Search results for "Rogue wave"

showing 10 items of 66 documents

From Fredholm and Wronskian representations to rational solutions to the KPI equation depending on 2N − 2 parameters

2017

International audience; We have already constructed solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants and wronskians of order 2N. These solutions have been called solutions of order N and they depend on 2N −1 parameters. We construct here N-order rational solutions. We prove that they can be written as a quotient of 2 polynomials of degree 2N(N +1) in x, y and t depending on 2N−2 parameters. We explicitly construct the expressions of the rational solutions of order 4 depending on 6 real parameters and we study the patterns of their modulus in the plane (x, y) and their evolution according to time and parameters a1, a2, a3, b1, b2, b3.

PACS numbers : 33Q55 37K10 4710A- 4735Fg 4754BdRogue WavesWronskians[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]Kadomtsev Petviashvili Equation[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]Fredholm Determinants[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]Lumps
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6-th order rational solutions to the KPI equation depending on 10 parameters

2017

International audience; Here we constuct rational solutions of order 6 to the Kadomtsev-Petviashvili equation (KPI) as a quotient of 2 polynomials of degree 84 in x, y and t depending on 10 parameters. We verify that the maximum of modulus of these solutions at order 6 is equal to 2(2N + 1)2 = 338. We study the patterns of their modulus in the plane (x, y) and their evolution according time and parameters a1, a2, a3, a4, a5, b1, b2, b3, b4, b5. When these parameters grow, triangle and rings structures are obtained.

PACS: 33Q55 37K10 47.10A- 47.35.Fg 47.54.Bd[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]WronskiansRogue waves[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph][MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]KP equationLumpsFredholm determinants
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Hydrodynamics of periodic breathers

2014

We report the first experimental observation of periodic breathers in water waves. One of them is Kuznetsov–Ma soliton and another one is Akhmediev breather. Each of them is a localized solution of the nonlinear Schrödinger equation (NLS) on a constant background. The difference is in localization which is either in time or in space. The experiments conducted in a water wave flume show results that are in good agreement with the NLS theory. Basic features of the breathers that include the maximal amplitudes and spectra are consistent with the theoretical predictions.

PhysicsBreatherGeneral MathematicsGeneral EngineeringGeneral Physics and AstronomySpace (mathematics)Flumesymbols.namesakeNonlinear Sciences::Exactly Solvable and Integrable SystemsClassical mechanicsAmplitudeQuantum mechanicssymbolsSolitonRogue waveConstant (mathematics)Nonlinear Sciences::Pattern Formation and SolitonsNonlinear Schrödinger equationPhilosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
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Tenth Peregrine breather solution to the NLS equation

2015

We go on in this paper, in the study of the solutions of the focusing NLS equation. With a new representation given in a preceding paper, a very compact formulation without limit as a quotient of two determinants, we construct the Peregrine breather of order N=10. The explicit analytical expression of the Akhmediev's solution is completely given.

PhysicsBreatherGeneral Physics and AstronomyExpression (computer science)symbols.namesakesymbolsPeregrine solitonLimit (mathematics)Rogue waveRepresentation (mathematics)Nonlinear Sciences::Pattern Formation and SolitonsNonlinear Schrödinger equationQuotientMathematical physicsAnnals of Physics
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Dark-and-bright rogue waves in long wave-short wave resonance

2014

Nonlinear Photonics, Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, in Proceedings Advanced Photonics, Part of Advanced Photonics, Barcelona, Spain, 28-31 July 2014

PhysicsComputer simulationWave propagationNonlinear opticsPhysics::OpticsAstrophysics::Cosmology and Extragalactic AstrophysicsModulational instabilityNonlinear Sciences::Exactly Solvable and Integrable SystemsClassical mechanicsSurface waveQuantum electrodynamicsPeregrine solitonRogue wavePhase velocityNonlinear Sciences::Pattern Formation and Solitons
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Watch-hand-like optical rogue waves in three-wave interactions

2015

11 págs.; 6 figs.; OCIS codes: (190.3100) Instabilities and chaos; (190.5530) Pulse propagation and temporal solitons; (190.4410) Nonlinear optics, parametric processes.

