A two-complex-variable approach to the right-angled no-contrast penetrable wedge diffraction problem #

Valentin Kunz, Raphael Assier

13:50 Tuesday in 2Q49.

Part of the IMA Lighthill-Thwaites prize session.

Abstract #

We study the two dimensional problem of diffraction of a time-harmonic plane wave incident on a right-angled no-contrast penetrable wedge, by using a two-complex-variables approach. Central to this approach is that the physical problem leads to a Wiener-Hopf type equation in two complex variables. This equation involves unknown ‘spectral’ functions. We present these functions’ singularities and discuss their importance, with focus on the ‘real traces’ – the intersection of the singularities with the real plane. Finally, we outline how we plan to exploit this knowledge on the singularities to obtain closed-form far-field asymptotics of the diffracted physical fields.