Time-reversal generation of rogue waves.
Amin Chabchoub,Mathias Fink +1 more
TLDR
The time-reversal invariance of the NLS is used to propose and experimentally demonstrate a new approach to constructing strongly nonlinear localized waves focused in both time and space.Abstract:
The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schrodinger equation (NLS). Within the class of exact NLS breather solutions on a finite background, which describe the modulational instability of monochromatic wave trains, the hierarchy of rational solutions localized in both time and space is considered to provide appropriate prototypes to model rogue wave dynamics. Here, we use the time-reversal invariance of the NLS to propose and experimentally demonstrate a new approach to constructing strongly nonlinear localized waves focused in both time and space. The potential applications of this time-reversal approach include remote sensing and motivated analogous experimental analysis in other nonlinear dispersive media, such as optics, Bose-Einstein condensates, and plasma, where the wave motion dynamics is governed by the NLS.read more
Citations
More filters
Journal ArticleDOI
Roadmap on optical rogue waves and extreme events
Nail Akhmediev,Bertrand Kibler,Fabio Baronio,Milivoj R. Belic,Wei-Ping Zhong,Yiqi Zhang,Wonkeun Chang,Jose M. Soto-Crespo,Peter Vouzas,Philippe Grelu,Caroline Lecaplain,Kamal Hammani,Sergio Rica,Antonio Picozzi,Mustapha Tlidi,Krassimir Panajotov,Arnaud Mussot,Abdelkrim Bendahmane,Pascal Szriftgiser,Goëry Genty,John M. Dudley,Alexandre Kudlinski,Ayhan Demircan,Uwe Morgner,Shalva Amiraranashvili,Carsten Brée,G. Steinmeyer,Cristina Masoller,Neil G. R. Broderick,Antoine F. J. Runge,Miro Erkintalo,Stefania Residori,Umberto Bortolozzo,F. T. Arecchi,Stefan Wabnitz,C.G.L. Tiofack,Saliya Coulibaly,Majid Taki +37 more
TL;DR: The concept of optical rogue wave was introduced by Solli et al. as discussed by the authors, who defined it as "an optical pulse whose amplitude or intensity is much higher than that of the surrounding pulses".
Journal ArticleDOI
Time reversal and holography with spacetime transformations
TL;DR: In this article, a water bath subject to a sudden vertical jolt is used to demonstrate the concept of a "time mirror" where time-reversed waves return to their point source following a downward jolt.
Journal ArticleDOI
A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation
Deniz Bilman,Peter D. Miller +1 more
TL;DR: In this article, a modification of the standard inverse scattering transform for the focusing nonlinear Schrodinger equation (also other equations by natural generalization) formulated with nonzero boundary conditions at infinity is proposed.
Journal ArticleDOI
The nonlinear Schrödinger equation and the propagation of weakly nonlinear waves in optical fibers and on the water surface
Amin Chabchoub,Bertrand Kibler,Christophe Finot,Guy Millot,Miguel Onorato,Miguel Onorato,John M. Dudley,Alexander V. Babanin +7 more
TL;DR: In this paper, the similarity between wave propagation in optical Kerr media and water waves was investigated, and the Benjamin-Feir index was derived for the probability of formation of rogue waves in incoherent wave trains.
Journal ArticleDOI
Generation of higher-order rogue waves from multibreathers by double degeneracy in an optical fiber.
TL;DR: A special kind of breather solution of the nonlinear Schrödinger (NLS) equation, the so-called breather-positon, which can be obtained by taking the limit λ_{j}→λ_{1} of the Lax pair eigenvalues in the order-n periodic solution, which is generated by the n-fold Darboux transformation from a special "seed" solution-plane wave.
References
More filters
Journal ArticleDOI
Stability of periodic waves of finite amplitude on the surface of a deep fluid
TL;DR: In this article, the stability of steady nonlinear waves on the surface of an infinitely deep fluid with a free surface was studied. And the authors considered the problem of stability of surface waves as part of the more general problem of nonlinear wave in media with dispersion.
Journal ArticleDOI
The disintegration of wave trains on deep water Part 1. Theory
T. Brooke Benjamin,J. E. Feir +1 more
TL;DR: In this paper, a theoretical analysis of the stability of periodic wave trains to small disturbances in the form of a pair of side-band modes is presented, where the wave train becomes highly irregular far from its origin, even when the departures from periodicity are scarcely detectable at the start.
Journal ArticleDOI
The Peregrine soliton in nonlinear fibre optics
Bertrand Kibler,Julien Fatome,Christophe Finot,Guy Millot,Frédéric Dias,Frédéric Dias,Goëry Genty,Nail Akhmediev,John M. Dudley +8 more
TL;DR: The Peregrine soliton was observed experimentally for the first time by using femtosecond pulses in an optical fiber as mentioned in this paper, which gave some insight into freak waves that can appear out of nowhere before simply disappearing.
Journal ArticleDOI
Waves that appear from nowhere and disappear without a trace
TL;DR: In this article, a hierarchy of rational solutions of the nonlinear Schrodinger equation (NLSE) with increasing order and with progressively increasing amplitude is presented. And the authors apply the WANDT title to two objects: rogue waves in the ocean and rational solution of the NLSE.
Journal ArticleDOI
Rogue wave observation in a water wave tank.
TL;DR: This work presents the first experimental results with observations of the Peregrine soliton in a water wave tank, and proposes a new approach to modeling deep water waves using the nonlinear Schrödinger equation.