Dynamics of the internal gravity waves in the heterogeneous and   nonstationary stratified mediums
  In the present paper in the assumption of the slowness of variation of the vertically stratified medium parameters in the horizontal direction within the time we have analyzed the evolution of the non-harmonic wave trains of the internal gravity waves. The particular form of the wave train can be expressed through some special functions, for example, Airy functions, Fresnel integrals, Pearsy integrals, etc., and is determined by the local behavior of the dispersion curves of the separate modes near to the corresponding singular points. The solution of this problem is possible using the modified version of the space-time ray-tracing method offered by the authors (the method of the ray optics), the fundamental difference of which consists, that the asymptotic notation of such a solution should be searched for in the form of the series using the non-integral degrees of some small parameter, the asymptotic forms of the solution at analysis of evolution of the non-harmonic wave trains present in the stratified non-stationary horizontally-non-uniform mediums is searched in the form of the series using the non-integral degrees of some small parameter, at that the exponent depends on the concrete type of the wave train notation. The particular form of the notation is determined from the asymptotical behavior of the solution in the stationary horizontally-homogeneous event. The phase of the wave train will be determined from the corresponding eikonal equation, which can be solved numerically using the characteristics (rays). The amplitude of the wave train is determined from some law of preservation along the characteristics (rays). 
Vitaly V. Bulatov and Yuriy V. Vladimirov (Institute for Problems in   Mechanics, Russian Academy of Sciences)