Open AccessThe stability of matter-wave solitons in 2D linear and nonlinear optical lattices
Author(s) -
Haijun Chen,
Xiangfu Li
Publication year - 2013
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.62.070302
Subject(s) - physics , nonlinear system , stability (learning theory) , bose–einstein condensate , linear stability , variational method , matter wave , stability criterion , variational analysis , nonlinear optics , gross–pitaevskii equation , quantum mechanics , classical mechanics , quantum , mathematical analysis , mathematics , machine learning , computer science , statistics , discrete time and continuous time
By means of variational solution and direct numerical simulation of the Gross-Pitaevskii equation (GPE), we have studied the stability of matter-wave solitons in two-dimensional (2D) Bose-Einstein condensations (BECs), with 2D linear and nonlinear optical lattices (OLs). Using the static variational approach and Vakhitov-Kolokolov criterion necessary for stability, we obtain the stability condition for solitons in different combinations of OL's parameters. We show that the 2D linear and nonlinear optical lattices allow us to stabilize 2D solitons for both attractive and repulsive interactions. We also study the time-evolution problems of 2D BECs, using the time-dependent variational approach and numerical solution of GPE for 2D linear and nonlinear OLs. Very good agreement between the results corresponding to both treatments is observed.