The problem of the diffraction of internal waves at the edge of a semi- infinite film (Q1110403)

In a continuation of the research described e.g. by the author in Zh. Vychisl. Mat. Mat. Fiz. 25, No 3, 413-421 (1985; Zbl 0588.73045) on the diffraction of waves, described by the Klein-Gordon equation, the diffractin of external waves at the boundary of a semi-infinity film situated on the surface of a stratified liquid is considered. The need to take into account the properties of the surface covering the liquid led to a study of the boundary value problem for the Helmholtz equation with boundary conditions containing higher-order derivatives than the equation itself. Consideration of the surface tension of a semi-infinite film leads to a similar situation. However, in this case the propagation of the waves is described by an equation of the hyperbolic and not the elliptic type.