Non-local singularities as the point-source images in the generalized method of D. A. Grave for solving wave-scattering problems. (On the possible origin of a legend about optical properties of werewolves and ghosts)

The method of D. A. Grave (1885) in the theory of two-dimensional boundary-value problems for the Laplace equation in domains with smooth analytical (algebraic) boundaries represents the solution as an infinite superposition of static fields of external sources with alternating signs, located along an infinite curve orthogonal to the boundary. This method is a generalization of the classical method of images for the simplest boundaries (half-plane, flat strip, circular, and rectangular cylinders). All of the images are local singularities of the pole type of the solution continuation outside the boundary. The type of solution of D. A. Grave may be obtained for convex algebraic boundaries as a result of a certain regular procedure. In the case of the Helmholtz equation, a generalization of this method for curved boundaries is also possible, but leads to more complicated non-local singularities. Besides the poles, it also contains a series of weak singularities, distributed along an infinite set of segments