N. Akhmediev

Imperial College London, Londinium, England, United Kingdom

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Publications (135)244.72 Total impact

  • A Chowdury, A Ankiewicz, N Akhmediev
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    ABSTRACT: We derive exact and approximate localized solutions for the Manakov-type continuous and discrete equations. We establish the correspondence between the solutions of the coupled Ablowitz-Ladik equations and the solutions of the coupled higher-order Manakov equations.
    07/2014;
  • D. J. Kedziora, A. Ankiewicz, N. Akhmediev
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    ABSTRACT: Solutions of the nonlinear Schrödinger equation, appearing as rogue waves on a spatially-periodic background envelope, are obtained using the Darboux transformation scheme. Several particular examples are illustrated numerically. These include soliton and breather solutions on a periodic background as well as higher-order structures. The results enrich our knowledge of possible analytic solutions that describe the appearance of rogue waves in a variety of situations. This work is prepared on the occasion of Prof. Helmut Brand's 60th birthday. He has made significant contributions to the science of solitons and his ideas have inspired our research into localised formations in various physical contexts.
    The European Physical Journal Special Topics 12/2013; 223(1). · 1.80 Impact Factor
  • A. Chabchoub, N. Akhmediev
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    ABSTRACT: Doubly-localised breather solutions of the nonlinear Schrödinger equation (NLS) are considered to be appropriate models to describe rogue waves in water waves as well as in other nonlinear dispersive media such as fibre optics. Within the hierarchy of this type of formations, the Peregrine breather (PB) is the lowest-order rational solution. Higher-order solutions of this kind may be understood as a nonlinear superposition of fundamental Peregrine solutions. These superpositions are nontrivial and admit only a fixed well prescribed number of elementary breathers in each higher-order solution. Here, we report first observation of second-order solution which in reality is a triplet of rogue waves.
    Physics Letters A 11/2013; 377(38):2590-2593. · 1.77 Impact Factor
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    ABSTRACT: We report the experimental observation of multi-bound-soliton solutions of the nonlinear Schrödinger equation (NLS) in the context of hydrodynamic surface gravity waves. Higher-order N-soliton solutions with N=2, 3 are studied in detail and shown to be associated with self-focusing in the wave group dynamics and the generation of a steep localized carrier wave underneath the group envelope. We also show that for larger input soliton numbers, the wave group experiences irreversible spectral broadening, which we refer to as a hydrodynamic supercontinuum by analogy with optics. This process is shown to be associated with the fission of the initial multisoliton into individual fundamental solitons due to higher-order nonlinear perturbations to the NLS. Numerical simulations using an extended NLS model described by the modified nonlinear Schrödinger equation, show excellent agreement with experiment and highlight the universal role that higher-order nonlinear perturbations to the NLS play in supercontinuum generation.
    Physical Review Letters 08/2013; 111(5):054104. · 7.94 Impact Factor
  • Source
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    ABSTRACT: The rogue wave solutions (rational multibreathers) of the nonlinear Schrödinger equation (NLS) are tested in numerical simulations of weakly nonlinear and fully nonlinear hydrodynamic equations. Only the lowest order solutions from 1 to 5 are considered. A higher accuracy of wave propagation in space is reached using the modified NLS equation, also known as the Dysthe equation. This numerical modeling allowed us to directly compare simulations with recent results of laboratory measurements in Chabchoub et al. [Phys. Rev. E 86, 056601 (2012)]. In order to achieve even higher physical accuracy, we employed fully nonlinear simulations of potential Euler equations. These simulations provided us with basic characteristics of long time evolution of rational solutions of the NLS equation in the case of near-breaking conditions. The analytic NLS solutions are found to describe the actual wave dynamics of steep waves reasonably well.
    Physical Review E 07/2013; 88(1-1):012909. · 2.31 Impact Factor
  • U. Bandelow, N. Akhmediev
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    ABSTRACT: We present the most general multi-parameter family of a soliton on background solutions to the Sasa–Satsuma equation. These solutions contain a set of several free parameters that control the background amplitude as well as the soliton itself. This family of solutions admits nontrivial limiting cases, such as rogue waves and classical solitons, that are considered in detail.
    Journal of Optics 06/2013; 15(6):4006-.
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    ABSTRACT: The full text of this article is available in the PDF provided.
    Journal of Optics 06/2013; 15(6):0201-.
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    ABSTRACT: We provide a simple technique for finding the correspondence between the solutions of Ablowitz-Ladik and nonlinear Schrödinger equations. Even though they belong to different classes, in that one is continuous and one is discrete, there are matching solutions. This fact allows us to discern common features and obtain solutions of the continuous equation from solutions of the discrete equation. We consider several examples. We provide tables, with selected solutions, which allow us to easily match the pairs of solutions. We show that our technique can be extended to the case of coupled Ablowitz-Ladik and nonlinear Schrödinger (i.e. Manakov) equations. We provide some new solutions.
    Journal of Optics 06/2013; 15(6):4008-.
  • N. Akhmediev, J.M. Soto-Crespo, H.R. Brand
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    ABSTRACT: We consider a combined model of dissipative solitons that are generated due to the balance between gain and loss of energy as well as to the balance between input and output of matter. The system is governed by the generic complex Ginzburg–Landau equation, which is coupled to a common reaction–diffusion (RD) system. Such a composite dynamical system may describe nerve pulses with a significant part of electromagnetic energy involved. We present examples of such composite dissipative solitons and analyse their internal balances between energy and matter generation and dissipation.
    Physics Letters A 05/2013; 377(13):968–974. · 1.77 Impact Factor
  • The European Conference on Lasers and Electro-Optics; 05/2013
  • Source
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    ABSTRACT: We demonstrate experimentally multi-bound-soliton solutions of the Nonlinear Schr\"odinger equation (NLS) in the context of surface gravity waves. In particular, the Satsuma-Yajima N-soliton solution with N=2,3,4 is investigated in detail. Such solutions, also known as breathers on zero background, lead to periodic self-focussing in the wave group dynamics, and the consequent generation of a steep localized carrier wave underneath the group envelope. Our experimental results are compared with predictions from the NLS for low steepness initial conditions where wave-breaking does not occur, with very good agreement. We also show the first detailed experimental study of irreversible massive spectral broadening of the water wave spectrum, which we refer to by analogy with optics as the first controlled observation of hydrodynamic supercontinuum a process which is shown to be associated with the fission of the initial multi-soliton bound state into individual fundamental solitons similar to what has been observe in optics.
