Parabolic Equations

  • Finn B. Jensen
  • William A. Kuperman
  • Michael B. Porter
  • Henrik Schmidt
Part of the Modern Acoustics and Signal Processing book series (MASP)


The pioneering work on parabolic wave equations goes back to the mid-1940s when Leontovich and Fock [1] applied a PE method to the problem of radio wave propagation in the atmosphere. Since then, parabolic equations have been used in several branches of physics, including the fields of optics, plasma physics, seismics, and underwater acoustics. It is the application of PE methods to wave-propagation problems in the ocean that is the subject of this chapter.


Sound Speed Phase Error Helmholtz Equation Propagation Angle Gaussian Source 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Finn B. Jensen
    • 1
  • William A. Kuperman
    • 2
  • Michael B. Porter
    • 3
  • Henrik Schmidt
    • 4
  1. 1.NATO Undersea Research CentreLa SpeziaItaly
  2. 2.Marine Physical Lab.Scripps Institution of OceanographyLa JollaUSA
  3. 3.Heat, Light, and Sound Research, Inc.La JollaUSA
  4. 4.Massachusetts Institute of Technology (MIT)CambridgeUSA

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