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Showing papers on "Rogue wave published in 2019"


Journal ArticleDOI
01 Nov 2019
TL;DR: A review of the work in hydrodynamics includes results that support both nonlinear and linear interpretations of rogue wave formation in the ocean, and in optics, also provide an overview of the emerging area of research applying the measurement techniques developed for the study of rogue waves to dissipative soliton systems as mentioned in this paper.
Abstract: Over a decade ago, an analogy was drawn between the generation of large ocean waves and the propagation of light fields in optical fibres. This analogy drove numerous experimental studies in both systems, which we review here. In optics, we focus on results arising from the use of real-time measurement techniques, whereas in oceanography we consider insights obtained from analysis of real-world ocean wave data and controlled experiments in wave tanks. This Review of the work in hydrodynamics includes results that support both nonlinear and linear interpretations of rogue wave formation in the ocean, and in optics, we also provide an overview of the emerging area of research applying the measurement techniques developed for the study of rogue waves to dissipative soliton systems. We discuss the insights gained from the analogy between the two systems and its limitations in modelling real-world ocean wave scenarios that include physical effects that go beyond a one-dimensional propagation model. An analogy between wave propagation in hydrodynamics and in optics has yielded new insights into the mechanisms leading to the formation of giant rogue waves on the ocean. We review experimental progress and field measurements in this area.

196 citations


Journal ArticleDOI
TL;DR: A generalized AB system, which is used to describe certain baroclinic instability processes in the geophysical flows, is investigated, and the Darboux and generalizedDarboux transformations are derived, both relevant to the coefficient of the nonlinear term and coefficient related to the shear.

107 citations


Journal ArticleDOI
TL;DR: In this paper, a generalized B-dimensional Kadomtsev-Petviashvili equation for the water waves is investigated, and two kinds of the hybrid solutions composed of the breathers, lumps, line rogue waves and kink solitons are given.
Abstract: Water waves are one of the most common phenomena in nature, the study of which helps in designing the related industries. In this paper, a generalized ( $$3+1$$ )-dimensional B-type Kadomtsev–Petviashvili equation for the water waves is investigated. Gramian solutions are constructed via the Kadomtsev–Petviashvili hierarchy reduction. Based on the Gramian solutions, we construct the breathers. We graphically analyze the breather solutions and find that the breathers can be reduced to the homoclinic orbits. For the higher-order breather solutions, we obtain the mixed solutions consisting of the breathers and homoclinic orbits. According to the long-wave limit method, rational solutions are constructed. We look at two types of the rational solutions, i.e., the lump and line rogue wave solutions, and give the condition for the lumps being reduced to the line rogue waves. Taking another set of the parameters for the Gramian solutions, we also derive the kinky breather solutions which can be reduced to the kink solitons. For the higher-order kinky breather solutions, we obtain the mixed solutions consisting of the breathers and kink solitons. Combining the breather and rational solutions, we construct two kinds of the hybrid solutions composed of the breathers, lumps, line rogue waves and kink solitons. Characteristics of those hybrid solutions are graphically analyzed and the conditions for the generation of those hybrid solutions are given.

92 citations


Journal ArticleDOI
TL;DR: Based on the robust inverse scattering method, the high-order rogue wave of generalized nonlinear Schrodinger equation with nonzero boundary is given using the elementary Darboux transformation but not with the limit progress, which is more convenient than before.

89 citations


Journal ArticleDOI
TL;DR: A generalized nonlinear Schrodinger system is investigated in this article, which can be used to describe the optical pulse propagation in inhomogeneous optical fibers with the fourth-and third-order dispersions operators.
Abstract: A generalized nonlinear Schrodinger system is investigated, which can be used to describe the optical pulse propagation in inhomogeneous optical fibers with the fourth- and third-order dispersions operators. The Darboux transformation method is extended to construct a mixed breather and rogue wave solution for the system. The interaction behaviors between the breather and rogue wave are studied. As a novel result, the energy transition between the breather and rogue wave is observed. Furthermore, the impacts of the different operators on the mixed solution are analyzed.

