Decay exponents and diffraction coefficients for surface waves on surfaces of nonconstant curvature

The decay exponents and diffraction coefficients for a cylindrical surface of nonconstant curvature are computed by two methods which yield the same results. The results consist of leading terms which depend upon the curvature of the surface and corrections which depend upon the derivative of the curvature. The leading terms coincide with those found previously. With these corrections, the geometric theory of diffraction can be used at longer wavelengths than before. In the first method the solution for diffraction by an elliptic cylinder is expanded asymptotically for wavelengths small compared to the cylinder dimensions. From the expansion the decay exponents and diffraction coefficients are determined. They are then expressed in terms of the curvature and its derivative, and in this form they are assumed to apply to a cylinder of arbitrary convex cross section. This assumption is verified by comparison with the corresponding results for a parabolic cylinder. Then the same results are obtained by asymptotically solving the integral equation for the field on a cylinder of arbitrary convex cross section.