Pattern forming dynamical instabilities of Bose-Einstein condensates

Dimitri J. Frantzeskakis

Department of Physics, University of Athens, Panepistimiopolis, GR 15784 Athens, Greece

In the framewrk of the Gross-Pitaevskii equation, the modulational instability in one dimension (1D) and the snaking instability in two dimensions (2D) are considered as typical examples of pattern forming instabilities of Bose-Einstein condensates (BECs). It is shown that such long-wavelength instabilities can destabilize the BECs, leading to the formation of patterns of coherent structures in them. Trains of bright matter-wave solitons in 1D, and vortex arrays in 2D, are prototypical examples of the resulting nonlinear patterns, which are briefly discussed as well.