Analytical continuation of two-dimensional wave fields.

Wave fields obeying the two-dimensional Helmholtz equation on branched surfaces (Sommerfeld surfaces) are studied. Such surfaces appear naturally as a result of applying the reflection method to diffraction problems with straight scatterers bearing ideal boundary conditions. This is for example the case for the classical canonical problems of diffraction by a half-line or a segment.

Precursor wave in a layered waveguide.

The precursor wave (often called the first arriving signal) in a layered waveguide is investigated. It is known that the velocity of such a signal is close to the velocity of the fastest medium in the waveguide, and it may be bigger than the fastest group velocity given by the dispersion diagram of the waveguide. Usually the precursor pulse decays with the propagation distance.