An application of scattering theory to one hydrodynamics problem

The linearized equation of motion of a layer of an ideal incompressible liquid over an uneven bottom is written as an equation of form $if'=Af$ in a Hubert space with a certain self-adjoint operator $A$. Scattering theory methods are used to study the spectrum and to describe the eigenfunctions of operator $A$ under the assumption that only the compact part of the bottom differs from a horizontal plane.