On matching of asymptotic representation of a whispering gallery wave propagating along a smooth surface in ℝ3 and the wavefield of a source

Abstract

The paper is devoted to development of the new concept of surface waves propagation along smooth surfaces in ℝ3, proposed in [1]. We introduce an asymptotic representation of surface waves resulted from summation of solutions localized in neighborhoods of geodesic lines. Matching with surface waves generated by a source positioned in the vicinity of surface uniquely specifies the asymptotic representation.