Geodesic
An asymptotic solution of the problem of the moving with acceleration source of high frequency oscillations in nonhomogeneous media
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 28, Tome 257 (1999), pp. 288-297 
A. S. Starkov. An asymptotic solution of the problem of the moving with acceleration source of high frequency oscillations in nonhomogeneous media. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 28, Tome 257 (1999), pp. 288-297. http://geodesic.mathdoc.fr/item/ZNSL_1999_257_a15/
@article{ZNSL_1999_257_a15,
     author = {A. S. Starkov},
     title = {An asymptotic solution of the problem of the moving with acceleration source of high frequency oscillations in nonhomogeneous media},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {288--297},
     year = {1999},
     volume = {257},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1999_257_a15/}
}
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The problem of the moving source wave field is considered in nonhomogeneous media. It is supposed that velocity of the source is less than the sound velocity for $t<0$ and greater this one for $t>0$ (subsonic – supersonic transition). An asymptotic expansion for the wave field in an neighborhood of the source is constructed on the basis of well known Hadamard's Anzatz. The derived expansion is uniform with respect to the velocity of the source and contains new special functions. These functions are generalization of Hankel and Bessel functions and possess some remarkable properties.