Short Pulse Evolution Equation

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


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.


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.



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


  1. 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. 2.
    J.V. Moloney, A.C. Newell, Nonlinear Optics, 2nd edn. (Westview Press, Boulder, CO, 2001)Google Scholar
  3. 3.
    E.A. Kuznetsov, S.L. Musher, A.V. Shafarenko, JETP Lett. 37(5), 241 (1983)ADSGoogle Scholar
  4. 4.
    S.K. Turitsyn, E.G. Falkovich, Sov. Phys. JETP 62(1), 146 (1985)Google Scholar
  5. 5.
    A.A. Balakin, A.G. Litvak, V.A. Mironov, S.A. Skobelev, J. Exp. Theor. Phys. 104(3), 363 (2007)CrossRefADSGoogle Scholar
  6. 6.
    K. Glasner, M. Kolesik, J.V. Moloney, A.C. Newell, Int. J. Optics 2012, 868274 (2012)CrossRefGoogle Scholar
  7. 7.
    O.G. Kosareva, W. Liu, N.A. Panov, J. Bernhardt, Z. Ji, M. Sharifi, R. Li, Z. Xu, J. Liu, Z. Want, J. Ju, X. Lu, Y. Jiang, Y. Leng, X. Liang, V.P. Kandidov, S.L. Chin, Laser Phys. 19(8), 1776 (2009)CrossRefADSGoogle Scholar
  8. 8.
    A. Debayle, L. Gremillet, L. Bergé, C. Köhler, Opt. Express 22(11), 13691 (2014)CrossRefADSGoogle Scholar
  9. 9.
    M. Kolesik, J.V. Moloney, Rep. Prog. Phys. 77(1), 016401 (2014)CrossRefADSGoogle Scholar
  10. 10.
    M. Kolesik, J.V. Moloney, Phys. Rev. E 70(3), 036604 (2004)CrossRefADSGoogle Scholar
  11. 11.
    D. Alterman, J. Rauch, Phys. Lett. A 264(5), 390 (2000)zbMATHMathSciNetCrossRefADSGoogle Scholar
  12. 12.
    T. Schaffer, C.E. Wayne, Physica D 196(1–2), 90 (2004)MathSciNetCrossRefADSGoogle Scholar
  13. 13.
    G. Luther, J.V. Moloney, A.C. Newell, Physica D 74(1–2), 59 (1996)ADSGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ArizonaTucsonUSA

Personalised recommendations