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Proceedings of the American Mathematical Society

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Solution of paraxial wave equation for inhomogeneous media in linear and quadratic approximation
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by Alex Mahalov and Sergei K. Suslov PDF
Proc. Amer. Math. Soc. 143 (2015), 595-610 Request permission


We construct explicit solutions of the inhomogeneous parabolic wave equation in a linear and quadratic approximation. As examples, oscillating laser beams in a $1D$ parabolic waveguide, spiral light beams in $2D$ varying media and an effect of superfocusing of particle beams in a thin monocrystal film are briefly discussed. Transformations of nonlinear equations into the corresponding autonomous and homogeneous forms are found and a review of important applications is also given.
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Additional Information
  • Alex Mahalov
  • Affiliation: School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287–1804
  • Email:
  • Sergei K. Suslov
  • Affiliation: School of Mathematical and Statistical Sciences, Arizona State University, Tempe, Arizona 85287–1804
  • Email:
  • Received by editor(s): March 26, 2013
  • Published electronically: October 28, 2014
  • Additional Notes: This research was partially supported by AFOSR grant FA9550-11-1-0220.
  • Communicated by: Ken Ono
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 143 (2015), 595-610
  • MSC (2010): Primary 35Q55, 35Q51; Secondary 35C05, 81Q05
  • DOI:
  • MathSciNet review: 3283647