    Physical Review Letters 03/2013; 111(5). · 7.94 Impact Factor
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    ABSTRACT: We study the propagation of few-cycle optical solitons in nonlinear media with an anomalous, but otherwise arbitrary, dispersion and a cubic nonlinearity. Our approach does not derive from the slowly varying envelope approximation. The optical field is derived directly from Maxwell's equations under the assumption that generation of the third harmonic is a nonresonant process or at least cannot destroy the pulse prior to inevitable linear damping. The solitary wave solutions are obtained numerically up to nearly single-cycle duration using the spectral renormalization method originally developed for the envelope solitons. The theory explicitly distinguishes contributions between the essential physical effects such as higher-order dispersion, self-steepening, and backscattering, as well as quantifies their influence on ultrashort optical solitons.
    Physical Review A 01/2013; 87(1). · 3.04 Impact Factor
  • Source
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    ABSTRACT: We present the first ever observation of dark solitons on the surface of water. It takes the form of an amplitude drop of the carrier wave which does not change shape in propagation. The shape and width of the soliton depend on the water depth, carrier frequency, and the amplitude of the background wave. The experimental data taken in a water tank show an excellent agreement with the theory. These results may improve our understanding of the nonlinear dynamics of water waves at finite depths.
    Physical Review Letters 01/2013; 110(12):124101. · 7.94 Impact Factor
  • S. Amiranashvili, U. Bandelow, N. Akhmediev
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    ABSTRACT: We consider propagation of ultrashort optical pulses in nonlinear fibers and suggest a new theoretical framework for description of pulse dynamics and exact characterization of solitary solutions. Our approach deals with a proper complex generalization of the nonlinear Maxwell equations and completely avoids the use of the slowly varying envelope approximation. The only essential restriction is that fiber dispersion does not favor both the so-called Cherenkov radiation, as well as the resonant generation of the third harmonics, as these effects destroy ultrashort solitons. Assuming that it is not the case, we derive a continuous family of solitary solutions connecting fundamental solitons to nearly single-cycle ultrashort ones for arbitrary anomalous dispersion and cubic nonlinearity.
    Numerical Simulation of Optoelectronic Devices (NUSOD), 2013 13th International Conference on; 01/2013
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    ABSTRACT: Being considered as a prototype for description of oceanic rogue waves (RWs), the Peregrine breather solution of the nonlinear Schr\"odinger equation (NLS) has been recently observed and intensely investigated experimentally in particular within the context of water waves. Here, we report the experimental results showing the evolution of the Peregrine solution in the presence of wind forcing in the direction of wave propagation. The results show the persistence of the breather evolution dynamics even in the presence of strong wind and chaotic wave field generated by it. Furthermore, we have shown that characteristic spectrum of the Peregrine breather persists even at the highest values of the generated wind velocities thus making it a viable characteristic for prediction of rogue waves.
    Physics of Fluids 01/2013; 25:101704. · 1.94 Impact Factor
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    ABSTRACT: The Peregrine soliton, which is commonly considered to be a prototype of a rogue wave in deep water, is observed and measured in a wave tank. Using the measured data of water elevation, we calculated the spectra of the Peregrine soliton and confirmed that they have triangular shapes, in accordance with the theory.
    Journal of Geophysical Research (Oceans). 11/2012; 117(C11).
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    ABSTRACT: Benjamin-Feir (1967) modulational instabilities can lead to the onset of recurrent extreme waves (breather) whose amplitude may exceed three to five times the amplitude of the initial wave-train. We conducted experiments in different wave tanks to simulate breather formation and propagation. Breathers are correctly generated, even the high order soliton pulses with amplification greater than 5. By shifting by 180 ° the carrier phase, the large crest becomes an extreme through. In finite depth, it is possible to maintain in the tank the propagation of a dark soliton (quiet zone between two groups of waves). Finally, the first tests carried out in the presence of wind show that the breather is not damped by the wind.
    13th Hydrodynamic days (13eme journées de l'hydrodynamique), Chatou, France; 11/2012
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    ABSTRACT: We present experimental observations of the hierarchy of rational breather solutions of the nonlinear Schrödinger equation (NLS) generated in a water wave tank. First, five breathers of the infinite hierarchy have been successfully generated, thus confirming the theoretical predictions of their existence. Breathers of orders higher than five appeared to be unstable relative to the wave-breaking effect of water waves. Due to the strong influence of the wave breaking and relatively small carrier steepness values of the experiment these results for the higher-order solutions do not directly explain the formation of giant oceanic rogue waves. However, our results are important in understanding the dynamics of rogue water waves and may initiate similar experiments in other nonlinear dispersive media such as fiber optics and plasma physics, where the wave propagation is governed by the NLS.
    Physical Review E 11/2012; 86(5-2):056601. · 2.31 Impact Factor
  • A. Chabchoub, N. P. Hoffmann, N. Akhmediev
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    ABSTRACT: Rogue waves in the ocean can take two forms. One form is an elevated wall of water that appears and disappears locally. Another form is a deep hole between the two crests on the surface of water. The latter one can be considered as an inverted profile of the former. For holes, the depth from crest to trough can reach more than twice the significant wave height. That allows us to consider them as rogue events. The existence of rogue holes follow from theoretical analysis but has never been proven experimentally. Here, we present the results confirming the existence of rogue wave holes on the water surface observed in a water wave tank.
    Journal of Geophysical Research (Oceans). 11/2012; 117(C11).
  • U. Bandelow, N. Akhmediev
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    ABSTRACT: We present a multiparameter family of a soliton on a background solution to the Sasa-Satsuma equation. The solution is controlled by a set of several free parameters that control the background amplitude as well as the soliton itself. This family of solutions admits a few nontrivial limiting cases that are considered in detail. Among these special cases is the nonlinear Schrödinger equation limit and the limit of rogue wave solutions.
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 08/2012; 86(2).

