Geodesic
On asymptotic behavior of non-stationary wave field singularities near the space-time caustic
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 16, Tome 156 (1986), pp. 98-108
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Cauchy problem for wave equation in the case of discontinuity on the initial front is investigated. The discontinuity is given by homogeneous generalized function (degree $\lambda$). The transformation of initial front passed the space-time caustic is examined and as a result uniform wave field asymptotics expressed in terms of polynomial Legendre is obtained. 
@article{ZNSL_1986_156_a8,
     author = {N. Ya. Kirpichnikova},
     title = {On asymptotic behavior of non-stationary wave field singularities near the space-time caustic},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {98--108},
     year = {1986},
     volume = {156},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1986_156_a8/}
}
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N. Ya. Kirpichnikova. On asymptotic behavior of non-stationary wave field singularities near the space-time caustic. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 16, Tome 156 (1986), pp. 98-108. http://geodesic.mathdoc.fr/item/ZNSL_1986_156_a8/