Quenched dynamics of two-dimensional solitons and vortices in the   Gross-Pitaevskii equation
  We consider a two-dimensional (2D) counterpart of the experiment that led to the creation of quasi-1D bright solitons in Bose-Einstein condensates (BECs) [Nature 417, 150--153 (2002)]. We start by identifying the ground state of the 2D Gross-Pitaevskii equation for repulsive interactions, with a harmonic-oscillator (HO) trap, and with or without an optical lattice (OL). Subsequently, we switch the sign of the interaction to induce interatomic attraction and monitor the ensuing dynamics. Regions of the stable self-trapping and catastrophic collapse of 2D fundamental solitons are identified in the parameter plane of the OL strength and BEC norm. The increase of the OL strength expands the persistence domain for the solitons to larger norms. For single-charged solitary vortices, in addition to the survival and collapse regimes, an intermediate one is identified, where the vortex resists the collapse but loses its structure, transforming into a fundamental soliton. The same setting may also be implemented in the context of optical solitons and vortices, using photonic-crystal fibers. 
Qian-Yong Chen and P. G. Kevrekidis and Boris A. Malomed
nlin.PS cond-mat.quant-gas physics.optics