Scattering of a plane wave by a cylindrical surface with a long perturbation

The Helmholtz equation in the exterior of a surface $S$: $r=dF(z/l)$ in $\mathbf R^3$, where $F(z)\equiv1$ for $|z|\geqslant1/2$, and the problem of the scattering of a plane wave for Dirichlet, Neumann and impedance boundary conditions on $S$ are considered. The asymptotics of the scattered field and the scattering amplitudes are found under the conditions $kl\to\infty$, $kd\thicksim1$, $\cos{\theta_0}\leqslant c<1$, where $k$, $\theta_0$, $\varphi_0$ are the spherical coordinates of the wave vector of the plane wave.
Bibliography: 21 titles.