Application of the modified method of discrete sources and the pattern equations method to solution of the problem of wave diffraction by a body with rough boundary

A two-dimensional problem of diffraction on a cylindrical body with a rough boundary is considered. In this work, two aspects of the problem of diffraction on the body with irregular boundary are investigated. First, the problem of diffraction by bodies with random perturbations of the boundary is considered. As an example, diffraction by a rough circular cylinder is considered. The results of calculating the averaged scattering diagram obtained using the modified method of discrete sources are compared with the results obtained using the method of small perturbations. The second goal of this work is to clarify the degree of influence of the small perturbations of the scatterer boundary on the geometry of the set of singularities of the analytical continuation of the diffraction field. As an example, the problem of diffraction by the cylindrical body with a cross-section in the form of a rough multi-leaf, specified in polar and elliptical coordinates, is considered.