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The propagation of an initially Gaussian wave packet of width $\Delta_0$ in acubic non-linear Schrodinger equation with a negative coupling constant for thenonlinear term is considered . It is predicted analytically and verifiednumerically that for a free particle if $\Delta_0$ is less than a criticalvalue $\Delta_c$, then the packet will propagate in time with linearly growingwidth but for $\Delta>\Delta_c$, the packet will start becoming narrow andcease to be a Gaussian . For a simple harmonic oscillator, we find that for$\Delta_0$ smaller than a critical value, there always exist a couplingstrength for which the packet simply oscillates about the mean position withoutchanging its shape.

Wave packet dynamics for a non-linear Schrodinger equation: Qualitative changes with changes in the initial width