81 citations


Journal ArticleDOI
TL;DR: It is found that the wave packets can be modulated by certain long waves, resulting in different behaviors from those in the existing literature, and the modulations of the breathers and rogue waves are distorted and stretched.
Abstract: Investigated in this paper is a quasigeostrophic two-layer model for the wave packets in a marginally stable or unstable baroclinic shear flow. We find that the wave packets can be modulated by certain long waves, resulting in different behaviors from those in the existing literature. Via the bilinear method, we construct the modulated $N\mathrm{th}$-order ($N=1,2,...$) solitary waves, breathers, and rogue waves for the wave-packet equations. Based on the modulation effects of the long waves, the solitary waves are classified into three types, i.e., Type-I, Type-II, and Type-III solitary waves. Type-I solitary waves, without the modulations, are the bell shaped and propagate with constant velocities; Type-II solitary waves, with the weak modulations, are shape changing within a short time and subsequently return to the bell-shaped state; and Type-III solitary waves, with the strong modulations, show not only the variations of shapes but also the appearances, splits, combinations, and disappearances of certain bulges in the evolution. For the interaction between the two unmodulated solitary waves, two Type-I solitary waves can bring about the oscillations in the interaction zone when they possess different velocities, and bring into being the bound-state, oscillation-state, and bi-oscillation-state solitary waves when they possess the same velocity. For the two interactive modulated solitary waves, bound-state, oscillation-state, and bi-oscillation-state solitary waves with the short-time variations of shapes or appearances of bulges can occur. Due to the modulations of the long waves, breathers and rogue waves are distorted and stretched, mainly in two aspects: one is the evolution trajectories for the breathers; the other is the shape variations for each element of the breathers and rogue waves. Numbers of the peaks and valleys for the rogue waves are adjustable via the modulations. In addition, modulated breathers and rogue waves can degenerate into the M- or W-shaped or multipeak solitary waves under certain conditions.

78 citations


Journal ArticleDOI
TL;DR: The double-periodic solutions of the focusing nonlinear Schrödinger equation are constructed by using an algebraic method with two eigenvalues and the Lax spectrum is characterized and rogue waves arising on the background of such solutions are analyzed.
Abstract: The double-periodic solutions of the focusing nonlinear Schr\"odinger equation have been previously obtained by the method of separation of variables. We construct these solutions by using an algebraic method with two eigenvalues. Furthermore, we characterize the Lax spectrum for the double-periodic solutions and analyze rogue waves arising on the background of such solutions. Magnification of the rogue waves is studied numerically.

77 citations


Journal ArticleDOI
TL;DR: In this paper, the authors review the state-of-the-art of rogue wave studies in optical and hydrodynamics, aiming to clearly identify similarities and differences between the results obtained in the two fields.
Abstract: We review the study of rogue waves and related instabilities in optical and oceanic environments, with particular focus on recent experimental developments. In optics, we emphasize results arising from the use of real-time measurement techniques, whilst in oceanography we consider insights obtained from analysis of real-world ocean wave data and controlled experiments in wave tanks. Although significant progress in understanding rogue waves has been made based on an analogy between wave dynamics in optics and hydrodynamics, these comparisons have predominantly focused on one-dimensional nonlinear propagation scenarios. As a result, there remains significant debate about the dominant physical mechanisms driving the generation of ocean rogue waves in the complex environment of the open sea. Here, we review state-of-the-art of rogue wave studies in optics and hydrodynamics, aiming to clearly identify similarities and differences between the results obtained in the two fields. In hydrodynamics, we take care to review results that support both nonlinear and linear interpretations of ocean rogue wave formation, and in optics, we also summarise results from an emerging area of research applying the measurement techniques developed for the study of rogue waves to dissipative soliton systems. We conclude with a discussion of important future research directions.

