TRAPPING WAVES BY A SUBMERGED CYLINDER

For large values of the wavenumber k in the direction of cylinder, there is only one trapped wave. We construct asymptotics of these trapped modes and their frequencies as k → ∞ in the case of one submerged cylinder into a plane water layer by means of reducing the initial problem to three integral equations on the boundaries and then solving them using a method suggested by Zhevandrov and Merzon (Amer. Math. Soc. Translations (2) 208, 235–284 (2003)).