  The stability regimes and nonlinear dynamics of bright solitons created in a
harmonic potential which is transversely attractive and longitudinally
expulsive are presented. This choice of potential is motivated by the recent
creation of a matter-wave bright soliton from an attractive Bose-Einstein
condensate (L. Khaykovich {\it et al.}, Science 296, 1290 (2002)). The critical
branches for collapse due to the three-dimensional character of the gas and
explosion caused by the expulsive potential are derived based on variational
studies. Particle loss from the soliton due to sudden changes in the trapping
potential and scattering length are quantified. It is shown that higher order
solitons can also be created in present experiments by an abrupt change of a
factor of four in the scattering length. It is demonstrated that quantum
evaporation occurs by nonlinear tunneling of particles out of the soliton,
leading eventually to its explosion.
