Abstract
The nature of traveling wave solutions to equations of hydrodynamics of a 3D electron gas with parabolic dispersion law depends on whether the motion is subsonic or supersonic. Solitons representing localized depressions of the electrostatic potential and electron density are predicted to exist in the subsonic regime: at rest the solitons are dark while in motion they are grey. Two types of periodic waves are found in the supersonic regime: (i) smooth waves whose small amplitude limit is described by harmonic theory, and (ii) waves with sharp troughs and smooth crests of the potential with the electrons accumulating in the troughs.