ABSTRACT
A. Sommerfeld published in 1896 his habilitation thesis studying the diffraction of plane time-harmonic acoustical waves by a half-plane or a wedge. He used series expansions and reformulation by integrals. These Sommerfeld integrals were systematically used by Russian authors. Their approach is called the Maliushinets method. Western authors preferably use the Wiener-Hopf method, based on the Fourier transforms and symbol factorization of the related boundary integral equations.
Many new results, including electromagnetic and elastodynamic waves with different kind of boundary conditions, different media, plane surfaces, and aperiodic initial boundary conditions, using generalized eigenfunction expansions, have been achieved during the last decade. Still a lot of open problems exist. The paper reports on more recent results obtained together with co-workers.
