A Combined Method for Calculating the Field of a Point Source in a Waveguide (Slightly Curved Media)

The two-dimensional problem of propagating the waves generated by a point source in a depth slightly curved waveguide is investigated. The Dirichlet condition is given on the boundary of the waveguide, and also two consistency conditions are defined on the interface between the fluid and the bottom. The velocity of the acoustic wave is assumed to be arbitrarily dependent on the depth of the waveguide and weakly dependent on the trace coordinate. With the help of rather cumbersome transformations, the solution is expressed as a sum of geometric-optical waves, normal waves, and a remainder. Sufficient conditions on the total amount of detached normal and geometric-optical waves are obtained. Bibliography: 2 titles. Dedicated to P. V. Krauklis on the occasion of his seventieth birthday __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 308, 2004, pp. 225–234.