Stabilization of Unsteady Nonlinear Waves by Phase-Space Manipulation

Gomel, Alexis; Chabchoub, Amin; Brunetti, Maura; Trillo, Stefano; Kasparian, Jérôme; Armaroli, Andrea

doi:10.1103/physrevlett.126.174501

Cited by 12 publications

(9 citation statements)

References 41 publications

(55 reference statements)

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“…Together with theoretical advances, there have been numerous recent experimental breakthroughs in the observation of breather solutions in water wave tanks (Chabchoub, Hoffmann & Akhmediev 2011; Chabchoub et al 2012; Kimmoun et al 2016; Gomel et al 2021). In an experimental context, the waves evolve in space rather than time, and the evolution equations must be changed to reflect this: for unidirectional waves, the temporal Zakharov equation (2.1) can be replaced by an analogous spatial Zakharov equation, derived by Shemer et al (2001), Shemer, Kit & Jiao (2002).…”

Section: Discussionmentioning

confidence: 99%

The nonlinear Benjamin–Feir instability – Hamiltonian dynamics, discrete breathers and steady solutions

Andrade

Stuhlmeier

2023

J. Fluid Mech.

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We develop a general framework to describe the cubically nonlinear interaction of a degenerate quartet of deep-water gravity waves in one or two spatial dimensions. Starting from the discretised Zakharov equation, and thus without restriction on spectral bandwidth, we derive a planar Hamiltonian system in terms of the dynamic phase and a modal amplitude. This is characterised by two free parameters: the wave action and the mode separation between the carrier and the sidebands. For unidirectional waves, the mode separation serves as a bifurcation parameter, which allows us to fully classify the dynamics. Centres of our system correspond to non-trivial, steady-state nearly resonant degenerate quartets. The existence of saddle-points is connected to the instability of uniform and bichromatic wave trains, generalising the classical picture of the Benjamin–Feir instability. Moreover, heteroclinic orbits are found to correspond to discrete, three-mode breather solutions, including an analogue of the famed Akhmediev breather solution of the nonlinear Schrödinger equation.

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Section: Discussionmentioning

confidence: 99%

The nonlinear Benjamin–Feir instability – Hamiltonian dynamics, discrete breathers and steady solutions

Andrade

Stuhlmeier

2023

J. Fluid Mech.

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“…Equation (11) gives a simple link between the two normalized mismatch κ for the transformation from the train of solitonic ABs to a stable solitons train evolving independently. Clearly, such solitonic conversion requires that the physical sideband detuning f m remains the same.…”

Section: Stabilization Scheme For Breather Wavesmentioning

confidence: 99%

“…Consequently, all possibilities to 'stabilize' a breather wave and especially to freeze breather's amplitude and phase in a controllable manner are of great interest [11][12][13][14]. Recently, Gomel et al experimentally investigated the parametric stabilization of unsteady nonlinear waves in a wave flume with an abrupt bathymetry change [11].…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, coherent seed-induced breathers in various conservative setting inevitably manifest as a synchronized periodic oscillation along longitudinal evolution [7][8][9][10]. Consequently, all possibilities to 'stabilize' a breather wave and especially to freeze breather's amplitude and phase in a controllable manner are of great interest [11][12][13][14]. Recently, Gomel et al experimentally investigated the parametric stabilization of unsteady nonlinear waves in a wave flume with an abrupt bathymetry change [11].…”

Section: Introductionmentioning

confidence: 99%

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Manipulation of breather waves with split-dispersion cascaded fibers

et al. 2022

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A stabilization scheme is proposed for the dynamics of breather waves induced by the coherent-seed modulation instability based on manipulation of phase-space trajectory. Theoretical and numerical analysis show that carefully dispersion- and nonlinearity-managed cascades of fiber configuration allows the system evolution to be stabilized around an elliptic centre point, forming stable pulse trains with ultrahigh contrast efficiently. We also demonstrate that the scheme proposed works equally well for near-separatrix dynamics. Our results provide an alternative means to control the unsteady nonlinear waves by abruptly changing the waveguide properties.

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“…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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Stabilization of Unsteady Nonlinear Waves by Phase-Space Manipulation

Cited by 12 publications

References 41 publications

The nonlinear Benjamin–Feir instability – Hamiltonian dynamics, discrete breathers and steady solutions

The nonlinear Benjamin–Feir instability – Hamiltonian dynamics, discrete breathers and steady solutions

Manipulation of breather waves with split-dispersion cascaded fibers

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

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