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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
Article

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.

Keywords

Exact Solution Wave Equation Arbitrary Function Gaussian Beam Real Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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