On behavior of a nonstationary wave field with a singularity (the homogeneous generalized function) on the initial front near the caustic

Cauchy problem for the wave equation in the case of a discontinuity on the initial front is investigated. The discontinuity is discribed by the homogeneous generalized function of degree $\lambda$. The transformation of the initial front passing the space-time caustic is studied. The structure of the wave front and space-time roys near the caustic is established.