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It is demonstrated that the equation iol/J/ot+ l/Jxx+ K 1¢ 121/1= 0, which describes plane self-focusing and one-dimensional self-modulation can be solved exactly by reducing it to the inverse scattering problem for a certain linear differential operator. In this case exact solutions can be obtained which describe the interaction of solitary wave packets--solitons. It is shown that the amplitude and velocity of interacting solitons do not change, whereas the phase has a discontinuity. It is also demonstrated that only paired collisions of solitons occur. The results obtained are used for assessing the nonlinear stage of development of self-modulated instability.