Short Pulse Evolution Equation
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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.
KeywordsElectric Field Gradient Secular Term Ultra Short Pulse Weak Dispersion High Intensity Pulse
The author is grateful for support from The Air Force contract FA 9550-10-1-US61 and from NSF DMS 1308862.
- 1.A.C. Newell, Solitons in Mathematics and Physics. CBMS-NSF Regional Conference Series in Applied Mathematics, vol. 48 (SIAM, Philadelphia, 1985)Google Scholar
- 2.J.V. Moloney, A.C. Newell, Nonlinear Optics, 2nd edn. (Westview Press, Boulder, CO, 2001)Google Scholar
- 4.S.K. Turitsyn, E.G. Falkovich, Sov. Phys. JETP 62(1), 146 (1985)Google Scholar