A nonstationary problem of diffraction of acoustic waves from a point source by an interface of two half-planes with positive effective curvature

A nonstationary problem of diffraction of acoustic waves excited by a point source by an interface between two acoustic media with positive effective curvature is considered. This is a model problem for wave phenomena arising near the ocean bottom in the approximation of the “liquid bottom”. Using the complex analysis techniques, we proposed a method for finding the exact solution to the studied class of problems. We propose a method for constructing exact solutions in the form of an integral representation of the problem stated.