Showing papers on "Rogue wave published in 2017"
TL;DR: This dissertation aims to provide a history of web exceptionalism from 1989 to 2002, a period chosen in order to explore its roots as well as specific cases up to and including the year in which descriptions of “Web 2.0” began to circulate.
Abstract: 79 pags., 30 figs., 3 apps. -- Open Access funded by Creative Commons Atribution Licence 3.0
175 citations
TL;DR: A combination of stripe soliton and lump soliton is discussed to a reduced (3+1)-dimensional Jimbo–Miwa equation, in which such solution gives rise to two different excitation phenomena: fusion and fission.
161 citations
TL;DR: The results imply that the extreme behavior of the breather solitary wave yields the rogue wave for the ( 2 + 1 )-dimensional Ito equation.
111 citations
11 Apr 2017
108 citations
TL;DR: The results show that rogue wave can come from the extreme behavior of the breather solitary wave for ( 2 + 1 ) -dimensional nonlinear wave fields.
95 citations
TL;DR: A direct method is employed to explicitly construct its rogue wave solutions with an ansatz function based on the bilinear formalism, and the interaction phenomena between rogue waves and solitary waves are presented with a detailed derivation.
87 citations
TL;DR: The Hirota bilinear equation is investigated, which can be used to describe the nonlinear dynamic behavior in physics and its rational breather wave and rogue wave solutions are obtained by using the Homoclinic test method.
Abstract: In this paper, the ( 3 + 1 ) -dimensional Hirota bilinear equation is investigated, which can be used to describe the nonlinear dynamic behavior in physics. By using the Bell polynomials, the bilinear form of the equation is derived in a very natural way. Based on the resulting bilinear form, its N -solitary waves are further obtained by using the Hirota’s bilinear theory. Finally, by using the Homoclinic test method, we obtain its rational breather wave and rogue wave solutions, respectively. In order to better understand the dynamical behaviors of the equation, some graphical analyses are discussed for these exact solutions.
87 citations
TL;DR: In this article, a fully nonlinear, coupled tool for simulating focused wave impacts on generic WEC hull forms is described and compared with physical measurements, based on the 100-year wave at Wave Hub and using the NewWave formulation, have been reproduced numerically as have experiments in which a fixed truncated circular cylinder and a floating hemispherical-bottomed buoy are subject to these focused wave events.
87 citations
TL;DR: In this article, a vector generalization of the Fokas-Lenells system, which describes for nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order, is investigated.
Abstract: In this paper, a vector generalization of the Fokas–Lenells system, which describes for nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order, is investigated. Higher-order soliton, breather, and rogue wave solutions of the coupled Fokas–Lenells system are derived via the n -fold Darboux transformation. Meanwhile the dynamic characteristics of those solitary wave solutions have been discussed.
77 citations
TL;DR: The Darboux transformations with the nonzero plane-wave solutions are presented to derive the newly localized wave solutions including dark-dark and bright-dark solitons, breather-breather solutions, and different types of new vector rogue wave solutions, as well as interactions between distinct types of localizedWave solutions.
Abstract: We investigate the defocusing coupled nonlinear Schr\"odinger equations from a $3\ifmmode\times\else\texttimes\fi{}3$ Lax pair. The Darboux transformations with the nonzero plane-wave solutions are presented to derive the newly localized wave solutions including dark-dark and bright-dark solitons, breather-breather solutions, and different types of new vector rogue wave solutions, as well as interactions between distinct types of localized wave solutions. Moreover, we analyze these solutions by means of parameters modulation. Finally, the perturbed wave propagations of some obtained solutions are explored by means of systematic simulations, which demonstrates that nearly stable and strongly unstable solutions. Our research results could constitute a significant contribution to explore the distinct nonlinear waves (e.g., dark solitons, breather solutions, and rogue wave solutions) dynamics of the coupled system in related fields such as nonlinear optics, plasma physics, oceanography, and Bose-Einstein condensates.
76 citations
TL;DR: It is shown that rogue waves and heavy-tail statistics may develop naturally during the growth of the waves just before the wave height reaches a stationary condition.
