  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.
