In this paper, the ducting model has been generalized by considering the temporal pulse shape function used to formulate it. This generalized form of the ducting model can be used to describe the propagation of laser pulses with various temporal shapes. In particular, propagation of Gaussian shaped laser pulses has been simulated. The model results have been compared with the results of the multi-focus structure and the moving nonlinear foci models, and it is shown that good correspondence exists between the results of our ducting model and those of the other two models. Our simulation results indicate that the Gaussian laser pulse creates a multi-focus structure inside the nonlinear Kerr medium which moves inside it at a very fast velocity. It is shown that this fast movement of focal points can create filaments in the form of conical frustums during pulse propagation.

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