Diffraction of internal waves described by equation of slightly stratified fluid on half-plane

The diffraction of plane waves in a slilghtly exponentially stratified fluid on a plane barrier placed in this fluid was investigated. The problem is pertinent with respect to the study of internal waves in the ocean. The considered problem is regarded as highly unusual from the mathematical point of view because it is formulated as a boundary value problem for a hyperbolic equation with boundary conditions characteristic for elliptical equations. It was demontrated long ago that such a formulation is incorrect if only a limited region is examined but the problem is well formulated and has physical sense in the case of unlimited regions when there are appropriate conditions in the neighborhood of an infinitely distant point. The formulation and results are compared with a series of studies along these lines by S. A. Gabov, et al. It is shown that the diffraction pattern obtained with Beta squared yields O outside a restricted region differs qualitatively from the diffraction pattern examined by Gamov. Specifically, the neglecting of the term Beta squared U in the Klein-Gordon equation, employed by Gamov, gives erroneous results.