75 citations


Journal ArticleDOI
TL;DR: In this paper, the authors present the first experimental evidence of hydrodynamic instantons: extreme realizations of water surface elevation in a wave flume experiment in deep water conditions akin to those in the ocean.
Abstract: Extreme events are rare but they have an important impact on everyday life. Examples are heat waves, droughts, hurricanes or market crashes. In theory, these events can be described by instantons, saddle point configurations of the action associated with the stochastic model for the system. Indeed, instantons have been used successfully to predict the limiting behavior of the solutions of fluid equations. Here we present the first experimental evidence of hydrodynamic instantons: extreme realizations of water surface elevation in a wave flume experiment in deep water conditions akin to those in the ocean. Using a method building on large deviation theory and optimal control, we compute the instantons of the nonlinear Schroedinger equation with random initial data. We show that these peculiar solutions explain rogue waves in the flume for a wide range of parameters of the energy spectrum of deep water waves, no matter how nonlinear the system's dynamics is. In particular, the instanton bridges the two existing theories of the linear and highly nonlinear regimes, including them as its opposite limiting cases and generalizing the results to any intermediate conditions. The results are obtained in the one-dimensional set-up of the wave flume, but the method is general and can be extended to the fully two-dimensional case of the ocean. In principle, the framework is exportable to other nonlinear physical systems, to study the mechanisms underlying the extreme events and assess their risk.

74 citations


Journal ArticleDOI
TL;DR: In this article, a non-autonomous generalized AB system was investigated, which is used to describe certain baroclinic instability processes in the geophysical flows, and the two short waves and mean flow can evolve in the forms of the multi-rogue waves on the condition that the nonlinearity effect is positive.
Abstract: Investigated in this paper is a non-autonomous generalized AB system, which is used to describe certain baroclinic instability processes in the geophysical flows. We discover that the two short waves and mean flow can evolve in the forms of the multi-rogue waves on the condition that the nonlinearity effect $$\sigma $$ is positive. Via the Darboux and generalized Darboux transformations, we obtain the first- and second-order rogue waves as well as the algorithm to derive the Nth-order rogue waves. It is revealed that the perturbation function $$\delta (t)$$ has no effect on the two short waves while affects the mean flow by changing its evolution background. When $$\sigma $$ is negative, those rogue waves turn to be singular. In addition, we find that the two short waves and mean flow can also appear as the solitary waves, and they perform as the “bright” solitons under $$\sigma >0$$ while perform as the “dark” solitons under $$\sigma <0$$ . With the Hirota method, introducing the auxiliary function $$\alpha (t)$$ , we derive the first- and second-order bright and dark solitary waves. Both solitary wave velocities are related to $$\delta (t)$$ and $$\alpha (t)$$ . Besides, $$\delta (t)$$ and $$\alpha (t)$$ have no effect on the amplitudes of the two short waves but bring about controllable backgrounds and deformations of the solitary waves for the mean flow.

72 citations


Journal ArticleDOI
TL;DR: A new (2+1)-dimensional Heisenberg ferromagnetic spin chain equation is investigated, which can be used to describe magnetic soliton excitations in two dimensional space fields and a time field.
Abstract: A new (2+1)-dimensional Heisenberg ferromagnetic spin chain equation is investigated, which can be used to describe magnetic soliton excitations in two dimensional space fields and a time field. The Lax pair of the equation is first constructed. Based on the Lax pair, initial seed solution and Darboux transformation, the analytic first-, second- and third-order rogue wave solutions are obtained, and a general expression of the N th-order ( N > 3 ) rogue wave solutions is presented. The impacts of the system parameters on the rogue waves are demonstrated through numerical visualization method.

