A Note on the Plane Wave Diffraction by a Soft/Hard Half‐Plan

Abstract

The author considers the problem of diffraction on a half-plane with Dirichlet (soft) and Neumann (hard) boundary conditions on its upper and lower faces. He gives a solution of the considered problem by reducing it to a matrix Wiener-Hopf equation with symbol \(G(\alpha)= \left(\begin{smallmatrix} 1\\ K(\alpha)\end{smallmatrix} \begin{smallmatrix} K^{- 1}(\alpha)\\ 1\end{smallmatrix}\right)\), where \(K(\alpha)= \sqrt{k^ 2- \alpha^ 2}\). This solution is based on the explicit expression for the factor matrix Wiener-Hof problem in the factorization problem by the Daniele-Khrapkov method. Earlier the factorization of this matrix Wiener-Hopf problem was obtained by the Wiener-Hopf-Hilbert method by \textit{A. D. Rawlins} and \textit{W. E. Williams} [Q. J. Mech Appl. Math. 34, 1-8 (1981; Zbl 0458.15010)].