Search results for "Peregrine"
showing 10 items of 48 documents
Tenth order solutions to the NLS equation with eighteen parameters
2015
We present here new solutions of the focusing one dimensional non linear Schrödinger equation which appear as deformations of the Peregrine breather of order 10 with 18 real parameters. With this method, we obtain new families of quasi-rational solutions of the NLS equation, and we obtain explicit quotients of polynomial of degree 110 in x and t by a product of an exponential depending on t. We construct new patterns of different types of rogue waves and recover the triangular configurations as well as rings and concentric as found for the lower orders.
Deformations of third-order Peregrine breather solutions of the nonlinear Schrödinger equation with four parameters
2013
We present a new representation of solutions of the one-dimensional nonlinear focusing Schr\"odinger equation (NLS) as a quotient of two determinants. This formulation gives in the case of the order 3, new solutions with four parameters. This gives a very efficient procedure to construct families of quasirational solutions of the NLS equation and to describe the apparition of multirogue waves. With this method, we construct analytical expressions of four-parameters solutions; when all these parameters are equal to 0, we recover the Peregrine breather of order 3. It makes possible with this four-parameters representation, to generate all the types of patterns for the solutions, like the tria…
The Peregrine soliton in nonlinear fibre optics
2010
International audience; The Peregrine soliton is a localized nonlinear structure predicted to exist over 25 years ago, but not so far experimentally observed in any physical system. It is of fundamental significance because it is localized in both time and space, and because it defines the limit of a wide class of solutions to the nonlinear Schrödinger equation (NLSE). Here, we use an analytic description of NLSE breather propagation to implement experiments in optical fibre generating femtosecond pulses with strong temporal and spatial localization, and near-ideal temporal Peregrine soliton characteristics. In showing that Peregrine soliton characteristics appear with initial conditions th…
Nonlinear spectral shaping and optical rogue events in fiber-based systems
2012
International audience; We provide an overview of our recent work on the shaping and stability of optical continua in the long pulse regime. Fibers with normal group-velocity dispersion at all-wavelengths are shown to allow for highly coherent continua that can be nonlinearly shaped using appropriate initial conditions. In contrast, supercontinua generated in the anomalous dispersion regime are shown to exhibit large fluctuations in the temporal and spectral domains that can be controlled using a carefully chosen seed. A particular example of this is the first experimental observation of the Peregrine soliton which constitutes a prototype of optical rogue-waves.
Peregrine soliton generation and breakup in standard telecommunications fiber
2011
International audience; We present experimental and numerical results showing the generation and breakup of the Peregrine soliton in standard telecommunications fiber. The impact of non-ideal initial conditions is studied through direct cut back measurements of the longitudinal evolution of the emerging soliton dynamics, and is shown to be associated with the splitting of the Peregrine soliton into two subpulses, with each subpulse itself exhibiting Peregrine soliton characteristics. Experimental results are in good agreement with simulations.
Comparative Analysis of Lanner and Peregrine Trophic Niche in the Mediterranean
2017
Predators are highly sensitive to availability and changes of their prey, which are limiting factors for successful reproductive performances. We studied the diet of the increasing Peregrine falcon (F. p. brookei) and the declining Lanner falcon (F. b. feldeggii) populations in Sicily. The two species coexist in the same habitats of this large Mediterranean island and require similar feeding resources. We described the type and diversity of prey taken by both species in order to understand whether differences in foraging ecology could explain their diverse population status. During 2014-2016, we collected prey remains and pellets in 15 Peregrine and 6 Lanner nests and we compared the curren…
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
Soliton collisions with shape change by intensity redistribution in mixed coupled nonlinear Schrodinger equations
2006
International audience; A different kind of shape changing (intensity redistribution) collision with potential application to signal amplification is identified in the integrable N-coupled nonlinear Schrodinger (CNLS) equations with mixed signs of focusing- and defocusing-type nonlinearity coefficients. The corresponding soliton solutions for the N=2 case are obtained by using Hirota's bilinearization method. The distinguishing feature of the mixed sign CNLS equations is that the soliton solutions can both be singular and regular. Although the general soliton solution admits singularities we present parametric conditions for which nonsingular soliton propagation can occur. The multisoliton …
Propagation, Stability and Interactions of Novel Three-Wave Parametric Solitons
2006
International audience; We found a new class of analytic soliton solutions that describe the parametric wave mixing of optical pulses in quadratic nonlinear crystals. We analyze the stability properties, interactions and collisions of these solitons.