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The nonstationary (time-dependent) problem of longitudinal modulation instability of a self-focusing beam in a nonlinear medium with and without saturation is solved for the first time, to our knowledge, by using numerical methods. We present the dependence of instability growth rates on the modulation frequency for different saturation parameters. The radial profile of the complex perturbation function is also calculated. The result of modulation instability in the problem considered is the separation of the beam into a periodic sequence of light clumps (light bullets).

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