  An averaging method for getting uniformly valid asymptotic approximations of
the solution of hyperbolic systems of equations is presented. The averaged
system of equations disintegrates into independent equations for non-resonance
systems. We consider the resonance conditions for some classes of solutions.
The averaged system can be solved numerically in the resonance case. The
shallow water problem is considered as an example of the resonance system.
Results of numerical experiments are presented.