Journal ArticleDOI
TL;DR: In this article, the authors attempted to reproduce the full scaled crest amplitude and profile of the Draupner wave, including bound set-up, and found that the onset and type of wave breaking play a significant role and differ significantly for crossing and noncrossing waves.
Abstract: Freak or rogue waves are so called because of their unexpectedly large size relative to the population of smaller waves in which they occur. The 25.6 m high Draupner wave, observed in a sea state with a significant wave height of 12 m, was one of the first confirmed field measurements of a freak wave. The physical mechanisms that give rise to freak waves such as the Draupner wave are still contentious. Through physical experiments carried out in a circular wave tank, we attempt to recreate the freak wave measured at the Draupner platform and gain an understanding of the directional conditions capable of supporting such a large and steep wave. Herein, we recreate the full scaled crest amplitude and profile of the Draupner wave, including bound set-up. We find that the onset and type of wave breaking play a significant role and differ significantly for crossing and non-crossing waves. Crucially, breaking becomes less crest-amplitude limiting for sufficiently large crossing angles and involves the formation of near-vertical jets. In our experiments, we were only able to reproduce the scaled crest and total wave height of the wave measured at the Draupner platform for conditions where two wave systems cross at a large angle.


Journal ArticleDOI
TL;DR: A (2+1)-dimensional generalized breaking soliton system is under investigation, which can be used to describe the interaction between Riemann wave and long wave along with two space directions in nonlinear media.
Abstract: A (2+1)-dimensional generalized breaking soliton system is under investigation, which can be used to describe the interaction between Riemann wave and long wave along with two space directions in nonlinear media. Rogue wave solutions, two types of mixed soliton and rogue wave solutions are constructed through appropriately choosing the functions in the bilinear forms. The rogue wave structures and the interaction characteristics between the soliton and rogue wave are studied in details. Novel hidden rogue wave and hidden soliton, which are invisible but work, are observed during the interactions.

Journal ArticleDOI
TL;DR: In this paper, three types of rogue waves are derived, and their explicit expressions in terms of Schur polynomials are presented, showing a much wider variety than those in the local NLS equation.
Abstract: Rogue waves in the nonlocal $${\mathcal {PT}}$$ -symmetric nonlinear Schrodinger (NLS) equation are studied by Darboux transformation. Three types of rogue waves are derived, and their explicit expressions in terms of Schur polynomials are presented. These rogue waves show a much wider variety than those in the local NLS equation. For instance, the polynomial degrees of their denominators can be not only $$n(n+1)$$ , but also $$n(n-1)+1$$ and $$n^2$$ , where n is an arbitrary positive integer. Dynamics of these rogue waves is also examined. It is shown that these rogue waves can be bounded for all space and time or develop collapsing singularities, depending on their types as well as values of their free parameters. In addition, the solution dynamics exhibits rich patterns, most of which have no counterparts in the local NLS equation.


Journal ArticleDOI
TL;DR: In this paper, a generalized Kadomtsev-Petviashvili equation in fluid mechanics is investigated and the mixed lump-stripe wave and one-strip wave solutions are derived.

Journal ArticleDOI
TL;DR: Using Hirota bilinear method, four kinds of localized waves, solitons, breathers, lumps and rogue waves of the extended (3+1)-dimensional Jimbo–Miwa equation are constructed.

Journal ArticleDOI
TL;DR: A generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation, which describes the propagation of nonlinear waves in fluid dynamics, is investigated and it is shown that the one-periodic wave solutions approach theOne-soliton solutions when the amplitude η → 0.

