  We consider the axion field and electromagnetic waves with rapid time
dependence, coupled to a strong time independent, asymptotically approaching a
constant at infinity "mean" magnetic field, which takes into account the back
reaction from the axion field and electromagnetic waves with rapid time
dependence in a time averaged way. The direction of the self consistent mean
field is orthogonal to the common direction of propagation of the axion and
electromagnetic waves with rapid time dependence and parallel to the
polarization of these electromagnetic waves. Then, there is an effective U(1)
symmetry mixing axions and photons. Using the natural complex variables that
this U(1) symmetry suggests we find localized planar soliton solutions. These
solutions appear to be stable since they produce a different magnetic flux than
the state with only a constant magnetic field, which we take as our "ground
state". The solitons also have non trivial U(1) charge defined before,
different from the uncharged vacuum.
