“…The phase functions (model integrals) of asymptotic solutions are expressed in terms of various special functions: Fresnel integrals, Airy functions, Pearcey integrals, and others. The specific choice of the phase function (model integrals) is completely determined by the analytical properties of the dispersion relations [8,9,31,32]. The obtained analytical solutions of dispersion relations allow one to efficiently calculate the main phase characteristics of the excited IGW fields and, in addition, to qualitatively analyze the obtained solutions, which is important for the correct statement of more complicated mathematical models of wave dynamics in real natural stratified media (world ocean, Earth's atmosphere).…”