Abstract: We investigate experimentally the statistical properties of a wind-generated wave field and the spontaneous formation of rogue waves in an annular flume. Unlike many experiments on rogue waves where waves are mechanically generated, here the wave field is forced naturally by wind as it is in the ocean. What is unique about the present experiment is that the annular geometry of the tank makes waves propagating circularly in an unlimited-fetch condition. Within this peculiar framework, we discuss the temporal evolution of the statistical properties of the surface elevation. We show that rogue waves and heavy-tail statistics may develop naturally during the growth of the waves just before the wave height reaches a stationary condition. Our results shed new light on the formation of rogue waves in a natural environment.
TL;DR: Exact solutions for the rogue periodic waves are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov–Shabat spectral problem and the Darboux transformations to generalize the classical rogue wave.
Abstract: Rogue waves on the periodic background are considered for the nonlinear Schrodinger (NLS) equation in the focusing case. The two periodic wave solutions are expressed by the Jacobian elliptic functions dn and cn. Both periodic waves are modulationally unstable with respect to long-wave perturbations. Exact solutions for the rogue waves on the periodic background are constructed by using the explicit expressions for the periodic eigenfunctions of the Zakharov-Shabat spectral problem and the Darboux transformations. These exact solutions labeled as rogue periodic waves generalize the classical rogue wave (the so-called Peregrine's breather). The magnification factor of the rogue periodic waves is computed as a function of the wave amplitude (the elliptic modulus). Rogue periodic waves constructed here are compared with the rogue wave patterns obtained numerically in recent publications.
TL;DR: Based on the bilinear formalism and the extended homoclinic test method, the kinky breather wave solutions and rational breathing wave solutions of the Kadomtsev–Petviashvili equation are well constructed.
Abstract: Under investigation in this work is a generalized ( 3 + 1 )-dimensional Kadomtsev–Petviashvili (GKP) equation, which can describe many nonlinear phenomena in fluid dynamics. By virtue of the Bell’s polynomials, an effective and straightforward way is presented to explicitly construct its bilinear form and soliton solution. Furthermore, based on the bilinear formalism and the extended homoclinic test method, the kinky breather wave solutions and rational breather wave solutions of the equation are well constructed. It is hoped that our results can be used to enrich the dynamical behavior of the ( 3 + 1 )-dimensional nonlinear wave fields.
TL;DR: In this paper, a bilinear method was used to obtain the exact solution of the (2+1)-dimensional Korteweg-de Vries (KdV) equation.
Abstract: Deformation rogue wave as exact solution of the (2+1)-dimensional Korteweg–de Vries (KdV) equation is obtained via the bilinear method. It is localized in both time and space and is derived by the interaction between lump soliton and a pair of resonance stripe solitons. In contrast to the general method to get the rogue wave, we mainly combine the positive quadratic function and the hyperbolic cosine function, and then the lump soliton can be evolved rogue wave. Under the small perturbation of parameter, rich dynamic phenomena are depicted both theoretically and graphically so as to understand the property of (2+1)-dimensional KdV equation deeply. In general terms, these deformations mainly have three types: two rogue waves, one rogue wave or no rogue wave.
TL;DR: A special kind of breather solution of the nonlinear Schrödinger (NLS) equation, the so-called breather-positon, which can be obtained by taking the limit λ_{j}→λ_{1} of the Lax pair eigenvalues in the order-n periodic solution, which is generated by the n-fold Darboux transformation from a special "seed" solution-plane wave.
