  Formation of multi-solitons and vortex bright solitons in Bose-condensed
alkali-metal atoms is analyzed by using the nonpolynomial Schordinger equation.
A train of bright solitons is obtained from an axially homogeneous
Bose-Einstein condensate by a sudden change of the scattering length from
repulsive to attractive. We derive an analytical expression for the number of
bright solitons generated by using this mechanism. The formula generalizes a
previous formula obtained with the 1D Gross-Pitaevskii equation. In the second
part we consider vortex bright solitons, namely cigar-shaped bright solitons
with a nonzero angular quantum number $k$ along the axial direction. By using a
variational approach we determine the shape of vortex bright solitons, showing
that the critical number of atoms for the collapse of the vortex soliton
increases with a larger $k$. Finally we calculate monopole and quadrupole
collective oscillations of these vortex bright solitons.
