On the structure of surface waves

Abstract

There is considerable confusion in the engineering and physics literature with regard to the existence and properties of surface waves; it has even been suggested [3] that the term “surface wave” be deleted from the language entirely! Now, in the general mathematical context of initial boundary value problems for hyperbolic equations, it is altogether clear when surface waves exist. The present paper is devoted to describing the structure of these waves for three such problems (cf. [5, 61): 1) Maxwell’s equations in the half space R$ with a “strange” boundary condition; 2) Maxwell’s equations in RI with a “completely reactive” boundary condition; 3) the equations of elasticity in R: with the classical condition for a free boundary. A principal source of the confusion surrounding surface waves is that it has been more or less customary to seek a solution to a particular problem in the form of an Ansatz considered appropriate to a special source or set of initial data. The interpretation of the resulting solution is thus Ansatzdependent: in one form the solution may seem to contain surface waves with certain properties, while these properties or even the surface wave itself may not be evident in another form [2]. In the context of the general initial boundary value problem in R: with arbitrary finite-energy sources or initial data, the representation of the solution in our approach.involves construct212