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.
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.
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.
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.
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
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.
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…
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…
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.
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