Developing the eikonal method in nonlinear electrodynamics based on the geometrization principle

We derive the eikonal equation for an electromagnetic wave propagating in an external electromagnetic field according to the laws of nonlinear electrodynamics. Based on Logunov's geometrization principle, we determine the metric tensors of the effective Riemannian spaces for the Born–Infeld electrodynamics, nonlinear Heisenberg–Euler electrodynamics, and a parameterized post-Maxwellian electrodynamics. We analyze the main properties of these nonlinear electrodynamics.