This paper presents a method for factorizing matrix Wiener-Hopf kernels which govern diffraction when mode conversion and corner singularities are significant physical features. Hitherto there are no known methods for resolving such kernels except in a handful of particular examples in elastodynamics which have special symmetries.
To illustrate the method, we consider a generalization of the Rawlins problem. A. D. Rawlins [Proc. Roy. Soc. London, Ser. A 346, 469-484 (1975; Zbl 0325.76120)] observed that if one specifies different boundary conditions on opposite sides of a diffracting screen immersed in an acoustic medium then the diffraction problem reduces to a matrix Wiener-Hopf system. He closes the Dirichlet boundary condition on one side and the Neumann condition on the other.
In this paper we add the extra physical ingredient of mode conversion by replacing the “soft-hard” screen by interface conditions between two different acoustic half-spaces. This generalised Rawlins problem leads to a matrix Wiener-Hopf problem whose kernel cannot be factorized using any of the established methods. We show that the solution we obtain reduces to the solution obtained by Rawlins when the half-spaces have the same acoustic parameters.
For the entire collection see [Zbl 0856.00033].