THE INFLUENCE OF NONLINEAR CONDUCTION ON SINGULARITY FORMATION IN THE INTENSE PLANE-WAVE, NONLINEAR DIELECTRIC INTERACTION PROBLEM

Abstract

The propagation of an intense plane-wave pulse into a nonlinear dielectric half-space is considered; it is assumed that the dielectric is not a perfect nonconductor and that the conduction vector J is given by a simple nonlinear Ohm's law. Under these conditions we prove that singularities form in the propagating electromagnetic wave provided the initial gradients of the electromagnetic fields in the wave are positive, and pointwise sufficiently large. Our results point to the fact that nonlinear conduction currents may provide a natural dissipative mechanism in the plane-wave-nonlinear dielectric interaction problem.