We show that the law of the soliton adaptation to varying-in-time external potentials indicates conclusively the way for solitonlike bullets generation in three-dimensional nonautonomous nonlinear and dispersive systems. It turns out that the generation of matter-wave soliton bullets can be realized if periodic variations of non-linearity and confining sign-reversal varying-in-time harmonic oscillator potential are opposite in phases so that peaks of nonlinearity inside the atomic cloud coincide in time with repulsive character of trapping potential during reversal periodic transformations from cigar-shaped to ball-shaped trapping structures. In nonlinear optical applications, periodic graded-index nonlinear structures with alternating waveguiding and antiwaveguiding segments can be used to simulate complicated processes of matter-wave soliton bullets generation.

An analytical approach to the theory of electromagnetic waves in nonlinear vacuum is developed. The evolution of the pulse is governed by a system of nonlinear wave vector equations. An exact solution with its own angular momentum in the form of a shock wave is obtained.

The observation of discrete lines in the white spectrum at the initial stage of filamentation of powerful femtosecond laser pulses, propagating in silica glasses, as well as the filamentation without plasma channels observed in the experiments in air, pushed us to look for other nonlinear mechanisms for describing these effects. In this paper, we present a new parametric conversion mechanism for asymmetric spectrum broadening of femtosecond laser pulses towards higher frequencies in isotropic media. This mechanism includes cascade generation with THz spectral shift for solids and GHz shift for gases. The process works simultaneously with the four-photon parametric wave mixing. The theoretical model proposed agrees well with the experimental data.