Publication Stats

2k Citations
244.72 Total Impact Points

Institutions

  • 2013
    • Imperial College London
      Londinium, England, United Kingdom
    • Nizhny Novgorod State Technical University
      Gorkey, Nizjnij Novgorod, Russia
  • 1993–2013
    • Australian National University
      • Research School of Physics & Engineering
      Canberra, Australian Capital Territory, Australia
  • 2012
    • Weierstrass Institute for Applied Analysis and Stochastics
      Berlín, Berlin, Germany
  • 2011–2012
    • Technische Universität Hamburg-Harburg
      • Institut für Mechanik und Meerestechnik
      Hamburg, Hamburg, Germany
    • Laboratoire Interdisciplinaire Carnot de Bourgogne
      Champagne-Ardenne, France
  • 2009–2012
    • University of Burgundy
      • Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB)
      Dijon, Bourgogne, France
    • French National Centre for Scientific Research
      Lutetia Parisorum, Île-de-France, France
    • University of Minho
      • Centro de Física
      Braga, Distrito de Braga, Portugal
    • University of Franche-Comté
      • Institut FEMTO-ST
      Besançon, Franche-Comte, France
  • 2010
    • Northeast Institute of Geography and Agroecology
      • Institute of Systems Science
      Beijing, Beijing Shi, China
  • 2001–2009
    • Spanish National Research Council
      • Institute of Optics "Daza de Valdés"
      Madrid, Madrid, Spain
  • 2008
    • Université des Sciences et Technologies de Lille 1
      Lille, Nord-Pas-de-Calais, France
  • 1998
    • University of Central Florida
      • Center for Research and Education in Optics and Lasers
      Orlando, Florida, United States