Reflection and transmission of high frequency pulses at an interface

Abstract

We study spatially localized solutions to the n-dimensional wave equation u_tt = [c(x)]² δ u, where c(x) = c₁ X_x1>0(X) + c₂ X_xb>0(X), Explicit formulas are obtained for pulses which are approximate solutions to the wave equation. These approximate solutions are asymptotic to exact solutions in the high frequency limit in the sense that the energy of the error term tends to zero as the frequency tends to infinity.