Self-similar shock wave solutions of the nonlinear Maxwell equations

In our study we consider nonlinear, power-law field-dependent electrical permittivity and magnetic permeability and investigate the time-dependent Maxwell equations with self-similar ansatz. This is a first-order hyperbolic partial differential equation system which can conserve non-continuous initial conditions describing electromagnetic shock. Such phenomena may happen in complex materials induced by the planned powerful Extreme Light Infrastructure laser pulses.