The DOI matches its Crossref record; 22 of the 22 references it cites were found in a registry or an index.
Multidimensional solitons in periodic potentials
Open accessAbstract
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.
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Cites
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Discrete Solitons and Breathers with Dilute Bose-Einstein Condensates
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A Bose-Einstein condensate in an optical lattice
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Controlling collapse in Bose-Einstein condensates by temporal modulation of the scattering length
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Self-citationNonlinear excitations in arrays of Bose-Einstein condensates
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Self-citation
Cited by
Solitons in nonlinear lattices
Kartashov, Y. V., Malomed, B. A., & Torner, L. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.247 · Cited by 1,014
Self-citationObservation of Discrete Vortex Solitons in Optically Induced Photonic Lattices
Neshev, D. N., Alexander, T. J., Ostrovskaya, E. A., Kivshar, Y. S., Martin, H., Makasyuk, I., & Chen, Z. (2004) · Physical Review Letters · doi:10.1103/physrevlett.92.123903 · Cited by 472
Fundamental and vortex solitons in a two-dimensional optical lattice
Yang, J., & Musslimani, Z. H. (2003) · Optics Letters · doi:10.1364/ol.28.002094 · Cited by 349
Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques
Carretero-González, R., Frantzeskakis, D. J., & Kevrekidis, P. G. (2008) · Nonlinearity · doi:10.1088/0951-7715/21/7/r01 · Cited by 339
Metadata
- Authors
- Baizakov, B. B., Malomed, B. A., & Salerno, M.
- Venue
- Europhysics Letters (EPL)
- Publisher
- IOP Publishing
- Published
- 2003-09
- Volume
- 63
- Issue
- 5
- Pages
- 642-648
- ISSN
- 0295-5075 (ISSN-L)
- 1286-4854
- OpenAlex
- W2068504208
- Cited by
- 290
- References
- 22
- FWCI
- 13.60
- Type
- journal article
- Language
- en
- Open access
- green
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