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We present a particular class of solutions in Cartesian, cylindrical andspherical coordinates of the non-dispersive travelling wave variety thatpropagate an envelope of varying vorticity some of which include topologicalwaves with parallel electric and magnetic components. The significance of thesesolutions is examined in the recently proposed Axion-Maxwell field theory withpotential applications in material science and topological insulators.

Beltrami Flows, Non-Diffracting Waves and the Axion Beltrami-Maxwell Postulates