Abstract: In this paper, we construct a special kind of breather solution of the nonlinear Schrodinger (NLS) equation, the so-called breather-positon (b-positon for short), which can be obtained by taking the limit λ_{j}→λ_{1} of the Lax pair eigenvalues in the order-n periodic solution, which is generated by the n-fold Darboux transformation from a special "seed" solution-plane wave. Further, an order-n b-positon gives an order-n rogue wave under a limit λ_{1}→λ_{0}. Here, λ_{0} is a special eigenvalue in a breather of the NLS equation such that its period goes to infinity. Several analytical plots of order-2 breather confirm visually this double degeneration. The last limit in this double degeneration can be realized approximately in an optical fiber governed by the NLS equation, in which an injected initial ideal pulse is created by a frequency comb system and a programable optical filter (wave shaper) according to the profile of an analytical form of the b-positon at a certain position z_{0}. We also suggest a new way to observe higher-order rogue waves generation in an optical fiber, namely, measure the patterns at the central region of the higher-order b-positon generated by above ideal initial pulses when λ_{1} is very close to the λ_{0}. The excellent agreement between the numerical solutions generated from initial ideal inputs with a low signal-to-noise ratio and analytical solutions of order-2 b-positon supports strongly this way in a realistic optical fiber system. Our results also show the validity of the generating mechanism of a higher-order rogue waves from a multibreathers through the double degeneration.
TL;DR: These semi-rational solutions consisting of rogue waves, breathers, and solitons are given in terms of determinants whose matrix elements have simple algebraic expressions and have a new phenomenon: lumps form on darksolitons and gradual separation from the dark sol itons is observed.
Abstract: General dark solitons and mixed solutions consisting of dark solitons and breathers for the third-type Davey-Stewartson (DS-III) equation are derived by employing the bilinear method. By introducing the two differential operators, semi-rational solutions consisting of rogue waves, breathers, and solitons are generated. These semi-rational solutions are given in terms of determinants whose matrix elements have simple algebraic expressions. Under suitable parametric conditions, we derive general rogue wave solutions expressed in terms of rational functions. It is shown that the fundamental (simplest) rogue waves are line rogue waves. It is also shown that the multi-rogue waves describe interactions of several fundamental rogue waves, which would generate interesting curvy wave patterns. The higher order rogue waves originate from a localized lump and retreat back to it. Several types of hybrid solutions composed of rogue waves, breathers, and solitons have also been illustrated. Specifically, these semi-rational solutions have a new phenomenon: lumps form on dark solitons and gradual separation from the dark solitons is observed.
TL;DR: In this paper, the Lax pair and Darboux transformation for the variable-coefficients coupled Hirota equations is constructed based on modulation instability and by taking the limit approach, two types of Nth-order rogue wave solutions with different dynamic structures in compact determinant representations.
TL;DR: In this paper, the authors derived general rogue wave solutions expressed in terms of rational functions under suitable parametric conditions, and showed that the fundamental (simplest) rogue waves are line rogue waves.
Abstract: General dark solitons and mixed solutions consisting of dark solitons and breathers for the third-type Davey-Stewartson (DS-III) equation are derived by employing the bilinear method. By introducing the two differential operators, semi-rational solutions consisting of rogue waves, breathers and solitons are generated. These semi-rational solutions are given in terms of determinants whose matrix elements have simple algebraic expressions. Under suitable parametric conditions, we derive general rogue wave solutions expressed in terms of rational functions. It is shown that the fundamental (simplest) rogue waves are line rogue waves. It is also shown that the multi-rogue waves describe interactions of several fundamental rogue waves, which would generate interesting curvy wave patterns. The higher order rogue waves originate from a localized lump and retreat back to it. Several types of hybrid solutions composed of rogue waves, breathers and solitons have also been illustrated. Specifically, these semi-rational solutions have a new phenomenon: lumps form on dark solitons and gradual separation from the dark solitons is observed.
TL;DR: It is found that the nonlinear terms affect the widths and velocities of the RWs, although the amplitudes of these waves remain unchanged, and the semirational RW solution is derived to describe the interaction between the RW and multi-breather.
TL;DR: In this paper, a (3+1)-dimensional coupled nonlinear Schrodinger equation with different inhomogeneous diffractions and dispersion is investigated, and rogue wave and combined breather solutions are constructed.
Abstract: A (3+1)-dimensional coupled nonlinear Schrodinger equation with different inhomogeneous diffractions and dispersion is investigated, and rogue wave and combined breather solutions are constructed. Different diffractions and dispersion of medium lead to the repeatedly excited behaviors of rogue wave and combined breather in the dispersion/diffraction decreasing system. These repeated behaviors including complete excitation, rear excitation, peak excitation and initial excitation are discussed.
