  We study the wave propagation in nonlinear electrodynamical models.
Particular attention is paid to the derivation and the analysis of the Fresnel
equation for the wave covectors. For the class of general nonlinear Lagrangian
models, we demonstrate how the originally quartic Fresnel equation factorizes,
yielding the generic birefringence effect. We show that the closure of the
effective constitutive (or jump) tensor is necessary and sufficient for the
absence of birefringence, i.e., for the existence of a unique light cone
structure. As another application of the Fresnel approach, we analyze the light
propagation in a moving isotropic nonlinear medium. The corresponding effective
constitutive tensor contains non-trivial skewon and axion pieces. For
nonmagnetic matter, we find that birefringence is induced by the nonlinearity,
and derive the corresponding optical metrics.
