Diffraction limit in theory of light bullets

An averaged variational procedure has been developed to study the propagation of light bullets in optical fibers using the propagation of light pulses in media with Kerr and quadratic nonlinearities as examples. Criteria for the correct choice of trial solutions are discussed. The condition under which the dispersion length is much greater than the length of diffraction spreading is called the diffraction limit. It is shown that, in this limit, the temporal and spatial dynamics of a bullet are independent of each other, while finding the dynamic parameters of a soliton is reduced to finding various solutions of the nonstationary linear Schrödinger equation for an imaginary quantum particle. The efficiency of the proposed approach is demonstrated by the example of finding solutions in the form of optical vortices in a waveguide for nonlinearities of both types.