Creeping waves on a strongly elongated body of revolution

The creeping waves in the problem of diffraction by smooth convex body play an important role as they give the asymptotics of the diffracted field in the shaddow. The known results, obtained by the boundary layer method do not explain the properties of the creeping waves on strongly elongated bodies. In this paper the creeping waves on strongly elongated bodies when the binormal curvature is asymptoticaly large are studied. The derived asymptotics contains solutions of the Heun differential equation. The numerical analysis of the dispersion euqation is carried out and shows that magnetic creeping wave travels along the surface of elongated body with essentially smaller attenuation compared to the predication of usual theory.