  We study fundamental and vortical solitons in disk-morphed Bose-Einstein
condensates (BECs) subject to strong confinement along the axial direction.
Starting from the three-dimensional (3D) Gross-Pitaevskii equation (GPE), we
proceed to an effective 2D nonpolynomial Schroeodinger equation (NPSE) derived
by means of the integration over the axial coordinate. Results produced by the
latter equation are in very good agreement with those obtained from the full 3D
GPE, including cases when the formal 2D equation with the cubic nonlinearity is
unreliable. The 2D NPSE is used to predict density profiles and dynamical
stability of repulsive and attractive BECs with zero and finite topological
charge in various planar trapping configurations, including the axisymmetric
harmonic confinement and 1D periodic potential. In particular, we find a stable
dynamical regime that was not reported before, viz., periodic splitting and
recombination of trapped vortices with topological charge 2 or 3 in the
self-attractive BEC.
