Journal ArticleDOI
The random and deterministic dynamics of ‘rogue waves’ in unidirectional, deep-water wave trains ☆
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TLDR
In this paper, the authors provide a new perspective on the nonlinear wave dynamics for this problem in the particular case of unidirectional wave propagation, based upon the well-known nonlinear Schroedinger equation that governs the space/time dynamics of narrow banded, deep-water wave trains to leading order in cubic nonlinearity.About:
This article is published in Marine Structures.The article was published on 2001-05-01. It has received 72 citations till now. The article focuses on the topics: Rogue wave & Wave propagation.read more
Citations
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Rogue waves and rational solutions of the nonlinear Schrödinger equation
TL;DR: This work can elucidate the appearance of rogue waves in the deep ocean and can be applied to the observation of rogue light pulse waves in optical fibers.
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Matter rogue waves
TL;DR: In this article, the existence of rogue waves in Bose-Einstein condensates either loaded into a parabolic trap or embedded in an optical lattice was shown to be possible.
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Extreme waves that appear from nowhere: On the nature of rogue waves
TL;DR: In this article, a plane wave is modulated by relatively weak random waves, and it is shown that the peaks with highest amplitude of the resulting wave composition can be described in terms of exact solutions of the focusing nonlinear Schrrodinger equation in the form of the collision of Akhmediev breathers.
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How to excite a rogue wave
TL;DR: In this article, the authors propose initial conditions that facilitate the excitation of rogue waves, which is useful both in attempts to avoid them by seafarers and in generating highly energetic pulses in optical fibers.
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Are rogue waves robust against perturbations
TL;DR: In this article, the effect of various perturbations on the fundamental rational solution of the nonlinear Schrodinger equation (NLSE) was studied, and it was shown that the rational solution remains rational and localized in each direction, thus representing a modified rogue wave.
References
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Method for solving the Korteweg-deVries equation
TL;DR: In this paper, a method for solving the initial value problem of the Korteweg-deVries equation is presented which is applicable to initial data that approach a constant sufficiently rapidly as
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Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
Book
Solitons and the Inverse Scattering Transform
Mark J. Ablowitz,Harvey Segur +1 more
TL;DR: In this paper, the authors developed the theory of the inverse scattering transform (IST) for ocean wave evolution, which can be solved exactly by the soliton solution of the Korteweg-deVries equation.
Journal Article
Exact Theory of Two-dimensional Self-focusing and One-dimensional Self-modulation of Waves in Nonlinear Media
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Stability of periodic waves of finite amplitude on the surface of a deep fluid
TL;DR: In this article, the stability of steady nonlinear waves on the surface of an infinitely deep fluid with a free surface was studied. And the authors considered the problem of stability of surface waves as part of the more general problem of nonlinear wave in media with dispersion.