To the problem of diffraction by an ideal flat cone (quarter-plane)

Abstract

New analytical results are presented for the problem of a plane acoustic wave scattering by a flat cone (a quarter plane) with Dirichlet boundary conditions. The results are obtained within a general framework developed by author for the strip/slit diffraction problem. These results include (i) embedding formulae representing the diffraction coefficient in the factorized form through the edge Green's functions depending separately on the direction of incidence and scattering, and (ii) the coordinate equations for the auxiliary functions that reduce the partial differential problem to a boundary problem for a system of ordinary differential equations. The new approach can be treated as a generalization of the separation of variables technique.