Invariant solutions for equations of axion electrodynamics

► A number of exact solutions of field equations of axion electrodynamics is presented. ► A generalized weak transversality approach is proposed which enables to obtain additional solutions. ► The most general of obtained solutions includes six arbitrary functions. ► The possibility of superluminal motion of wave fronts is indicated. ► The energy velocity of wave fronts does not exceed the velocity of light.