Rogue waves in the atmosphere

Stenflo, L.; Marklund, Mattias

doi:10.1017/s0022377809990481

Cited by 287 publications

(127 citation statements)

References 13 publications

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“…This example is directly related to the description of matter wave dynamics in the mean-field approximation (where the NLS equation is also known as the GrossPitaevskii equation), thus representing a unique possibility of creating and observing three-dimensional rogue matter waves. We note that the conventional rogue waves are either two-dimensional, as it happens, e.g., in the ocean [12], in wide aperture optical cavities [13] and in capillary wave experiments [14] or one-dimensional and they appear in many fields including nonlinear optics [15][16][17][18], cigar-shaped BECs [19], atmosphere [20], and finances [21].…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional rogue waves in nonstationary parabolic potentials

2010

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Using symmetry analysis we systematically present a higher-dimensional similarity transformation reducing the (3+1)-dimensional inhomogeneous nonlinear Schrödinger (NLS) equation with variable coefficients and parabolic potential to the (1+1)-dimensional NLS equation with constant coefficients. This transformation allows us to relate certain class of localized exact solutions of the (3+1)-dimensional case to the variety of solutions of integrable NLS equation of (1+1)-dimensional case. As an example, we illustrated our technique using two lowest order rational solutions of the NLS equation as seeding functions to obtain rogue wave-like solutions localized in three dimensions that have complicated evolution in time including interactions between two time-dependent rogue wave solutions. The obtained three-dimensional rogue wave-like solutions may raise the possibility of relative experiments and potential applications in nonlinear optics and BECs.

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Section: Introductionmentioning

confidence: 99%

Three-dimensional rogue waves in nonstationary parabolic potentials

2010

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“…Recently, the phenomena of rogue waves has also been observed and demonstrated in optics [10][11][12], in plasmas [13], in Bose-Einstein condensates [14], atmosphere [15], in superfluid helium [16], in capillary waves [17] and even in finance [18]. These discoveries indicate that rogue waves may be rather universal.…”

Section: Introductionmentioning

confidence: 89%

Rogue waves in Lugiato-Lefever equation with variable coefficients

Kol

Kingni²,

Woafo

2014

Open Physics

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Abstract:In this paper, we theoretically investigate the generation of optical rogue waves from a Lugiato-Lefever equation with variable coefficients by using the nonlinear Schrödinger equation-based constructive method. Exact explicit rogue-wave solutions of the Lugiato-Lefever equation with constant dispersion, detuning and dissipation are derived and presented. The bright rogue wave, intermediate rogue wave and the dark rogue wave are obtained by changing the value of one parameter in the exact explicit solutions corresponding to the external pump power of a continuous-wave laser. PACS

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“…Our goal in this study is to generalize the method of [19] to a more generalized NLS equation that includes higher order terms such as quintic nonlinearity term, |u| 4 u, and higher order nonlinearity terms such as (|u| 2 u) x and (|u| 2 ) x u. The addition of these terms are necessary for stability of the solitary-like wave solutions.…”

Section: U(zt) = ρ(Z)u(z(z) T (Zt))e Iφ (Zt)mentioning

confidence: 99%

“…(5) transforms into a desirable form by choosing the phase imprint in such a way that generates higher order terms of physically significant in the most natural way. The process involves selecting θ t and θ x as the expressions of involving higher order terms such as |u| 4 , u * u x , uu * x , |u| 2 , and so on. The addition of higher order terms to Eq.…”

Section: The Modelmentioning

confidence: 99%

Stable solitary-waves in a higher order generalized nonlinear Schrödinger equation with space- and time-variable coefficients

Zakeri¹,

Yomba²

2013

AIP Conference Proceedings

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Abstract. We developed a method that combines a similarity transformation with a mapping that solves a generalized nonautonomous nonlinear Schrödinger (NLS) equation containing cubic, quintic and higher order terms in the conjunction with spatially and temporary varying dispersion, containing higher nonlinearities, and external potential. We have studied various classes of solutions in closed form representing front, bright and dark solitary-like waves. We introduced a transformation that solves the related transformed NLS in the constant coefficients. As an application of this technique, we have analyzed the dynamical behavior of several specific classes of solutions such as moving, breathing, resonant both for periodic and quasiperiodic solitary-like waves. The stability of the obtained solitary-like waves is examined using analytical and numerical methods.

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Rogue waves in the atmosphere

Cited by 287 publications

References 13 publications

Three-dimensional rogue waves in nonstationary parabolic potentials

Three-dimensional rogue waves in nonstationary parabolic potentials

Rogue waves in Lugiato-Lefever equation with variable coefficients

Stable solitary-waves in a higher order generalized nonlinear Schrödinger equation with space- and time-variable coefficients

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