Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2005-07-04
Nonlinear Sciences
Pattern Formation and Solitons
8 pages, 6 figures, to appear in Physical Review A
Scientific paper
10.1103/PhysRevA.72.021601
The existence and stability of solitons in Bose-Einstein condensates with attractive inter-atomic interactions, described by the Gross-Pitaevskii equation with a three-dimensional (3D) periodic potential, are investigated in a systematic form. We find a one-parameter family of stable 3D solitons in a certain interval of values of their norm, provided that the strength of the potential exceeds a threshold value. The minimum number of $^{7}$Li atoms in the stable solitons is 60, and the energy of the soliton at the stability threshold is $\approx 6$ recoil energies in the lattice. The respective energy-vs.-norm diagram features two cuspidal points, resulting in a typical \textit{swallowtail pattern}, which is a generic feature of 3D solitons supported by low- (2D) or fully-dimensional lattice potentials.
Crasovan Lucian-Cornel
Kartashov Yaroslav V.
Lederer Falk
Malomed Boris A.
Mazilu Dan
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