Uniform asymptotic profiles of stationary wave propagation in perturbed two‐layered media
Hiroshi Isozaki, Mitsuteru Kadowaki, Michiyuki Watanabe · Mathematical Methods in the Applied Sciences · 2020
We derive an asymptotic expansion as |x|→∞, uniform with respect to the direction x/|x|, varying over , of solutions to the reduced wave equation (the Helmholtz equation) in locally perturbed two‐layered media in . The main difficulties arise from the conical singularities of the generalized eigenfunctions, caused by the transmitted (refracted) waves at the interface. They are overcome by the classical method of stationary phase.