N. Akhmediev

Australian National University, Canberra, Australian Capital Territory, Australia

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Publications (136)250.12 Total impact

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    ABSTRACT: It seems to be self-evident that stable optical pulses cannot be considerably shorter than a single oscillation of the carrier field. From the mathematical point of view the solitary solutions of pulse propagation equations should loose stability or demonstrate some kind of singular behavior. Typically, an unphysical cusp develops at the soliton top, preventing the soliton from being too short. Consequently, the power spectrum of the limiting solution has a special behavior: the standard exponential decay is replaced by an algebraic one. We derive the shortest soliton and explicitly calculate its spectrum for the so-called short pulse equation. The latter applies to ultra-short solitons in transparent materials like fused silica that are relevant for optical fibers.
    Optics Express 12/2014; 22(24). · 3.55 Impact Factor
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    ABSTRACT: 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.
    Philosophical transactions. Series A, Mathematical, physical, and engineering sciences. 10/2014; 372(2027).
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    ABSTRACT: We present the fifth-order equation of the nonlinear Schrödinger hierarchy. This integrable partial differential equation contains fifth-order dispersion and nonlinear terms related to it. We present the Lax pair and use Darboux transformations to derive exact expressions for the most representative soliton solutions. This set includes two-soliton collisions and the degenerate case of the two-soliton solution, as well as beating structures composed of two or three solitons. Ultimately, the new quintic operator and the terms it adds to the standard nonlinear Schrödinger equation (NLSE) are found to primarily affect the velocity of solutions, with complicated flow-on effects. Furthermore, we present a new structure, composed of coincident equal-amplitude solitons, which cannot exist for the standard NLSE.
    Physical review. E, Statistical, nonlinear, and soft matter physics. 09/2014; 90(3-1):032922.
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    ABSTRACT: We study the properties of the chaotic wave fields generated in the frame of the Sasa-Satsuma equation (SSE). Modulation instability results in a chaotic pattern of small-scale filaments with a free parameter-the propagation constant k. The average velocity of the filaments is approximately given by the group velocity calculated from the dispersion relation for the plane-wave solution. Remarkably, our results reveal the reason for the skewed profile of the exact SSE rogue-wave solutions, which was one of their distinctive unexplained features. We have also calculated the probability density functions for various values of the propagation constant k, showing that probability of appearance of rogue waves depends on k.
    Physical Review E 09/2014; 90(3-1):032902. · 2.31 Impact Factor
  • 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.
    Physical Review E 07/2014; 90(1-1). · 2.31 Impact Factor
  • 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. · 1.63 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; 10/2013
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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. · 7.73 Impact Factor
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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-. · 2.01 Impact Factor
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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-. · 2.01 Impact Factor
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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-. · 2.01 Impact Factor
  • 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. · 1.63 Impact Factor
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    ABSTRACT: The Fermi Pasta Ulam (FPU) recurrence is an ubiquitous phenomenon observable in many fields of physics. Its dynamics is mathematically well described by the nonlinear Schrödinger equation (NLSE), in particular through a class of solutions known as Akhmediev Breathers (ABs). This phenomenon been demonstrated experimentally in optical fibers a few years ago, in a system which was modeled by a pure NLSE. More recently, the renew of interest on ABs due to the major role they play in rogue wave dynamics motivated new investigations in the low dispersion regime, where third-order dispersion must be accounted for. In this work, we demonstrate experimentally and numerically that this convective term leads to multiple disappearance and restorations of the FPU process when approaching the zero dispersion region of the optical fiber.
    The European Conference on Lasers and Electro-Optics; 05/2013
  • The European Conference on Lasers and Electro-Optics; 05/2013
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    ABSTRACT: form only given. Initiated first in the context of oceanography, the notion of rogue waves (RW) covers unexpected waves of extreme amplitude that are held responsible for lots of maritime disasters. The major challenge for scientific research worldwide is to progress in the prediction of these extreme events. The analogy with nonlinear optics greatly helps in developing useful experimental tools to progress in the understanding of RW phenomena. Recent reports have placed a special emphasis on the role of dissipative systems as to drive instabilities generating extreme pulses, reminding us that natural physical systems are inherently dissipative. In that respect, the laser cavity is becoming a paradigmatic rogue wave generator. Recently, we used a mode-locked fiber laser to present the first experimental demonstration of a new mechanism for rogue wave generation, following earlier theoretical predictions. Extreme peak-optical intensity events result from the nonlinear interactions and collisions of several pulses having chaotic relative motions, while they propagate round the laser cavity. The challenge is to record in real time the intensity fluctuations that take place inside of a pulse bunch of nanosecond duration. Thus, dissipative rogue wave observation is found to depend strongly on the electronic bandwidth of the optical intensity detection scheme. This peculiar feature shall be developed in our presentation, and compared to numerical simulations. We shall also explore the range of cavity settings where dissipative rogue wave (DRW) manifest, and clarify the observation of DRWs with respect to other pulsating regimes, such as Q-switched mode locking and noise-like pulse emission. Finally, the influence of a potential control, through external source injection, on DRW generation is also discussed.
    International Quantum Electronics Conference; 05/2013
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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). · 7.73 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
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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. · 7.73 Impact Factor

Publication Stats

2k Citations
250.12 Total Impact Points

Institutions

  • 1993–2014
    • Australian National University
      • Research School of Physics & Engineering
      Canberra, Australian Capital Territory, Australia
  • 2013
    • Nizhny Novgorod State Technical University
      Gorkey, Nizjnij Novgorod, Russia
    • Imperial College London
      Londinium, England, United Kingdom
  • 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
    • University of Franche-Comté
      • Institut FEMTO-ST
      Besançon, Franche-Comte, France
    • University of Minho
      • Centro de Física
      Braga, Distrito de Braga, Portugal
  • 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