Journal ArticleDOI
TL;DR: It is shown that Darboux transformations with the non-periodic solutions to the Lax equations produce rogue waves on the periodic background, which are either brought from infinity by propagating algebraic solitons or formed in a finite region of the time-space plane.
Abstract: We address the most general periodic travelling wave of the modified Korteweg–de Vries (mKdV) equation written as a rational function of Jacobian elliptic functions. By applying an algebraic method which relates the periodic travelling waves and the squared periodic eigenfunctions of the Lax operators, we characterize explicitly the location of eigenvalues in the periodic spectral problem away from the imaginary axis. We show that Darboux transformations with the periodic eigenfunctions remain in the class of the same periodic travelling waves of the mKdV equation. In a general setting, there exist three symmetric pairs of simple eigenvalues away from the imaginary axis, and we give a new representation of the second non-periodic solution to the Lax equations for the same eigenvalues. We show that Darboux transformations with the non-periodic solutions to the Lax equations produce rogue waves on the periodic background, which are either brought from infinity by propagating algebraic solitons or formed in a finite region of the time-space plane.

Journal ArticleDOI
TL;DR: In this paper, the Simulating WAves Nearshore (SWAN) model is forced with the ERA-Interim wind database from 1979 to 2017 with a resolution of 0.25° in both longitude and latitude.


Journal ArticleDOI
TL;DR: In this article, the Gerdjikov-Ivanov equation is considered as a plasma-physics model for the Alfven waves propagating parallel to the ambient magnetic field, and two types of the breathers and rogue waves on the periodic background are derived via the Taylor expansion when N = 2 k + 1 with k being a nonnegative integer.
Abstract: Alfven waves in the magnetized astrophysical plasmas are invoked to explain the heating of the stellar coronae, acceleration of the stellar winds, as well as the origin and formation of the galactic and extragalactic jets. Under investigation in this paper is the Gerdjikov-Ivanov equation which is considered as a plasma-physics model for the Alfven waves propagating parallel to the ambient magnetic field. Based on the existing N-th order analytic solutions for the Gerdjikov-Ivanov equation with N being a positive integer, we construct two types of the breathers on the periodic background, and the k-th order rogue waves on the periodic background in terms of the determinant expression for the transverse magnetic field perturbation are derived via the Taylor expansion when N = 2 k + 1 with k being a non-negative integer. We show that the breathers and rogue waves are located in the periodic background rather than in the constant background. We obtain four different structures, which are the so-called fundamental, triangular, ring and ring-triangular structures, for the higher-order rogue waves on the periodic background. We graphically demonstrate some solutions for the transverse magnetic field perturbation to analyse the characteristics of the four different structures.

Journal ArticleDOI
TL;DR: In this article, a (2 + 1)-dimensional reduced YTSF equation is studied and the lump solutions more general than those in the existing literature, which orient in all directions of space and time with more parameters.
Abstract: Lattices and liquids are common in physics, engineering, science, nature and life. The Yu-Toda-Sasa-Fukuyama (YTSF) equation describes the elastic quasiplane wave in a lattice or interfacial wave in a two-layer liquid. A (2 + 1)-dimensional reduced YTSF equation is studied in this paper. With symbolic computation, we get the lump solutions more general than those in the existing literature, which orient in all directions of space and time with more parameters. Via the lump solutions, we get the moving path of lump waves, lumpoff solutions and moving path of the lumpoff waves, which describe interactions between one stripe soliton and a lump wave. When the lump solutions produce the one stripe solitons, the lumpoff solutions are constructed. When a pair of stripe solitons cut lump wave, the rogue wave emerges. Time and place for the rogue wave to appear can be obtained from the coordinates of the interaction points between a pair of stripe solitons and the lump wave.

