Geodesic
Evolution of wave field jumps near caustics (elementary approach)
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 45, Tome 438 (2015), pp. 46-72

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The Poisson formula solving a $3$-dim Cauchy problem for the wave equation is applied to study behavior of the wave field singularities (jumps) near caustics in the $2$-dim and $3$-dim cases. The approach of quite elementary character enables one to describe the focusing effects in detail. 
@article{ZNSL_2015_438_a3,
     author = {M. I. Belishev and A. F. Vakulenko and A. Ya. Kazakov},
     title = {Evolution of wave field jumps near caustics (elementary approach)},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {46--72},
     publisher = {mathdoc},
     volume = {438},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_438_a3/}
}
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M. I. Belishev; A. F. Vakulenko; A. Ya. Kazakov. Evolution of wave field jumps near caustics (elementary approach). Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 45, Tome 438 (2015), pp. 46-72. http://geodesic.mathdoc.fr/item/ZNSL_2015_438_a3/