  The propagation of an initially Gaussian wave packet of width $\Delta_0$ in a
cubic non-linear Schrodinger equation with a negative coupling constant for the
nonlinear term is considered . It is predicted analytically and verified
numerically that for a free particle if $\Delta_0$ is less than a critical
value $\Delta_c$, then the packet will propagate in time with linearly growing
width but for $\Delta>\Delta_c$, the packet will start becoming narrow and
cease to be a Gaussian . For a simple harmonic oscillator, we find that for
$\Delta_0$ smaller than a critical value, there always exist a coupling
strength for which the packet simply oscillates about the mean position without
changing its shape.
