  We analyze the behavior of shock waves in nonlinear theories of
electrodynamics. For this, by use of generalized Hadamard step functions of
increasing order, the electromagnetic potential is developed in a series
expansion near the shock wave front. This brings about a corresponding
expansion of the respective electromagnetic field equations which allows for
deriving relations that determine the jump coefficients in the expansion series
of the potential. We compute the components of a suitable gauge-normalized
version of the jump coefficients given for a prescribed tetrad compatible with
the shock front foliation. The solution of the first-order jump relations shows
that, in contrast to linear Maxwell's electrodynamics, in general the
propagation of shock waves in nonlinear theories is governed by optical metrics
and polarization conditions describing the propagation of two differently
polarized waves (leading to a possible appearance of birefringence). In detail,
shock waves are analyzed in the Born and Born-Infeld theories verifying that
the Born-Infeld model exhibits no birefringence and the Born model does. The
obtained results are compared to those ones found in literature. New results
for the polarization of the two different waves are derived for Born-type
electrodynamics.
