An application of scattering theory to one hydrodynamics problem
Zapiski Nauchnykh Seminarov POMI, Questions of quantum field theory and statistical physics, Tome 77 (1978), pp. 57-75
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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.