An analytical as well as numerical analysis is made of the dynamics induced on a weak signal wave pulse by a co-propagating strong pump wave pulse in a nonlinear Kerr medium. Emphasis is given to the situation where the group velocity dispersion and the non-linearity of the signal pulse have opposite signs. In this defocusing situation, it is demonstrated that the pump splits the signal pulse into two frequency shifted pulse fragments which separate in time, asymptotically with constant separation velocity. Explicit analytical predictions for the velocity of separation are obtained and corroborated by numerical simulations.