Evaluating the robustness of rogue waves under perturbations

Ward, C. B.; Kevrekidis, P. G.; Whitaker, N.

doi:10.1016/j.physleta.2019.05.030

Cited by 15 publications

(8 citation statements)

References 37 publications

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“…Nevertheless, our work naturally poses the question of whether a setting can be engineered for the observation (and potential harnessing) of this phenomenon. From a theoretical perspective numerous extensions of the ideas reported herein can also be pursued, including the extension and numerical identification of such states beyond the integrable limit considered herein, using, for example, recent ideas such as those of [46]. Another extension of interest is to consider two-dimensional variants of the present model and whether rogue waves of the present type can be identified in suitable generalizations of settings related to the Davey–Stewartson and Benney–Roskes models where two-dimensional rogue patterns were considered in [47].…”

Section: Conclusion/future Workmentioning

confidence: 99%

Rogue waves of ultra-high peak amplitude: a mechanism for reaching up to a thousand times the background level

2021

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We unveil a mechanism enabling a fundamental rogue wave, expressed by a rational function of fourth degree, to reach a peak amplitude as high as a thousand times the background level in a system of coupled nonlinear Schrödinger equations involving both incoherent and coherent coupling terms with suitable coefficients. We obtain the exact explicit vector rational solutions using a Darboux-dressing transformation. We show that both components of such coupled equations can reach extremely high amplitudes. The mechanism is confirmed in direct numerical simulations and its robustness is confirmed upon noisy perturbations. Additionally, we showcase the fact that extremely high peak-amplitude vector fundamental rogue waves (of about 80 times the background level) can be excited even within a chaotic background field .

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Section: Conclusion/future Workmentioning

confidence: 99%

Rogue waves of ultra-high peak amplitude: a mechanism for reaching up to a thousand times the background level

2021

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“…This most naturally poses the question of whether a direct (or an engineered) observation of this phenomenon can arise and can be accordingly harnessed. From a theoretical perspective numerous extensions of the ideas reported herein can also be pursued including the extension and numerical identification of such states beyond the integrable limit considered herein, utilizing, e.g., recent ideas such as those of [43]. Another extension of interest is to consider two-dimensional variants of the present model and whether rogue wave of the present type can be identified in suitable generalizations of settings related to the Davey-Stewartson and Benney-Roskes models where two-dimensional rogue patterns were recently considered in [44].…”

Section: Conclusion/future Workmentioning

confidence: 99%

Rogue waves of Ultra-High Peak Amplitude: A Mechanism for Reaching up to Thousand Times the Background Level

Sun,

Liu,

Kevrekidis

2020

Preprint

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We unveil a mechanism enabling a fundamental rogue wave, expressed by a rational function of fourth degree, to reach a peak amplitude as high as a thousand times the background level in a system of coupled nonlinear Schrödinger equations involving both incoherent and coherent coupling terms with suitable coefficients. We obtain the exact explicit vector rational solutions using a Darboux-dressing transformation. We show that both components of such coupled equations can reach extremely high amplitudes. The mechanism is confirmed in direct numerical simulations and its robustness confirmed upon noisy perturbations. Additionally, we showcase the fact that extremely high peak-amplitude vector fundamental rogue waves (of about 80 times the background level) can be excited even within a chaotic background field.

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“…Over the past few years, we have attempted to address some of the relevant extensions of the understanding of rogue waves past the strict realm of integrable systems. On the one hand, some of the present authors have attempted to develop rogue-wave identifying methods that go beyond the integrable realm [36,37] such as tracing these solutions as fixed points in spacetime. On the other hand, a different subset of the present authors has developed techniques for understanding the stability of these states, considering the Floquet analysis of the KM waves and examining the Peregrine states as natural limiting states thereof [38].…”

Section: Introductionmentioning

confidence: 99%

Kuznetsov–Ma breather-like solutions in the Salerno model

et al. 2020

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The Salerno model is a discrete variant of the celebrated nonlinear Schrödinger (NLS) equation interpolating between the discrete NLS (DNLS) equation and completely integrable Ablowitz-Ladik (AL) model by appropriately tuning the relevant homotopy parameter. Although the AL model possesses an explicit time-periodic solution known as the Kuznetsov-Ma (KM) breather, the existence of time-periodic solutions away from the integrable limit has not been studied as of yet. It is thus the purpose of this work to shed light on the existence and stability of time-periodic solutions of the Salerno model. In particular, we vary the homotopy parameter of the model by employing a pseudo-arclength continuation algorithm where time-periodic solutions are identified via fixed-point iterations. We show that the solutions transform into time-periodic patterns featuring small, yet non-decaying far-field oscillations. Remarkably, our numerical results support the existence of previously unknown time-periodic solutions even at the integrable case whose stability is explored by using Floquet theory. A continuation of these patterns towards the DNLS limit is also discussed.

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Evaluating the robustness of rogue waves under perturbations

Cited by 15 publications

References 37 publications

Rogue waves of ultra-high peak amplitude: a mechanism for reaching up to a thousand times the background level

Rogue waves of ultra-high peak amplitude: a mechanism for reaching up to a thousand times the background level

Rogue waves of Ultra-High Peak Amplitude: A Mechanism for Reaching up to Thousand Times the Background Level

Kuznetsov–Ma breather-like solutions in the Salerno model

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