Journal of Mathematical Sciences

, Volume 185, Issue 4, pp 605–610 | Cite as

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

  • A. P. KiselevEmail author
  • A. B. Plachenov

A review of earlier generalizations of the classical Bateman solution, which involves an arbitrary function, is given. Further generalizations of it, getting the phase parametrized by m(m – 1) free real parameters, are built. Under a proper choice of the arbitrary function, such a solution may describe a Gaussian beam or a Gaussian packet. The approach is based upon a certain connection between solutions of a Srödinger-type equation and the wave equation. Bibliography: 37 titles.


Exact Solution Wave Equation Arbitrary Function Gaussian Beam Real Parameter 
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Copyright information

© Springer Science+Business Media, Inc. 2012

Authors and Affiliations

  1. 1.St. Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia
  2. 2.Moscow State Technical University of Radio EngineeringElectronics and AutomaticsMoscowRussia

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