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We consider a two-dimensional (2D) counterpart of the experiment that led tothe creation of quasi-1D bright solitons in Bose-Einstein condensates (BECs)[Nature 417, 150--153 (2002)]. We start by identifying the ground state of the2D Gross-Pitaevskii equation for repulsive interactions, with aharmonic-oscillator (HO) trap, and with or without an optical lattice (OL).Subsequently, we switch the sign of the interaction to induce interatomicattraction and monitor the ensuing dynamics. Regions of the stableself-trapping and catastrophic collapse of 2D fundamental solitons areidentified in the parameter plane of the OL strength and BEC norm. The increaseof the OL strength expands the persistence domain for the solitons to largernorms. For single-charged solitary vortices, in addition to the survival andcollapse regimes, an intermediate one is identified, where the vortex resiststhe collapse but loses its structure, transforming into a fundamental soliton.The same setting may also be implemented in the context of optical solitons andvortices, using photonic-crystal fibers.

Quenched dynamics of two-dimensional solitons and vortices in the Gross-Pitaevskii equation