Slightly generalized Maxwell system and longitudinal components of solution

We consider slightly generalized Maxwell equations with electric and magnetic currents and charges densities of the gradient type. Among other versions of the Maxwell system these equations differ by the extended symmetry properties. Such system of equations is invariant with respect to a 256-dimensional algebra, and this algebra is not yet the maximum of possible symmetry. The longitudinal components of both vectors of electric and magnetic field strengths, together with two corresponded scalar waves, are found as the exact solution of such generalized Maxwell equations. The longitudinal wave component of the electric field strength vector itself is found as an exact solution of the standard Maxwell equations with fixed current and charge of the gradient type. This wave is corresponded to the scalar wave component, which is propagated in the same direction. 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. The relationship with modern experiments is considered briefly. (paper)