  We study the formation of bright solitons in a Bose-Einstein condensate of
$^7$Li atoms induced by a sudden change in the sign of the scattering length
from positive to negative, as reported in a recent experiment (Nature {\bf
417}, 150 (2002)). The numerical simulations are performed by using the 3D
Gross-Pitaevskii equation (GPE) with a dissipative three-body term. We show
that a number of bright solitons is produced and this can be interpreted in
terms of the modulational instability of the time-dependent macroscopic wave
function of the Bose condensate. In particular, we derive a simple formula for
the number of solitons that is in good agreement with the numerical results of
3D GPE. By investigating the long time evolution of the soliton train solving
the 1D GPE with three-body dissipation we find that adjacent solitons repel
each other due to their phase difference. In addition, we find that during the
motion of the soliton train in an axial harmonic potential the number of
solitonic peaks changes in time and the density of individual peaks shows an
intermittent behavior. Such a complex dynamics explains the ``missing
solitons'' frequently found in the experiment.
