the critical norm leading to collapse). Both "single-cell" and "multi-cell" solitons are found, which occupy, respectively, one or several cells of the periodic potential, depending on the soliton's norm. Solitons of the former type and their stability are well predicted by VA. Stable 2D vortex solitons are found too.
Comments: 13 pages, 3 figures, Europhys. Lett., in press
Subjects: Soft Condensed Matter (cond-mat.soft); Pattern Formation and Solitons (nlin.PS)
Cite as: arXiv:cond-mat/0306645 [cond-mat.soft]
  (or arXiv:cond-mat/0306645v1 [cond-mat.soft] for this version)
  https://doi.org/10.48550/arXiv.cond-mat/0306645
Journal reference: Europhys. Lett., 63, 642 (2003).
Related DOI: https://doi.org/10.1209/epl/i2003-00579-4

Submission history

From: Bakhtiyor Baizakov [view email]
[v1] Wed, 25 Jun 2003 13:45:21 UTC (127 KB)
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