Time-domain Green’s function associated to the interface problem for the Klein–Gordon equation

Abstract

In this work we present a representation formula for the Green’s function associated with the source or interface problem for the Klein–Gordon equation from a known result on solution for the non-dispersive wave equation. The results can extend to more general situations, in particular stratified media where the Cagniard-de Hoop method fails for reasons of non-homogeneity of the amplitude and the phase of the exponential in the Laplace transform. Examples and numerical applications are given in two dimensions for the interface problem associated to a dispersive wave equation where the reflected and incident fields are obtained. The calculation of the transmitted field is omitted for the sake of simplicity of the paper. Such a representation formula can be useful to study other qualitative properties of dispersive waves from those known on non-dispersive ones.