Abstract
We consider the system of Maxwell equations in which the current density dependsnonlinearly on the electric field. In our case, the system is determined by four coefficientsdepending on the spatial variables. These coefficients are supposed to be compactly supported ina ball \(B(R)\) of radius \(R\) . For the electrodynamic equations, we posea problem on a plane running wave with a sharp front incident on an inhomogeneity localized inthe ball \(B(R)\) . A formula for the calculation of the waveamplitude is derived. Further, we consider an inverse problem of finding the four coefficientsdetermining the current from the wave front amplitude given for various directions of the incidentplane wave on part of the boundary of \(B(R)\) . We show thatthis inverse problem splits into four separate problems, one of which is the usual X-raytomography problem and the other three are identical problems of integral geometry for a familyof straight lines. These problems are studied, and a stability estimate for their solutions is found.