Journal ArticleDOI
TL;DR: The Sea surface KInematics multiscale monitoring (SKIM) satellite mission is designed to explore ocean surface current and waves from space as mentioned in this paper, where the main instrument is a Ka-band conically scanning, multi-beam Doppler radar altimeter/wave scatterometer that includes a state-of-the-art nadir beam comparable to the Poseidon-4 instrument on Sentinel 6.
Abstract: The Sea surface KInematics Multiscale monitoring (SKIM) satellite mission is designed to explore ocean surface current and waves. This includes tropical currents, notably the poorly known patterns of divergence and their impact on the ocean heat budget, and monitoring of the emerging Arctic up to 82.5 • N. SKIM will also make unprecedented direct measurements of strong currents, from boundary currents to the Antarctic circumpolar current, and their interaction with ocean waves with expected impacts on air-sea fluxes and extreme waves. For the first time, SKIM will directly measure the ocean surface current vector from space. The main instrument on SKIM is a Ka-band conically scanning, multi-beam Doppler radar altimeter/wave scatterometer that includes a state-of-the-art nadir beam comparable to the Poseidon-4 instrument on Sentinel 6. The well proven Doppler pulse-pair technique will give a surface drift velocity representative of the top meter of the ocean, after subtracting a large wave-induced contribution. Horizontal velocity components will be obtained with an accuracy better than 7 cm/s for horizontal wavelengths larger than 80 km and time resolutions larger than 15 days, with a mean revisit time of 4 days for of 99% of the global oceans. This will provide unique and innovative measurements that will further our understanding of the transports in the upper ocean layer, permanently distributing heat, carbon, plankton, and plastics. SKIM will also benefit from co-located measurements of water vapor, rain rate, sea ice concentration, and wind vectors provided by the European operational satellite

Journal ArticleDOI
TL;DR: In this paper, a cylindrical Kadomtsev-Petviashvili (CKP) equation is derived from pair-ion-electron plasmas.
Abstract: A lot of work has been reported to present some numerical results on pair-ion–electron plasmas. However, very few works have reported the corresponding mathematical analytical results in these aspects. In this work, we study a cylindrical Kadomtsev-Petviashvili (CKP) equation, which can be derived from pair-ion–electron plasmas. We further report some interesting mathematical analytical results, including some dynamics of soliton waves, breather waves, and rogue waves in pair-ion–electron plasma via the CKP equation. Using a novel gauge transformation, the Grammian N-soliton solutions of the CKP equation are found analytically. Based on the bilinear transformation method, the breather wave solutions are obtained explicitly under some parameter constraints. Furthermore, we construct the rogue waves using the long wave limit method. In addition, some remarkable characteristics of these soliton solutions are analyzed graphically. According to analytic solutions, the influences of each parameter on the dynamics of the soliton waves, breather waves, and rogue waves are discussed, and the method of how to control such nonlinear phenomena is suggested.

Journal ArticleDOI
TL;DR: In this paper, the hydrodynamics of a two-body floating-point absorber (FPA) wave energy converter (WEC) under both extreme and operational wave conditions were evaluated for various regular wave conditions.

Journal ArticleDOI
TL;DR: In this paper, a deformed Fokas-Lenells equation with higher-order nonholonomic constraint is studied and the baseband modulation instability as an origin of rogue waves is displayed.
Abstract: We study a deformed Fokas–Lenells equation which is related to the integrable derivative nonlinear Schrodinger hierarchy with higher-order nonholonomic constraint. The baseband modulation instability as an origin of rogue waves is displayed. The explicit rogue wave solutions are obtained via the Darboux transformation. Typical rogue wave patterns such as the standard rogue wave, dark rogue wave and twisted rogue wave pair in three different components of the deformed Fokas–Lenells equation are presented. Besides, the state transitions between rogue waves and solitons are analytically found when the modulation instability growth rate tends to zero in the zero-frequency perturbation region. The explicit soliton solutions under the special parameter condition are given. The anti-dark and W-shaped solitons in their respective components are shown.

Journal ArticleDOI
TL;DR: A fourth-order coupled nonlinear Schrodinger equation, which describes the propagation of ultrashort optical pulses in the birefringent optical fiber, is investigated and it is found that the wave structure is affected by the relative background amplitudes and certain parameter in the solutions, and the range of the first-order rogue wave along the x axis increases with the increase of the fourth order term γ.

Journal ArticleDOI
TL;DR: The n -fold Darboux transformation is established for the Hirota equation such that ( 2 n − 1 , 2 n ) th-order rogue waves can be found simultaneously.