  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.
