Exact and asymptotic solutions of the equation of internal gravity waves in a wedge-shaped region

The field of internal gravity waves in a wedge-shaped region of a stratified medium is considered. Using a Kantorovich–Lebedev transformation, exact solutions are obtained which describe an individual mode and the complete wave field. The asymptotics of an individual wave mode are constructed by the WKB method, and are expressed in terms of a hypergeometric function, as well as the asymptotics of the complete wave field, which are expressed in terms of a semilogarithmic function. The results of numerical calculations of the wave field using the exact and asymptotic formulae are presented for the parameters of a stratified medium, characteristic for the dynamics of the ocean. The limits of their applicability are estimated.