PhysicsDiffractionComputer simulationbusiness.industryOptical rogue wavesAtomic and Molecular Physics and OpticsOpticsAmplitudeQuadratic equationGroup velocityRogue wavebusinessNonlinear Sciences::Pattern Formation and SolitonsPhotonic-crystal fiberOptics Express
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Statistical characterization of the internal structure of noiselike pulses using a nonlinear optical loop mirror

2016

Abstract In this work we study statistically the internal structure of noiselike pulses generated by a passively mode-locked fiber laser. For this purpose, we use a technique that allows estimating the distribution of the amplitudes of the sub-pulses in the bunch. The technique takes advantage of the fast response of the optical Kerr effect in a fiber nonlinear optical loop mirror (NOLM). It requires the measurement of the energy transfer characteristic of the pulses through the NOLM, and the numerical resolution of a system of nonlinear algebraic equations. The results yield a strongly asymmetric distribution, with a high-amplitude tail that is compatible with the existence of extreme-inte…

PhysicsKerr effectbusiness.industryPhysics::OpticsOptical rogue waves02 engineering and technology01 natural sciencesAtomic and Molecular Physics and OpticsElectronic Optical and Magnetic MaterialsPulse (physics)010309 opticsNonlinear systemComplex dynamics020210 optoelectronics & photonicsAmplitudeOpticsFiber laser0103 physical sciences0202 electrical engineering electronic engineering information engineeringElectrical and Electronic EngineeringPhysical and Theoretical ChemistryRogue wavebusinessOptics Communications
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Experimental and numerical investigations of a two-body floating-point absorber wave energy converter in regular waves

2019

Abstract This paper presents experimental and numerical studies on the hydrodynamics of a two-body floating-point absorber (FPA) wave energy converter (WEC) under both extreme and operational wave conditions. In this study, the responses of the WEC in heave, surge, and pitch were evaluated for various regular wave conditions. For extreme condition analysis, we assume the FPA system has a survival mode that locks the power-take-off (PTO) mechanism in extreme waves, and the WEC moves as a single body in this scenario. A series of Reynolds-averaged Navier–Stokes (RANS) simulations was performed for the survival condition analysis, and the results were validated with the measurements from exper…

PhysicsMechanical Engineering02 engineering and technologyMechanicsVortex shedding01 natural sciences010305 fluids & plasmasNonlinear systemFlow separation020303 mechanical engineering & transports0203 mechanical engineeringDrag0103 physical sciencesWave heightWave tankRogue waveReynolds-averaged Navier–Stokes equationsJournal of Fluids and Structures
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The fifth order Peregrine breather and its eight-parameters deformations solutions of the NLS equation.

2013

We construct here explicitly new deformations of the Peregrine breather of order 5 with 8 real parameters. This gives new families of quasi-rational solutions of the NLS equation and thus one can describe in a more precise way the phenomena of appearance of multi rogue waves. With this method, we construct new patterns of different types of rogue waves. We get at the same time, the triangular configurations as well as rings isolated. Moreover, one sees appearing for certain values of the parameters, new configurations of concentric rings.

PhysicsNLS equationPhysics and Astronomy (miscellaneous)BreatherPeregrine breathers[ MATH.MATH-MP ] Mathematics [math]/Mathematical Physics [math-ph]Order (ring theory)01 natural sciencesConcentric ring010305 fluids & plasmasAkhmediev's solutions.35Q55; 37K10Classical mechanics[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]Wronskians0103 physical sciencesPeregrine solitonAkhmediev's solutionsRogue wave[MATH.MATH-MP] Mathematics [math]/Mathematical Physics [math-ph]010306 general physicsNonlinear Sciences::Pattern Formation and Solitons
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Dark- and bright-rogue-wave solutions for media with long-wave–short-wave resonance

2014

5 pags.; 5 figs.; PACS number(s): 46.40.−f, 47.20.Ky, 47.35.−i, 47.52.+j

PhysicsNonlinear systemModulational instabilityClassical mechanicsNonlinear wave equationWave resonancePeregrine solitonAstrophysics::Cosmology and Extragalactic AstrophysicsRogue waveParametric statisticsPhysical Review E
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