On unique solvability in the problem of water waves above submerged bodies

Time-harmonic motion of an ideal unbounded fluid in the presence of rigid bodies located under fluid's free surface is considered. New criteria for unique solvability of the corresponding linear boundary-value problem are suggested. These criteria are based on introduction of two compact self-adjoint integral operators and investigation of their eigenvalues and eigenfunctions. For the two-dimensional problem an algorithm is developed for finding solutions to the homogeneous problem (so-called trapped modes). Examples of numerical computations illustrating the theoretical results are given. Bibl. – 18 titles.