Waves that appear from nowhere and disappear without a trace

By Nail Akhmediev, Adrian Ankiewicz, M. Taki. 2009

1,210 citations recorded by the source corpus.

Subfields: Oceanography, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/67cba5e57fe26395d8a652c6ac44726694a1d630

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In Oceanography

In Statistical and Nonlinear Physics

Citations in the corpus

Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions (2014, background): “It should also be noted that, in light of the relationship between these soliton solutions, the MI and rogue waves, it is likely that these soliton solutions are relevant to rogue waves [6] in water waves [7] as well as optics [39].”
Optical wave turbulence: Towards a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics (2014, background): “, breathers solutions [517,518,501,519,502], or more specifically their limiting cases of infinite spatial and temporal periods, the rational soliton solutions [520,521].”
Generalized Darboux transformation and localized waves in coupled Hirota equations (2013, background): “breather is localized in space or time, namely, Akhmedievbreather[3] or Ma breather [4]. While a rogue wave is localized in both space and time, it appears from nowhere and disappears without a trace [12], and has become a hottest topic in the research ﬁeld of localized waves in very recent years. M”
Recent progress in investigating optical rogue waves (2013, background): “When excited from special initial conditions, we can expect excitation of higher-order rogue wave structures [61–63] described by the higher-order rational solutions of the nonlinear Schrödinger equation [64–69] or its extensions such as”
What makes the Peregrine soliton so special as a prototype of freak waves? (2010, background): “To complete the picture we mention that there are also more general solutions (see [19,29,30]) and a solution resulting from the interaction between the simple solutions.”
Instabilities, breathers and rogue waves in optics (2014, methodology): “th even stronger localisation and higher intensities than the PS [21], such as higher-order rational solitons [25- 28,33] and AB collisions [34]. Figure 1(a) shows examples of both types of solutions [25,35,36]. The analytical results above have been used to design experiments with controlled initia”
General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation (2011, background): “lutions [12]. Indeed, rogue waves can be obtained from homoclinic solutions when the spatial period of homoclinic solutions goes to inﬁnity ∗Email: ohta@math.kobe-u.ac.jp †Email: jyang@math.uvm.edu 1 [13]. These rogue waves are also related to breather solutions which move on a non-zero constant bac”
The Darboux transformation of the Kundu–Eckhaus equation (2015, background): “[38] have provided a vivid description of the rogue characteristics—‘appear from nowhere and disappear without a trace’.”
Dynamics of rogue waves in the Davey–Stewartson II equation (2012, background): “Ik (Some figures may appear in colour only in the online journal)”
Roadmap on optical rogue waves and extreme events (2016, background): “For example, the first experimental observations of breather type solutions of the nonlinear Schrödinger equation, widely referred to as RW solutions [55, 108, 152], have been reported in fiber optics.”
Super Rogue Waves: Observation of a Higher-Order Breather in Water Waves (2012, background): “The higherorder rational solution, localized in both space and time, was presented in [18,25] and the polynomials for this solution are”