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

doi:10.1016/j.aop.2015.07.003

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

Not published at Aalto University

Research output: Contribution to journal › Article › Scientific › peer-review

85 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 language	English
Pages (from-to)	490-500
Number of pages	11
Journal	Annals of Physics
Volume	361
DOIs	https://doi.org/10.1016/j.aop.2015.07.003
Publication status	Published - 1 Oct 2015
MoE publication type	A1 Journal article-refereed

Keywords

Benjamin-Feir index
Electromagnetic waves
Nonlinear Schrödinger equation
Water waves

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10.1016/j.aop.2015.07.003

Cite this

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title = "The nonlinear Schr{\"o}dinger equation and the propagation of weakly nonlinear waves in optical fibers and on the water surface",

abstract = "The dynamics of waves in weakly nonlinear dispersive media can be described by the nonlinear Schr{\"o}dinger 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.",

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author = "A. Chabchoub and B. Kibler and C. Finot and G. Millot and M. Onorato and Dudley, \{J. M.\} and Babanin, \{A. V.\}",

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T1 - The nonlinear Schrödinger equation and the propagation of weakly nonlinear waves in optical fibers and on the water surface

AU - Chabchoub, A.

AU - Kibler, B.

AU - Finot, C.

AU - Millot, G.

AU - Onorato, M.

AU - Dudley, J. M.

AU - Babanin, A. V.

PY - 2015/10/1

Y1 - 2015/10/1

N2 - 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.

AB - 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.

KW - Benjamin-Feir index

KW - Electromagnetic waves

KW - Nonlinear Schrödinger equation

KW - Water waves

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DO - 10.1016/j.aop.2015.07.003

M3 - Article

AN - SCOPUS:84938487153

SN - 0003-4916

VL - 361

SP - 490

EP - 500

JO - Annals of Physics

JF - Annals of Physics

ER -

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

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Keywords

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