Nonexistence of smooth electromagnetic fields in nonlinear dielectrics: Shock development in a half-space

AbstractImplications of the Rankin-Hugoniot and Lax k-shock conditions are explored for a systems of hyperbolic conservation laws associated with the propagation of an intense plane wave into an isotropic nonlinear dielectric half-space. Asymptotic estimates are obtained for both tmaxand smax, respectively, the time elapsed and distance travelled by the wave into the half-space before shock development occurs