It is shown that beams of high-amplitude supersonic breather solitons, phonons, and subsonic excitations of new type (torsions) are generated in crystalline materials of different dimensions under high radiative and dynamic loads near the stability threshold. The dispersion dependences of solitons and phonons in 1D crystals are presented. It is shown that, in 2D crystals beams consisting of six or two (depending on the bombarding particle direction), breather solitons are generated and propagate in certain crystallographic directions. The masses of soliton excitations as particles (coupled complexes of massless phonons) have been determined. It is shown that the subsonic soliton waves of a new type with torsion atomic vibrations are generated in 3D nanotubes, along with supersonic soliton waves of longitudinal vibrations.