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

Chabchoub, Amin; Kibler, Bertrand; Finot, Christophe; Millot, Guy; Onorato, Miguel; Dudley, John M.; Babanin, Alexander V.

doi:10.1016/j.aop.2015.07.003

Cited by 89 publications

(64 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In optics, we prefer to avoid the detrimental effects of Raman scattering and third-order dispersion, whereas in hydrodynamics we try to restrain the impact of higher-order dispersion and the mean flow. Our work explicitly confirms the analogy of complex nonlinear dynamics between wave propagation in optical Kerr media and water waves and, therefore, in a general context of weakly nonlinear dispersive media, when the NLSE accurately approximates the governing equation of the media of interest [50]. Note that the main differences between our two experimental approaches lie in only two technical aspects related to substantially different temporal scales of breather waves: (i) the initial shaping of the perturbation on the plane wave and (ii) the measurement of wave profiles.…”

Section: Discussionsupporting

confidence: 54%

Superregular Breathers in Optics and Hydrodynamics: Omnipresent Modulation Instability beyond Simple Periodicity

et al. 2015

Self Cite

View full text Add to dashboard Cite

Since the 1960s, the Benjamin-Feir (or modulation) instability (MI) has been considered as the selfmodulation of the continuous "envelope waves" with respect to small periodic perturbations that precedes the emergence of highly localized wave structures. Nowadays, the universal nature of MI is established through numerous observations in physics. However, even now, 50 years later, more practical but complex forms of this old physical phenomenon at the frontier of nonlinear wave theory have still not been revealed (i.e., when perturbations beyond simple harmonic are involved). Here, we report the evidence of the broadest class of creation and annihilation dynamics of MI, also called superregular breathers. Observations are done in two different branches of wave physics, namely, in optics and hydrodynamics. Based on the common framework of the nonlinear Schrödinger equation, this multidisciplinary approach proves universality and reversibility of nonlinear wave formations from localized perturbations for drastically different spatial and temporal scales.

show abstract

Section: Discussionsupporting

confidence: 54%

Superregular Breathers in Optics and Hydrodynamics: Omnipresent Modulation Instability beyond Simple Periodicity

et al. 2015

Self Cite

View full text Add to dashboard Cite

show abstract

“…Since then, a lot of work has been done, trying to deepen the analogies between optical and hydrodynamical rogue waves [61]. The bridge for the analogy finds its roots in the universality of the NLS equation [37] and its capability of describing weakly nonlinear dispersive waves in different contexts. Indeed, exact breather solutions of the NLSE have been reproduced with some degree of success both in hydrodynamics and optics [33].…”

Section: Discussionmentioning

confidence: 99%

“…While NLSE provides only an approximation to the dynamics of water waves, we have found that its use has been of practical relevance for the design of the optical experiment and for the comparison between the hydrodyanmical and optical data sets. Indeed, the NLSE equation offers a common background over which nonlinear dynamics in different fields can be described [9,37]. For the present discussion, it is important to write the NLSE in the following form:…”

Section: A Unifying Descriptionmentioning

confidence: 99%

“…Experiments have also been performed in order to generate exact solutions of the NLSE in optical fibers and water wave tanks [31][32][33][34][35][36]. These observations have been of fundamental significance for establishing the bases of a potential bridge between the fields of optics and hydrodynamics (see also [37,38] for a detailed comparison between the NLSE in optics and hydrodynamics). In all these optical fibers and water experiments, the initial conditions are deterministic and specifically designed to match peculiar exact solutions of the NLSE.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Spontaneous emergence of rogue waves in partially coherent waves: A quantitative experimental comparison between hydrodynamics and optics

et al. 2018

Self Cite

View full text Add to dashboard Cite

Rogue waves are extreme and rare fluctuations of the wave field that have been discussed in many physical systems. Their presence substantially influences the statistical properties of an incoherent wave field. Their understanding is fundamental for the design of ships and offshore platforms. Except for very particular meteorological conditions, waves in the ocean are characterised by the so-called JONSWAP (Joint North Sea Wave Project) spectrum. Here we compare two unique experimental results: the first one has been performed in a 270-meter wave tank and the other in optical fibers. In both cases, waves characterised by a JONSWAP spectrum and random Fourier phases have been launched at the input of the experimental device. The quantitative comparison, based on an appropriate scaling of the two experiments, shows a very good agreement between the statistics in hydrodynamics and optics. Spontaneous emergence of heavy tails in the probability density function of the wave amplitude is observed in both systems. The results demonstrate the universal features of rogue waves and provide a fundamental and explicit bridge between two important fields of research. Numerical simulations are also compared with experimental results.

show abstract

“…Being an integrable equation, the NLS provides exact analytical solutions that describe the evolution of localised structures on the water surface in time and space, thus allowing subsequently the study and understanding of the dynamics of fundamental localised structures. The validity of the NLS has been experimentally confirmed even in the modelling of extreme localisations, beyond its well-known asymptotic limitations [4][5][6][7][8], and due to its interdisciplinary character analogies being able to be built into other nonlinear dispersive media, such as in optics [9], a research field in which several NLS applications have found strong interest [9][10][11][12][13][14]. Furthermore, the NLS admits basic models for the description of oceanic extreme events known as breathers [15][16][17].…”

Section: Introductionmentioning

confidence: 99%

The Hydrodynamic Nonlinear Schrödinger Equation: Space and Time

Chabchoub

Grimshaw

2016

Fluids

View full text Add to dashboard Cite

Abstract:The nonlinear Schrödinger equation (NLS) is a canonical evolution equation, which describes the dynamics of weakly nonlinear wave packets in time and space in a wide range of physical media, such as nonlinear optics, cold gases, plasmas and hydrodynamics. Due to its integrability, the NLS provides families of exact solutions describing the dynamics of localised structures which can be observed experimentally in applicable nonlinear and dispersive media of interest. Depending on the co-ordinate of wave propagation, it is known that the NLS can be either expressed as a space-or time-evolution equation. Here, we discuss and examine in detail the limitation of the first-order asymptotic equivalence between these forms of the water wave NLS. In particular, we show that the the equivalence fails for specific periodic solutions. We will also emphasise the impact of the studies on application in geophysics and ocean engineering. We expect the results to stimulate similar studies for higher-order weakly nonlinear evolution equations and motivate numerical as well as experimental studies in nonlinear dispersive media.

show abstract

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

Cited by 89 publications

References 39 publications

Superregular Breathers in Optics and Hydrodynamics: Omnipresent Modulation Instability beyond Simple Periodicity

Superregular Breathers in Optics and Hydrodynamics: Omnipresent Modulation Instability beyond Simple Periodicity

Spontaneous emergence of rogue waves in partially coherent waves: A quantitative experimental comparison between hydrodynamics and optics

The Hydrodynamic Nonlinear Schrödinger Equation: Space and Time

Contact Info

Product

Resources

About