Exact solutions of the $m$-dimensional wave equation from paraxial ones. Further generalization of the Bateman solution

A. P. Kiselev   ; A. B. Plachenov

Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 41, Tome 393 (2011), pp. 167-177

Résumé

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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