EXPLICITLY EXACT-SOLUTIONS FOR WAVES IN A FAMILY OF NONLINEAR MEDIA

Exact wave solutions are found for the electromagnetic field inside a family of strongly nonlinear dielectric media, in which the amplitude of the displacement field is a power of the external electric field. The time period of oscillation 1/omega, is shown to be linear in the spatial period 1/k, which allows for a particular standing wave solution in a finite system. The velocity of propagation along trajectories of constant field in space-time coordinates is found exactly and is proportional to a power of the amplitude of the local field. This leads to shock-wave-like solutions.