Search results for "Rogue wave"
showing 10 items of 66 documents
Rational solutions to the KPI equation and multi rogue waves
2016
Abstract We construct here rational solutions to the Kadomtsev–Petviashvili equation (KPI) as a quotient of two polynomials in x , y and t depending on several real parameters. This method provides an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2 N ( N + 1 ) in x , y and t depending on 2 N − 2 real parameters for each positive integer N . We give explicit expressions of the solutions in the simplest cases N = 1 and N = 2 and we study the patterns of their modulus in the ( x , y ) plane for different values of time t and parameters.
Dissipative rogue waves: extreme pulses generated by passively mode-locked lasers.
2011
We study numerically rogue waves in dissipative systems, taking as an example a unidirectional fiber laser in a nonstationary regime of operation. The choice of specific set of parameters allows the laser to generate a chaotic sequence of pulses with a random distribution of peak amplitudes. The probability density function for the intensity maxima has an elevated tail at higher intensities. We have found that the probability of producing extreme pulses in this setup is higher than in any other system considered so far. © 2011 American Physical Society.
Dissipative Rogue Waves Generated by Chaotic Pulse Bunching in a Mode-Locked Laser
2012
Rare events of extremely high optical intensity are experimentally recorded at the output of a mode-locked fiber laser that operates in a strongly dissipative regime of chaotic multiple-pulse generation. The probability distribution of these intensity fluctuations, which highly depend on the cavity parameters, features a long-tailed distribution. Recorded intensity fluctuations result from the ceaseless relative motion and nonlinear interaction of pulses within a temporally localized multisoliton phase. © 2012 American Physical Society.
Optical rogue-wave-like extreme value fluctuations in fiber Raman amplifiers
2008
International audience; We report experimental observation and characterization of rogue wave-like extreme value statistics arising from pump-signal noise transfer in a fiber Raman amplifier. Specifically, by exploiting Raman amplification with an incoherent pump, the amplified signal is shown to develop a series of temporal intensity spikes whose peak power follows a power-law probability distribution. The results are interpreted using a numerical model of the Raman gain process using coupled nonlinear Schrödinger equations, and the numerical model predicts results in good agreement with experiment.
AKNS and NLS hierarchies, MRW solutions, $P_n$ breathers, and beyond
2018
We describe a unified structure of rogue wave and multiple rogue wave solutions for all equations of the Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy and their mixed and deformed versions. The definition of the AKNS hierarchy and its deformed versions is given in the Sec. II. We also consider the continuous symmetries of the related equations and the related spectral curves. This work continues and summarises some of our previous studies dedicated to the rogue wave-like solutions associated with AKNS, nonlinear Schrodinger, and KP hierarchies. The general scheme is illustrated by the examples of small rank n, n ⩽ 7, rational or quasi-rational solutions. In particular, we consider rank-2 and …
Multi-rogue waves solutions: from the NLS to the KP-I equation
2013
Our discovery of multi-rogue wave (MRW) solutions in 2010 completely changed the viewpoint on the links between the theory of rogue waves and integrable systems, and helped explain many phenomena which were never understood before. It is enough to mention the famous Three Sister waves observed in oceans, the creation of a regular approach to studying higher Peregrine breathers, and the new understanding of 2 + 1 dimensional rogue waves via the NLS-KP correspondence. This article continues the study of the MRW solutions of the NLS equation and their links with the KP-I equation started in a previous series of articles (Dubard et al 2010 Eur. Phys. J. 185 247–58, Dubard and Matveev 2011 Natur…
Wronskian representation of solutions of NLS equation, and seventh order rogue wave.
2012
This work is a continuation of a recent paper in which we have constructed a multi-parametric family of the nonlinear Schrodinger equation in terms of wronskians. When we perform a special passage to the limit, we get a family of quasi-rational solutions expressed as a ratio of two determinants. We have already construct Peregrine breathers of orders N=4, 5, 6 in preceding works; we give here the Peregrine breather of order seven.
Emergence of rogue waves from optical turbulence
2011
International audience; We provide some general physical insights into the emergence of rogue wave events from optical turbulence by analyzing the long term evolution of the field. Depending on the amount of incoherence in the system (i.e., Hamiltonian), we identify three turbulent regimes that lead to the emergence of specific rogue wave events: (i) persistent and coherent rogue quasi-solitons, (ii) intermittent-like rogue quasi-solitons that appear and disappear erratically, and (iii) sporadic rogue waves events that emerge from turbulent fluctuations as bursts of light or intense flashes.
Shallow water rogue waves in nonlinear optical fibers
2013
The dynamics of extreme waves, often known as freak or rogue waves (RW), is presently a subject of intensive research. In oceanography, RW are mostly known as a sudden deep-water event which is responsible for ship wreakages and can be modeled by the 1D Nonlinear Schrodinger Equation (NLSE). In this framework, an ideal testbed is provided by optical pulse propagation in nonlinear optical fibers: extreme solitary wave emissions during supercontinuum generation or the first experimental observation of the Peregrine solitons have indeed been carried out exploiting the modulation instability occuring in fibers with anomalous dispersion.
Rogue wave description: Rational solitons and wave turbulence theory
2012
We show that rogue waves can emerge from optical turbulence and that their coherent deterministic description provided by the rational solutions is compatible with the statistical description provided by the wave turbulence theory.