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Short Pulse Evolution Equation

  • Alan C. NewellEmail author
Chapter
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Part of the CRM Series in Mathematical Physics book series (CRM)

Abstract

We introduce short pulse evolution equation (SPEE), first derived in a non-optical context in the 80s, the universal equation describing the propagation of short pulses in media which have weak dispersion in the propagation direction. We show how it connects with the first canonical examples of nonlinear wave propagation, the Korteweg–de Vries and nonlinear Schrödinger equations and argue that, in contexts for which SPEE is most useful, modifications of the latter simply do not capture the correct pulse behavior. We discuss some of SPEE’s main properties and, in particular, look at its potential singular behaviors in which both the electric field gradient and its amplitude can become large. Finally, we address the practical challenge of whether very high intensity femtosecond pulses can travel significant distances in gases such as the earth’s atmosphere.

Keywords

Electric Field Gradient Secular Term Ultra Short Pulse Weak Dispersion High Intensity Pulse 
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.

Notes

Acknowledgement

The author is grateful for support from The Air Force contract FA 9550-10-1-US61 and from NSF DMS 1308862.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ArizonaTucsonUSA

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