Europhys. Lett., 63 (5) , pp. 642-648 (2003)
Multidimensional solitons in periodic potentialsB. B. Baizakov1, B. A. Malomed2 and M. Salerno1
1 Dipartimento di Fisica "E. R. Caianiello" and INFM, Università di Salerno I-84081 Baronissi (SA), Italy
2 Department of Interdisciplinary Studies, Faculty of Engineering Tel Aviv University - Tel Aviv 69978, Israel
(Received 18 March 2003; accepted in final form 20 June 2003)
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.
03.75.Lm - Tunneling, Josephson effect, Bose-Einstein condensates in periodic potentials, solitons, vortices and topological excitations.
03.75.Kk - Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow.
05.45.Yv - Solitons.
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