We reveal the existence of stable dissipative soliton complexes with curvilinear motion of their center of mass. This type of motion results from the field distribution asymmetry and is well pronounced for asymmetric complexes of laser solitons with strong coupling. We present results of numerical simulations of such complexes in a model of wide-aperture lasers or laser amplifiers with saturable gain and absorption. The complex consists of a pair of strongly coupled vortex solitons weakly coupled with a number of other vortex solitons. Similar complexes are expected to exist in different spatially distributed nonlinear dissipative systems, including schemes with discrete dissipative solitons.

The evolution of the area of a pulse of optical radiation propagating in a nonlinear medium is analyzed. The role played by the medium relaxation and the correctness of the formulation of the problem on the propagation of short pulses are discussed.

The photoionization yield is analyzed for three-dimensional quantum systems with finite number of discrete spectrum states driven by unipolar subcycle and few-cycle electromagnetic pulse with a duration much less than “the Kepler period,” electron oscillation period in the ground state. The yield for such objects—symmetric quantum dots and those described by the zero-radius potential—is compared with the yield for hydrogen atom. In all these cases, the standard Keldysh ionization theory is inapplicable. It is shown that ionization probability is determined by the ratio of the electric pulse area (integral of the electric field strength over time) and its characteristic value inversely proportional to the size of the electron localization, and not by the pulse energy or its maximum intensity.

We predict a new class of three-dimensional (3D) topological dissipative optical one-component solitons in homogeneous laser media with fast saturable absorption. Their skeletons formed by vortex lines where the field vanishes are tangles, i.e., $N_c$ knotted or unknotted, linked or unlinked closed lines and $M$ unclosed lines that thread all the closed lines and end at the infinitely far soliton periphery. They are generated by embedding two-dimensional laser solitons or their complexes in 3D space after their rotation around an unclosed, infinite vortex line with topological charge $M_0$ ($N_c$, $M$, and $M_0$ are integers). With such structure propagation, the “hula-hoop” solitons form; their stability is confirmed numerically. For the solitons found, all vortex lines have unit topological charge: the number of closed lines $N_c=1$ and 2 (unknots, trefoils, and Solomon knots links); unclosed vortex lines are unknotted and unlinked, their number $M=1$, 2, and 3.

We predict and study a new type of three-dimensional soliton: asymmetric rotating and precessing stable topological-dissipative-optical localized structures in homogeneous media with saturable amplification and absorption. The crucial factor determining their dynamics is the ratio of the diffusion coefficients characterizing the frequency dispersion and angular selectivity (dichroism) of the scheme. These vortex solitons exist and are stable for overcritical values of the selectivity coefficients and can be realized in lasers of large sizes with saturable absorption.

Specific features of the transportation of extremely short radiation pulses in a metal waveguide are analyzed. It is inferred that the mode dispersion can be suppressed, thereby preserving the shape of pulses, including subcycle and unipolar pulses, at distances limited by the absorption in the metals.