Low-frequency, relativistic, subcycle solitary waves are found in
two-dimensional and three-dimensional particle-in-cell (PIC) numerical
simulations, as a result of the interaction of ultrashort,
high-intensity laser pulses with plasmas. Moreover, nondrifting,
subcycle relativistic electromagnetic solitons have been obtained as
solutions of the hydrodynamic equations for an electron–ion warm
plasma, by assuming the quasi-neutrality character of the plasma
response. In addition, the formation of long-living macroscopic
soliton-like structures has been experimentally observed by means of
the proton imaging diagnostics. Several common features result
from these investigations, as, for example, the quasi-neutral plasma
response to the soliton radiation, in the long-term evolution of the
system, which leads to the almost complete expulsion of the plasma from
the region where the electromagnetic radiation is concentrated, even at
subrelativistic field intensity. The results of the theoretical
investigations are reviewed with special attention to these
similarities.