Ebook: Stationary Diffraction by Wedges: Method of Automorphic Functions on Complex Characteristics

We present a complete solution to the classical problem of stationary diffraction
by wedges with general boundary conditions (b.c.). For the Dirichlet and Neumann
b.c., the solution was found by Sommerfeld in 1896 and for the impedance b.c. (or
Leontovich and Robin b.c.) by Malyuzhinetz in 1958. Our approach relies on a novel
“method of automorphic functions (MAF) on complex characteristics” which gives
all solutions to boundary problems for second-order elliptic operators with general
boundary conditions. This method is also applicable to the problems of guided water
waves on a sloping beach, scattering of seismic waves, etc.