Purpose. The long time discussion on existence, or not existence, of longitudinal electromagnetic waves both in nature and in Maxwell classical electrodynamics is under consideration. The modern experiments on the existence of such waves are reviewed briefly. The link between the longitudinal electromagnetic waves and the system of Maxwell equations is demonstrated.
Methods. Maxwell classical electrodynamics, Fourier method, Fourier transform, amplitude analysis.
Results. The longitudinal wave component of the electric field strength vector is found as an exact solution of the standard Maxwell equations with specific currents and charges of the gradient type. The corresponded scalar wave component, which is propagated in the same direction, is found as well. The longitudinal components of both electric and magnetic field strengths, together with two corresponded scalar waves, are found as the exact solution of generalized Maxwell equations, which are characterized by the maximally high symmetry properties.
Conclusions. The analysis of found solutions demonstrates that longitudinal components are located near the corresponded current and charge densities, which are the sources of such fields. It follows from the fact that current and charge densities and the corresponded longitudinal components in the solutions are determined by the same amplitudes. The best examples of corresponding physical reality are such big charges as the whole water area of closed sea, the planet Earth in general, their oscillations and corresponding longitudinal electric and scalar waves
Keywords: the Maxwell equations, electromagnetic field, classical electrodynamics, longitudinal electromagnetic waves