Observation of modulation instability and rogue breathers on stationary periodic waves

Xu, Gang; Chabchoub, Amin; Pelinovsky, Dmitry E.; Kibler, Bertrand

doi:10.1103/physrevresearch.2.033528

Cited by 46 publications

(45 citation statements)

References 36 publications

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“…Multi-periodic wave patterns in complex physical systems are modelled by the periodic standing wave solutions of the NLS equation. These periodic standing waves are also modulationally unstable [10] and rogue waves on their background exist as exact solutions of the NLS equation [11,12] and are observed in the numerical simulations [13] and optical and hydrodynamical experiments [14].…”

Section: Introductionmentioning

confidence: 77%

Rogue waves on the background of periodic standing waves in the derivative NLS equation

Chen,

Pelinovsky

2021

Preprint

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The derivative nonlinear Schrödinger (DNLS) equation is the canonical model for dynamics of nonlinear waves in plasma physics and optics. We study exact solutions describing rogue waves on the background of periodic standing waves in the DNLS equation. We show that the space-time localization of a rogue wave is only possible if the periodic standing wave is modulationally unstable. If the periodic standing wave is modulationally stable, the rogue wave solutions degenerate into algebraic solitons propagating along the background and interacting with the periodic standing waves. Maximal amplitudes of rogue waves are found analytically and confirmed numerically.

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Section: Introductionmentioning

confidence: 77%

Rogue waves on the background of periodic standing waves in the derivative NLS equation

Chen,

Pelinovsky

2021

Preprint

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“…We confirm that this peculiar phase-sensitive breather interaction is strictly different to the well-known soliton interactions. Our study paves the way for novel directions of investigation in the rich landscape of complex nonlinear wave dynamics [23][24][25][26].…”

Section: Introductionmentioning

confidence: 85%

Ghost Interaction of Breathers

Gelash

Chabchoub

et al. 2020

Front. Phys.

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Mutual interaction of localized nonlinear waves, e.g., solitons and modulation instability patterns, is a fascinating and intensively-studied topic of nonlinear science. Here we report the observation of a novel type of breather interaction in telecommunication optical fibers, in which two identical breathers propagate with opposite group velocities. Under controlled conditions, neither amplification nor annihilation occurs at the collision point and most interestingly, the respective envelope amplitude, resulting from the interaction, almost equals another envelope maximum of either oscillating and counterpropagating breather. This ghost-like breather interaction dynamics is fully described by an N-breather solution of the nonlinear Schrödinger equation.

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“…Note that a wave-absorbing installation is placed opposite to the wave maker to ensure a wave field propagation free of reflections. Exact schematics of both facilities can be found in [5,33]. A graphical guide to better understand the origin of the data as measured by the wave gauges along the flume can be found in [35].…”

Section: Laboratory Experimentsmentioning

confidence: 99%

The Peregrine Breather on the Zero-Background Limit as the Two-Soliton Degenerate Solution: An Experimental Study

et al. 2021

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Solitons are coherent structures that describe the nonlinear evolution of wave localizations in hydrodynamics, optics, plasma and Bose-Einstein condensates. While the Peregrine breather is known to amplify a single localized perturbation of a carrier wave of finite amplitude by a factor of three, there is a counterpart solution on zero background known as the degenerate two-soliton which also leads to high amplitude maxima. In this study, we report several observations of such multi-soliton with doubly-localized peaks in a water wave flume. The data collected in this experiment confirm the distinctive attainment of wave amplification by a factor of two in good agreement with the dynamics of the nonlinear Schrödinger equation solution. Advanced numerical simulations solving the problem of nonlinear free water surface boundary conditions of an ideal fluid quantify the physical limitations of the degenerate two-soliton in hydrodynamics.

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Observation of modulation instability and rogue breathers on stationary periodic waves

Cited by 46 publications

References 36 publications

Rogue waves on the background of periodic standing waves in the derivative NLS equation

Rogue waves on the background of periodic standing waves in the derivative NLS equation

Ghost Interaction of Breathers

The Peregrine Breather on the Zero-Background Limit as the Two-Soliton Degenerate Solution: An Experimental Study

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