TL;DR: The novel generalized perturbation (n, M)-fold Darboux transformations (DTs) are reported and a new phenomenon that the parameter (a) can control the wave structures of the KP equation from the higher-order rogue waves into higher- order rational solitons in (x, t)-space with y = const.
TL;DR: In this article, the authors construct the rogue periodic waves of the modified Korteweg-de Vries (mKdV) equation expressed by Jacobian elliptic functions dn and cn respectively.
Abstract: Traveling periodic waves of the modified Korteweg-de Vries (mKdV) equation are considered in the focusing case. By using one-fold and two-fold Darboux transformations, we construct explicitly the rogue periodic waves of the mKdV equation expressed by the Jacobian elliptic functions dn and cn respectively. The rogue dn-periodic wave describes propagation of an algebraically decaying soliton over the dn-periodic wave, the latter wave is modulationally stable with respect to long-wave perturbations. The rogue cn-periodic wave represents the outcome of the modulation instability of the cn-periodic wave with respect to long-wave perturbations and serves for the same purpose as the rogue wave of the nonlinear Schrodinger equation (NLS), where it is expressed by the rational function. We compute the magnification factor for the cn-periodic wave of the mKdV equation and show that it remains the same as in the small-amplitude NLS limit for all amplitudes. As a by-product of our work, we find explicit expressions for the periodic eigenfunctions of the AKNS spectral problem associated with the dn- and cn-periodic waves of the mKdV equation.
TL;DR: This work analytically studies the discrete rogue-wave solutions of AL equation with three free parameters, and considers the non-autonomous DRW solutions, parameters controlling and their interactions with variable coefficients, and predicts the long-living rogue wave solutions.
Abstract: Starting from a discrete spectral problem, we derive a hierarchy of nonlinear discrete equations which include the Ablowitz-Ladik (AL) equation. We analytically study the discrete rogue-wave (DRW) solutions of AL equation with three free parameters. The trajectories of peaks and depressions of profiles for the first- and second-order DRWs are produced by means of analytical and numerical methods. In particular, we study the solutions with dispersion in parity-time ( PT) symmetric potential for Ablowitz-Musslimani equation. And we consider the non-autonomous DRW solutions, parameters controlling and their interactions with variable coefficients, and predict the long-living rogue wave solutions. Our results might provide useful information for potential applications of synthetic PT symmetric systems in nonlinear optics and condensed matter physics.
TL;DR: In this paper, the Darboux transformation is applied to the non-local PT-symmetric nonlinear Schrodinger (NLS) equation and three types of rogue waves are derived, and their explicit expressions in terms of Schur polynomials are presented.
Abstract: Rogue waves in the nonlocal 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.
TL;DR: It is proved that the rogue wave can be excited in the baseband modulation instability regime and may provide evidence of the collision between the mixed ultrashort soliton and rogue wave.
Abstract: We report the existence and properties of vector breather and semirational rogue-wave solutions for the coupled higher-order nonlinear Schrodinger equations, which describe the propagation of ultrashort optical pulses in birefringent optical fibers. Analytic vector breather and semirational rogue-wave solutions are obtained with Darboux dressing transformation. We observe that the superposition of the dark and bright contributions in each of the two wave components can give rise to complicated breather and semirational rogue-wave dynamics. We show that the bright-dark type vector solitons (or breather-like vector solitons) with nonconstant speed interplay with Akhmediev breathers, Kuznetsov-Ma solitons, and rogue waves. By adjusting parameters, we note that the rogue wave and bright-dark soliton merge, generating the boomeron-type bright-dark solitons. We prove that the rogue wave can be excited in the baseband modulation instability regime. These results may provide evidence of the collision between the mixed ultrashort soliton and rogue wave.
TL;DR: In this paper, the generalized Darboux transformation was used to derive a simple multidimensional soliton formula for three-wave resonant interactions and numerical simulations were performed to predict whether these solitons and rogue waves are stable enough to propagate.
TL;DR: The rogue wave probability of occurrence is analyzed in the context of ST extreme value distributions, and it is concluded that rogue waves are more likely than previously reported.
