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Asymptotic Methods of Analysis using Advanced Saddle Point Techniques

  • Kurt E. Oughstun
Chapter
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Part of the Springer Series in Optical Sciences book series (SSOS, volume 144)

Abstract

The integral representation developed in Vol. 1 and reviewed in Chap. 9 of this volume provides an exact, formal solution to the problem of electromagnetic pulse propagation in homogeneous, isotropic, locally linear, temporally dispersive media either filling all of space or filling the half-space z > z 0. However, an exact, analytic evaluation of the resultant contour integral is typically not possible for a rather broad class of realistic initial pulse shapes. Consequently, a well-defined approximate evaluation of the integral representation for a given initial pulse is necessary in order to determine the behavior of the temporal phenomena of primary interest here. This includes the spatiotemporal properties of the precursor fields, the arrival of the signal, the signal velocity, and the spatiotemporal evolution of the pulse. To have complete confidence in the results, it is essential that this approxiamate evaluation procedure possess a useful, well-defined error bound.

Keywords

Saddle Point Asymptotic Expansion Steep Descent Asymptotic Approximation Airy Function 
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, LLC 2009

Authors and Affiliations

  • Kurt E. Oughstun
    • 1
  1. 1.College of Engineering & Mathematical Sciences School of EngineeringUniversity of VermontBurlingtonUSA

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