Bright solitary waves and trapped solutions in Bose-Einstein condensates with attractive interactions

We analyse the static solutions of attractive Bose-Einstein condensates under transverse confinement, both with and without axial confinement. By full numerical solution of the Gross-Pitaevskii equation and variational methods we map out the condensate solutions, their energetic properties, and their critical points for instability. With no axial confinement a bright solitary wave solution will tend to decay by dispersion unless the interaction energy is close to the critical value for collapse. In contrast, with axial confinement the only decay mechanism is collapse. The stability of a bright solitary wave solution increases with higher radial confinement. Finally we consider the stability of dynamical states containing up to four solitons and find good agreement with recent experiments.