Formation of multi-solitons and vortex bright solitons in Bose-condensed alkali-metal atoms

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.