The nonlinear Schrödinger equation and the propagation of weakly nonlinear waves in optical fibers and on the water surface

A. Chabchoub*, B. Kibler, C. Finot, G. Millot, M. Onorato, J. M. Dudley, A. V. Babanin

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

36 Citations (Scopus)

Abstract

The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schrödinger equation (NLSE). An important feature of the equation is that it can be derived in a number of different physical contexts; therefore, analogies between different fields, such as for example fiber optics, water waves, plasma waves and Bose-Einstein condensates, can be established. Here, we investigate the similarities between wave propagation in optical Kerr media and water waves. In particular, we discuss the modulation instability (MI) in both media. In analogy to the water wave problem, we derive for Kerr-media the Benjamin-Feir index, i.e. a nondimensional parameter related to the probability of formation of rogue waves in incoherent wave trains.

Original languageEnglish
Pages (from-to)490-500
Number of pages11
JournalANNALS OF PHYSICS
Volume361
DOIs
Publication statusPublished - 1 Oct 2015
MoE publication typeA1 Journal article-refereed

Keywords

  • Benjamin-Feir index
  • Electromagnetic waves
  • Nonlinear Schrödinger equation
  • Water waves

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