  A new method based on continuous wavelet transform with the complex Morlet
wavelet to analyze Saturn main rings is presented. It allows to investigate in
detail the resonance zones and reveal the coexistence of waves with stable
periods and the wave trains with a variable instant period. This method is
based on the replacing the integration of the fast--oscillation function by the
solution of the partial differential equations. It is shown that such an
approach is an effective tool for the study the radial structure of Saturn's A,
B, and C rings. All the analyzed images were obtained from the Cassini
spacecraft during 2004--2005 years.
