Scattering by Obstacles in Acoustic Waveguides

We study the scattering of acoustic waves by an obstacle embedded in a uniform waveguide with planar boundaries, which is a fundamental model in shallow ocean acoustics. Under certain geometric assumptions on the shape of the obstacle, we prove a Rellichtype uniqueness theorem in the case of soft obstacles. The solvability of the scattering problem is proved via boundary integral equations and the limiting absorption principle is established. An eigenfunction expansion in terms of the scattering solutions reveals the appropriate (partial) scattering amplitudes for the waveguide. We show that these scattering amplitudes for the propagating modes, at a fixed frequency, define uniquely the shape of a soft obstacle.