Abstract
A theory describing the propagation of nonlinear hyperbolic waves of any strength is developed. It is valid for small values of the wavelength, i. e. of the typical scale length of variation in the direction of propagation. At first the wave propagates along wave normals according to one-dimensional theory. It quickly splits up into a set of distinct waves, each of which soon becomes weak. The weak waves then propagate along rays according to weakly nonlinear geometrical optics.
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