Geodesic
On behavior of a nonstationary wave field with a singularity (the~homogeneous generalized function) on the initial front near the caustic
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 20, Tome 186 (1990), pp. 122-133

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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. 
@article{ZNSL_1990_186_a11,
     author = {N. Ya. Kirpichnikova},
     title = {On behavior of a nonstationary wave field with a singularity (the~homogeneous generalized function) on the initial front near the caustic},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {122--133},
     publisher = {mathdoc},
     volume = {186},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1990_186_a11/}
}
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N. Ya. Kirpichnikova. On behavior of a nonstationary wave field with a singularity (the~homogeneous generalized function) on the initial front near the caustic. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 20, Tome 186 (1990), pp. 122-133. http://geodesic.mathdoc.fr/item/ZNSL_1990_186_a11/