Complex analysis of elastic symbols and construction of plane wave solutions in the half-space

Dedicated to Professor Mitsuru IKAWA on his 60th birthday

Abstract

We examine plane waves of the elastic reduced wave equation in the half-space, and by linear combinations of them we construct the solution coinciding with any plane wave on the boundary. In the (dual) variable in the normal direction to the boundary, we apply the complex analysis to the inverse matrix of the elastic symbol.