Modified Smyshlyaev’s formulae for the problem of diffraction of a plane wave by an ideal quarter-plane

Abstract

We present new results related to quarter-plane diffraction problem. The Smyshlyaev’s framework of separation of radial variable is taken as the base. To modify this approach we apply the embedding methods to the problem. As the result, we obtain the embedding formula in the 3D space and the modified Smyshlyaev’s formula for the ν-plane. The main feature of the modified Smyshlyaev’s formula is that it uses the edge Green’s functions instead of the usual Green’s function on a sphere with a cut. The benefits of this are discussed.