Waves Trapped by Submerged Obstacles at High Frequencies

As is well known, submerged horizontal cylinders can serve as waveguides forsurface water waves. For large values of the wavenumber k in the direction of thecylinders, there is only one trapped wave. We construct asymptotics of these trappedmodes and their frequencies as k→∞ in the case of one or two submerged cylindersby means of reducing the initial problem to a system of integral equations on theboundaries and then solving them using a technique suggested by Zhevandrov andMerzon (2003)