Topic
Rogue wave
About: Rogue wave is a research topic. Over the lifetime, 2977 publications have been published within this topic receiving 70933 citations. The topic is also known as: freak wave & monster wave.
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TL;DR: In this paper, the authors use the winding of real tori to show the appearance of generalized rogue waves and derive an analytical criterion distinguishing finite-band potentials of the fNLS equation that exhibit generalised rogue waves.
Abstract: Rogue waves appearing on deep water or in optical fibres are often modelled by certain breather solutions of the focusing nonlinear Schrodinger (fNLS) equation which are referred to as solitons on finite background (SFBs). A more general modelling of rogue waves can be achieved via the consideration of multiphase, or finite-band, fNLS solutions of whom the standard SFBs and the structures forming due to their collisions represent particular, degenerate, cases. A generalised rogue wave notion then naturally enters as a large-amplitude localised coherent structure occurring within a finite-band fNLS solution. In this paper, we use the winding of real tori to show the mechanism of the appearance of such generalized rogue waves and derive an analytical criterion distinguishing finite-band potentials of the fNLS equation that exhibit generalised rogue waves.
34 citations
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TL;DR: In this paper, the authors used the nonlinear Schrodinger equation (NLSE) to derive an approximate analytical relationship for changes in wave group shape and applied scaling laws from the NLSE in terms of wave steepness and bandwidth to solutions of the full water wave equations.
Abstract: The evolution of steep waves in the open ocean is nonlinear. In narrow-banded but directionally spread seas, this nonlinearity does not produce significant extra elevation but does lead to a large change in the shape of the wave group, causing, relative to linear evolution, contraction in the mean wave direction and lateral expansion. We use the nonlinear Schrodinger equation (NLSE) to derive an approximate analytical relationship for these changes in group shape. This shows excellent agreement with the numerical results both for the NLSE and for the full water wave equations. We also consider the application of scaling laws from the NLSE in terms of wave steepness and bandwidth to solutions of the full water wave equations. We investigate these numerically. While some aspects of water wave evolution do not scale, the major changes that a wave group undergoes as it evolves scale very well.
33 citations
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TL;DR: In this paper, a series of simulations on rogue waves based on a breather solution of the cubic Schrodinger equation, in a numerical wave tank coded in Visual Basic language, were performed.
33 citations
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TL;DR: In this article, the dynamics of rogue waves in the partially PT -symmetric nonlocal DS systems were derived using the Darboux transformation method, and it was shown that the fundamental rogue waves are rational solutions which arises from a constant background at t → − ∞, and develops finite-time singularity on an entire hyperbola in the spatial plane at the critical time.
33 citations
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TL;DR: In this paper, the Darboux transformation and generalized DT were used to obtain the six-order variable-coefficient nonlinear Schrodinger equation in an ocean or optical fiber, where x is the scaled propagation variable.
Abstract: Under investigation in this paper is a sixth-order variable-coefficient nonlinear Schrodinger equation in an ocean or optical fiber. Through the Darboux transformation (DT) and generalized DT, we obtain the multi-soliton solutions, breathers and rogue waves. Choosing different values of $\alpha$
(x), $\beta$
(x), $\gamma$
(x) and $\delta$
(x), which are the coefficients of the third-, fourth-, fifth- and sixth-order dispersions, respectively, we investigate their effects on those solutions, where x is the scaled propagation variable. When $\alpha$
(x), $\beta$
(x), $\gamma$
(x) and $\delta$
(x) are chosen as the linear, parabolic and periodic functions, we obtain the parabolic, cubic and quasi-periodic solitons, respectively. Head-on and overtaking interactions between the two solitons are presented, and the interactions are elastic. Besides, with certain values of the spectral parameter $\lambda$
, a shock region between the two solitons appears, and the interaction is inelastic. Interactions between two kinds of the breathers are also studied, and we find that the interaction regions are similar to those of the second-order rogue waves. Rogue waves are split into some first-order rogue waves when $\alpha$
(x), $\beta$
(x), $\gamma$
(x) and $\delta$
(x) are the periodic or odd-numbered functions.
33 citations