  Theoretical comment for the registration of longitudinal electric waves in
interacting laser beams is given. Recent information on longitudinal electric
and scalar waves in plasma, plasmons, waveguides, antennas and nano-structures
is considered. The link between the longitudinal electromagnetic waves and the
system of Maxwell equations is demonstrated. The longitudinal wave component of
the electric field strength vector is found as the exact solution of the
standard Maxwell equations with specific gradient-type case of electric current
and charge densities. The corresponded scalar wave is found as well. The
necessary comment on the paper of K.J. van Vlaenderen and A. Waser is given.
The possible experimental situation is discussed briefly. Following the
Bialynicki-Birula's proposition to give the name for the well known complex
3-vector of electromagnetic field strengths, the suggestion to call the much
more interesting 4-vector of this kind as Riemann--Silberstein--Darwin vector
is given.
