The Sommerfeld half-plane problem revisited, V: The bifurcated guide with mixed boundary conditions on the septum From a paper presented at the conference on ‘Wiener–Hopf Problems and Applications’ held in Oberwolfach, West Germany, 20–26, July 1986.

Abstract

We discuss the solution of the boundary value problem in a duct with a centered septum [9]. On the lower wall of the duct a Neumann condition is applied while on the upper wall a Dirichlet condition is applied. On the septum we apply a Dirichlet condition on the lower side and a Neumann condition on the upper one. This problem is formulated as a pair of integral equations of the Wiener–Hopf type for which we supply solutions for two modes of excitation as well as real and complex wave number. A critical examination is made of the construction, which reduces the problem to one in complex analysis. For real wave number, the physical parameters are provided in very simple forms.