Wave amplification in the framework of forced nonlinear Schrödinger equation: The rogue wave context
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In this paper, it is shown that the adiabatically slow pumping (the time scale of forcing is much longer than the nonlinear time scale) results in selective enhancement of the solitary part of the wave ensemble.About:
This article is published in Physica D: Nonlinear Phenomena.The article was published on 2015-05-15 and is currently open access. It has received 41 citations till now. The article focuses on the topics: Nonlinear Schrödinger equation & Rogue wave.read more
Citations
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Nonlinear stage of Benjamin-Feir instability in forced/damped deep water waves
TL;DR: In this paper, a three-wave truncation of a damped/forced high-order nonlinear Schrodinger equation for deep-water gravity waves under the effect of wind and viscosity was studied.
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Interaction behaviors between breather and rogue wave in a Heisenberg ferromagnetic equation
TL;DR: In this paper, a (2+1)-dimensional Heisenberg ferromagnetic equation based on Schrodinger equation is used to model nonlinear wave propagation in ferromagnetagnetic spin chain.
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Excitation of Peregrine-type waveforms from vanishing initial conditions in the presence of periodic forcing
TL;DR: In this paper, it was shown that spatiotemporally localized wave forms, strongly reminiscent of the Peregrine rogue wave, can be excited by vanishing initial conditions for the periodically driven nonlinear Schrodinger equation.
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Deformation of bichromatic wave groups based on third order side band solution of Benjamin-Bona-Mahony equation
Vera Halfiani,Marwan Ramli +1 more
TL;DR: In this paper, the authors used the BBM model and third order side band approximation theory to investigate the peaking and splitting phenomena of the wave groups which is initially in bichromatic signal.
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Extreme wave events for a nonlinear Schrödinger equation with linear damping and Gaussian driving
Georgios Fotopoulos,Georgios Fotopoulos,Dimitri J. Frantzeskakis,Nikos I. Karachalios,Panayotis G. Kevrekidis,V. Koukouloyannis,V. Koukouloyannis,K. Vetas +7 more
TL;DR: In this paper, a numerical study of the initial-boundary value problem with vanishing boundary conditions is performed, where the authors identify Peregrine-like rogue waveforms, excited by two different types of vanishing initial data decaying at an algebraic or exponential rate.
References
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Journal Article
Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media
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The Inverse scattering transform fourier analysis for nonlinear problems
TL;DR: In this article, a systematic method is developed which allows one to identify certain important classes of evolution equations which can be solved by the method of inverse scattering, where the form of each evolution equation is characterized by the dispersion relation of its associated linearized version and an integro-differential operator.
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Water waves, nonlinear Schrödinger equations and their solutions
TL;DR: In this article, a number of ases in which these equations reduce to a one dimensional nonlinear Schrodinger (NLS) equation are enumerated, and several analytical solutions of NLS equations are presented, with discussion of their implications for describing the propagation of water waves.
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Physical Mechanisms of the Rogue Wave Phenomenon
Christian Kharif,Efim Pelinovsky +1 more
TL;DR: A review of physical mechanisms of the rogue wave phenomenon is given in this article, where the authors demonstrate that freak waves may appear in deep and shallow waters and demonstrate that these mechanisms remain valid but should be modified.
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Rogue wave observation in a water wave tank.
TL;DR: This work presents the first experimental results with observations of the Peregrine soliton in a water wave tank, and proposes a new approach to modeling deep water waves using the nonlinear Schrödinger equation.