On the propagation modes of light bullets in the gradient fibers

An analytical study of the propagation of a spatiotemporal optical soliton in a gradient fiber with the Kerr nonlinearity has been carried out. Two approaches were used, based on the heuristic method of the averaged Lagrangian. In the framework of the first approach, for the envelope of the light signal, a well-known factorized representation is used in the form of two functions that depend on the longitudinal and transverse coordinates, respectively. In the framework of the second approach was used a trial solution in the form of temporal soliton. However, the parameters of this soliton depend on the coordinates. By means of the second approach the approximate solutions are found in the form of stationary and pulsating light bullets. The conditions for their stability are determined. These conditions apply to the aperture and temporal duration of the soliton. I addition, the soliton power should be less than a certain threshould value. If the soliton power is much less than this threshould value, then both analytical approaches are consistent with each other.