An inverse problem for electrodynamic equations with nonlinear conductivity

The inverse problem of determining the variable conductivity coefficient in the system of electrodynamic equations with nonlinear conductivity is considered. The required coefficient is assumed to be a smooth compactly supported function of space variables in $\mathbb{R}^3$. A plane wave with a sharp front traveling from the homogeneous space in some direction $\nu$ is incident on an inhomogeneity. The direction is a parameter of the problem. The magnitude of the electric strength vector for some range of incident wave directions and for times close to those at which the wave arrives at points of the ball surface containing the inhomogeneity is given as information for solving the inverse problem. It is shown that this information reduces the inverse problem to an X-ray tomography problem, for which numerical solution algorithms are well developed.