Waves that appear from nowhere and disappear without a trace

Akhmediev, Nail; Ankiewicz, Adrian; Taki, Majid

doi:10.1016/j.physleta.2008.12.036

Cited by 1,182 publications

(995 citation statements)

References 21 publications

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“…[4,5], these extreme wave events were also observed in a wide class of physical systems, including capillary waves and surface ripples [6,7], plasmas [8], optical fibers [9,10], mode-locked lasers [11], and filaments [12]. These studies have uncovered general features of nonlinearity and complexity shared by rogue waves, e.g., they are extremely large and steep compared with typical events, occur in a nonlinear medium, and follow an unusual L-shaped statistics [9,[11][12][13]. Despite these diverse features, mathematical solutions of rogue waves can be expressed as rational functions localized in both space and time.…”

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confidence: 90%

Coexisting rogue waves within the (2+1)-component long-wave–short-wave resonance

2014

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The coexistence of two different types of fundamental rogue waves is unveiled, based on the coupled equations describing the (2+1)-component long-wave-short-wave resonance. For a wide range of asymptotic background fields, each family of three rogue wave components can be triggered by using a slight deterministic alteration to the otherwise identical background field. The ability to trigger markedly different rogue wave profiles from similar initial conditions is confirmed by numerical simulations. This remarkable feature, which is absent in the scalar nonlinear Schrödinger equation, is attributed to the specific three-wave interaction process and may be universal for a variety of multicomponent wave dynamics spanning from oceanography to nonlinear optics. [4,5], these extreme wave events were also observed in a wide class of physical systems, including capillary waves and surface ripples [6,7], plasmas [8], optical fibers [9,10], mode-locked lasers [11], and filaments [12]. These studies have uncovered general features of nonlinearity and complexity shared by rogue waves, e.g., they are extremely large and steep compared with typical events, occur in a nonlinear medium, and follow an unusual L-shaped statistics [9,[11][12][13]. Despite these diverse features, mathematical solutions of rogue waves can be expressed as rational functions localized in both space and time. One typical example is the Peregrine soliton [14], a well-known rogue wave prototype in various experimental fields [4,8,10], which is the lowest-order rational solution to the nonlinear Schrödinger (NLS) equation.Following the need to model complex physical systems more precisely, it has become important to study rogue wave phenomena beyond the framework of the NLS equation. Recent developments have taken into account dissipative effects [11,15,16], included higher-order nonlinear terms [17][18][19], or considered the coupling between several fields [20][21][22][23][24][25]. The latter investigations have led to the discovery of intricate rogue wave structures that are generally unattainable in the scalar models. In particular, we showed in Ref.[25] that the long-wave-short-wave (LWSW) resonance interaction can result in stable dark and bright rogue waves in spite of the onset of modulational instability (MI). This finding brings about the possibility to observe dark rogue waves in LWSW resonance systems such as negative index media [26] and capillary-gravity waves [6,27].Basically, the LWSW resonance is a general parametric process that manifests when the group velocity of the short wave matches the phase velocity of the long wave [28]. It has been predicted in different disciplines such as fluid dynamics [27], plasma physics [29], oceanography [30], and nonlinear optics [26,31]. Early works showed that both the LWSW and the NLS equations could be obtained from the same Davey-Stewartson system under the appropriate parameter conditions [27,32,33], although the former is currently less popular in use than the latter.In fact, it is possible to co...

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confidence: 90%

Coexisting rogue waves within the (2+1)-component long-wave–short-wave resonance

2014

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“…The latter can be considered as the extension of the modulation-instability process [10] beyond the linear approximation that captures the full nonlinear dynamics of the system. These exact solutions represent a fundamental tool for understanding optical phenomena that start with a strong monochromatic wave [4,5,[11][12][13][14][15]. Among them, there were the first experimental observations of the Peregrine [16] and Kusnetzov-Ma [17] breathers, well after their first theoretical predictions [18][19][20].…”

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confidence: 99%

Fermi-Pasta-Ulam Recurrence in Nonlinear Fiber Optics: The Role of Reversible and Irreversible Losses

et al. 2014

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The discovery of the Fermi-Pasta-Ulam (FPU) recurrence phenomenon in the 1950 s was a major step in science that later led to the discovery of solitons in nonlinear physics. More recently, it was shown that optical fibers can serve as a medium for observing the FPU phenomenon. In the present work, we have found experimentally and numerically that in the low-dispersion region of an optical fiber, the recurrence is strongly influenced by the third-order-dispersion (TOD) term. Namely, the presence of TOD leads to several disappearances and recoveries of the FPU recurrence when the central frequency of the pump wave is varied. The effect is highly nontrivial and can be explained in terms of reversible and irreversible losses caused by Cherenkov radiations interacting with a multiplicity of modes sharing the optical energy in the process of its partition.

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“…The same equation appears in many other fields, including biophysics, astrophysics and particle physics [36], and in the study of deep ocean waves [57]. The single-bright-soliton solution of the homogeneous 1D GPE is given by,…”

Section: Bright Soliton Solutionsmentioning

confidence: 95%

Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations

Malomed¹

2013

Progress in Optical Science and Photonics

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In recent years, bright soliton-like structures composed of gaseous Bose-Einstein condensates have been generated at ultracold temperature. The experimental capacity to precisely engineer the nonlinearity and potential landscape experienced by these solitary waves offers an attractive platform for fundamental study of solitonic structures. The presence of three spatial dimensions and trapping implies that these are strictly distinct objects to the true soliton solutions. Working within the zero-temperature mean-field description, we explore the solutions and stability of bright solitary waves, as well as their interactions. Emphasis is placed on elucidating their similarities and differences to the true bright soliton. The rich behaviour introduced in the bright solitary waves includes the collapse instability and symmetry-breaking collisions. We review the experimental formation and observation of bright solitary matter waves to date, and compare to theoretical predictions. Finally we discuss the current state-of-the-art of this area, including beyond-mean-field descriptions, exotic bright solitary waves, and proposals to exploit bright solitary waves in interferometry and as surface probes.

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Waves that appear from nowhere and disappear without a trace

Cited by 1,182 publications

References 21 publications

Coexisting rogue waves within the (2+1)-component long-wave–short-wave resonance

Coexisting rogue waves within the (2+1)-component long-wave–short-wave resonance

Fermi-Pasta-Ulam Recurrence in Nonlinear Fiber Optics: The Role of Reversible and Irreversible Losses

Spontaneous Symmetry Breaking, Self-Trapping, and Josephson Oscillations

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