  In the paper taking the assumption of the slowness of the change of the
parameters of the vertically stratified medium in the horizontal direction and
in time, the evolution of the non-harmonic wave packages of the internal
gravity waves has been analyzed. The concrete form of the wave packages can be
expressed through some model functions and is defined by the local behavior of
the dispersive curves of the separate modes near to the corresponding special
points. The solution of this problem is possible with the help of the modified
variant of the special-time ray method offered by the authors (the method of
geometrical optics), the basic difference of which consists that the asymptotic
representation of the solution may be found in the form the series of the
non-integer degrees of some small parameter. At that the exponent depends on
the concrete form of representation of this package. The obvious kind of the
representation is determined from the principle of the localness and the
asymptotic behavior of the solution in the stationary and the
horizontally-homogeneous case. The phases of the wave packages are determined
from the corresponding equations of the eikonal, which can be solved
numerically on the characteristics (rays). Amplitudes of the wave packages are
determined from the laws of conservation of the some invariants along the
characteristics (rays).