Abstract: We consider the observation and analysis of oceanic rogue waves collected within spatio-temporal (ST) records of 3D wave fields. This class of records, allowing a sea surface region to be retrieved, is appropriate for the observation of rogue waves, which come up as a random phenomenon that can occur at any time and location of the sea surface. To verify this aspect, we used three stereo wave imaging systems to gather ST records of the sea surface elevation, which were collected in different sea conditions. The wave with the ST maximum elevation (happening to be larger than the rogue threshold 1.25H
s) was then isolated within each record, along with its temporal profile. The rogue waves show similar profiles, in agreement with the theory of extreme wave groups. We analyze the rogue wave probability of occurrence, also in the context of ST extreme value distributions, and we conclude that rogue waves are more likely than previously reported; the key point is coming across them, in space as well as in time. The dependence of the rogue wave profile and likelihood on the sea state conditions is also investigated. Results may prove useful in predicting extreme wave occurrence probability and strength during oceanic storms.
TL;DR: One- and two-breather solutions of the fourth-order nonlinear Schrödinger equation with several parameters to play with are presented, including the general form and limiting cases when the modulation frequencies are 0 or coincide.
Abstract: We present one- and two-breather solutions of the fourth-order nonlinear Schr\"odinger equation. With several parameters to play with, the solution may take a variety of forms. We consider most of these cases including the general form and limiting cases when the modulation frequencies are 0 or coincide. The zero-frequency limit produces a combination of breather-soliton structures on a constant background. The case of equal modulation frequencies produces a degenerate solution that requires a special technique for deriving. A zero-frequency limit of this degenerate solution produces a rational second-order rogue wave solution with a stretching factor involved. Taking, in addition, the zero limit of the stretching factor transforms the second-order rogue waves into a soliton. Adding a differential shift in the degenerate solution results in structural changes in the wave profile. Moreover, the zero-frequency limit of the degenerate solution with differential shift results in a rogue wave triplet. The zero limit of the stretching factor in this solution, in turn, transforms the triplet into a singlet plus a low-amplitude soliton on the background. A large value of the differential shift parameter converts the triplet into a pure singlet.
TL;DR: High-resolution hindcast of hurricane-generated sea states and wave simulations are combined with novel probabilistic models to quantify the likelihood of rogue wave conditions and show that the largest simulated wave is generated by the constructive interference of elementary spectral components enhanced by bound nonlinearities.
Abstract: We present a study on the prediction of rogue waves during the 1-hour sea state of Hurricane Joaquin when the Merchant Vessel El Faro sank east of the Bahamas on October 1, 2015. High-resolution hindcast of hurricane-generated sea states and wave simulations are combined with novel probabilistic models to quantify the likelihood of rogue wave conditions. The data suggests that the El Faro vessel was drifting at an average speed of approximately 2.5 m/s prior to its sinking. As a result, we estimated that the probability that El Faro encounters a rogue wave whose crest height exceeds 14 meters while drifting over a time interval of 10 (50) minutes is ~1/400 (1/130). The largest simulated wave is generated by the constructive interference of elementary spectral components (linear dispersive focusing) enhanced by bound nonlinearities. Not surprisingly then, its characteristics are quite similar to those displayed by the Andrea, Draupner and Killard rogue waves.
TL;DR: The (2+1)-dimensional non-local nonlinear Schrodinger (NLS) equation with the self-induced parity-time symmetric potential is introduced in this article.
Abstract: The (2+1)-dimension nonlocal nonlinear Schrodinger (NLS) equation with the self-induced parity-time symmetric potential is introduced, which provides spatially two-dimensional analogues of the nonlocal NLS equation introduced by Ablowitz et al. [Phys. Rev. Lett. 110 (2013) 064105]. General periodic solutions are derived by the bilinear method. These periodic solutions behave as growing and decaying periodic line waves arising from the constant background and decaying back to the constant background again. By taking long wave limits of the obtained periodic solutions, rogue waves are obtained. It is also shown that these line rogue waves arise from the constant background with a line profile and disappear into the constant background again in the plane.