Geodesic
Exact solutions of the $m$-dimensional wave equation from paraxial ones. Further generalization of the Bateman solution
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 41, Tome 393 (2011), pp. 167-177

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A review of earlier generalizations of the classical Bateman solution, involving an arbitrary function, is presented. Its further generalization, described by $m(m-1)$ real parameters characterizing the phase, is given. Under a proper choice of the arbitrary function, it may describe Gaussian beam or Gaussian packet. 
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     author = {A. P. Kiselev and A. B. Plachenov},
     title = {Exact solutions of the $m$-dimensional wave equation from paraxial ones. {Further} generalization of the {Bateman} solution},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {167--177},
     publisher = {mathdoc},
     volume = {393},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_393_a11/}
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A. P. Kiselev; A. B. Plachenov. Exact solutions of the $m$-dimensional wave equation from paraxial ones. Further generalization of the Bateman solution. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 41, Tome 393 (2011), pp. 167-177. http://geodesic.mathdoc.fr/item/ZNSL_2011_393_a11/