Collapse instability of solitons in the nonpolynomial Schrödinger equation with dipole-dipole interactions

A model of the Bose-Einstein condensate (BEC) of dipolar atoms, confined in a combination of a cigar-shaped trap and optical lattice acting in the axial direction, is studied in the framework of the one-dimensional (1D) nonpolynomial Schrödinger equation (NPSE) with additional terms describing long-range dipoledipole (DD) interactions. The NPSE makes it possible to describe the collapse of localized modes, which was experimentally observed in the self-attractive BEC confined in tight traps, in the framework of the 1D description. We study the influence of the DD interactions on the dynamics of bright solitons, especially as concerns their collapseinduced instability. Both attractive and repulsive contact and DD interactions are considered. The results are summarized in the form of stability/collapse diagrams in a respective parametric space. In particular, it is shown that the attractive DD interactions may prevent the collapse instability in the condensate with attractive contact interactions. Collapse instability of solitons in the nonpolynomial Schrödinger equation with dipole-dipole interactions2 1 Vinča Institute of Nuclear Sciences, P.O. Box 522,11001 Belgrade, Serbia 2 Faculty of Sciences and Mathematics, University of Nǐs, P.O. Box 224, 18001 Nǐs, Serbia 3 Department of Physical Electronics, School of Electrical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel E-mail: [email protected]