Nail Akhmediev

Australian National University, Canberra, Australian Capital Territory, Australia

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Publications (396)793.26 Total impact

  • N. Akhmediev · N. Devine

    No preview · Article · Jan 2016 · Science
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    ABSTRACT: We study the infinite integrable nonlinear Schrödinger equation hierarchy beyond the Lakshmanan-Porsezian-Daniel equation which is a particular (fourth-order) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, Akhmediev breathers, Kuznetsov-Ma breathers, periodic solutions, and rogue wave solutions for this infinite-order hierarchy. We find that “even- order” equations in the set affect phase and “stretching factors” in the solutions, while “odd-order” equations affect the velocities. Hence odd-order equation solutions can be real functions, while even-order equation solutions are always complex.
    Full-text · Article · Jan 2016
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    ABSTRACT: We show, experimentally and numerically, that a mode-locked fiber laser can operate in a regime where two dissipative soliton solutions coexist and the laser will periodically switch between the solutions. The two dissipative solitons differ in their pulse energy and spectrum. The switching can be controlled by an external perturbation and triggered even when switching does not occur spontaneously. Numerical simulations unveil the importance of the double-minima loss spectrum and nonlinear gain to the switching dynamics.
    No preview · Article · Jan 2016 · Physical Review Letters
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    ABSTRACT: Since the 1960s, the Benjamin-Feir (or modulation) instability (MI) has been considered as the self-modulation of the continuous “envelope waves” with respect to small periodic perturbations that precedes the emergence of highly localized wave structures. Nowadays, the universal nature of MI is established through numerous observations in physics. However, even now, 50 years later, more practical but complex forms of this old physical phenomenon at the frontier of nonlinear wave theory have still not been revealed (i.e., when perturbations beyond simple harmonic are involved). Here, we report the evidence of the broadest class of creation and annihilation dynamics of MI, also called superregular breathers. Observations are done in two different branches of wave physics, namely, in optics and hydrodynamics. Based on the common framework of the nonlinear Schrödinger equation, this multidisciplinary approach proves universality and reversibility of nonlinear wave formations from localized perturbations for drastically different spatial and temporal scales.
    Full-text · Article · Nov 2015 · Physical Review X
  • D. J. Kedziora · A. Ankiewicz · A. Chowdury · N. Akhmediev
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    ABSTRACT: We present an infinite nonlinear Schrödinger equation hierarchy of integrable equations, together with the recurrence relations defining it. To demonstrate integrability, we present the Lax pairs for the whole hierarchy, specify its Darboux transformations and provide several examples of solutions. These resulting wavefunctions are given in exact analytical form. We then show that the Lax pair and Darboux transformation formalisms still apply in this scheme when the coefficients in the hierarchy depend on the propagation variable (e.g., time). This extension thus allows for the construction of complicated solutions within a greatly diversified domain of generalised nonlinear systems.
    No preview · Article · Oct 2015 · Chaos An Interdisciplinary Journal of Nonlinear Science
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    ABSTRACT: We have found a strongly pulsating regime of dissipative solitons in the laser model described by the complex cubic-quintic Ginzburg-Landau equation. The pulse energy within each period of pulsations may change more than two orders of magnitude. The soliton spectra in this regime also experience large variations. Period doubling phenomena and chaotic behaviors are observed in the boundaries of existence of these pulsating solutions.
    No preview · Article · Aug 2015 · Physical Review E
  • A. Chowdury · A. Ankiewicz · N. Akhmediev
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    ABSTRACT: We find that the Hirota equation admits breather-tosoliton conversion at special values of the solution eigenvalues. This occurs for the first-order, as well as higher orders, of breather solutions. An analytic expression for the condition of the transformation is given and several examples of transformations are presented. The values of these special eigenvalues depend on two free parameters that are present in the Hirota equation. We also find that higher order breathers generally have complicated quasi-periodic oscillations along the direction of propagation. Various breather solutions are considered, including the particular case of second-order breathers of the nonlinear Schrödinger equation. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
    No preview · Article · Aug 2015 · Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences
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    ABSTRACT: We have found new dissipative soliton in the laser model described by the complex cubic-quintic Ginzburg-Landau equation. The soliton periodically generates spikes with extreme amplitude and short duration. At certain range of the equation parameters, these extreme spikes appear in pairs of slightly unequal amplitude. The bifurcation diagram of spike amplitude versus dispersion parameter reveals the regions of both regular and chaotic evolution of the maximal amplitudes. (C) 2015 Optical Society of America
    No preview · Article · Jul 2015 · Optics Letters
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    ABSTRACT: We have found new dissipative solitons in the laser model described by the complex cubic-quintic Ginzburg- Landau equation. These objects can be called "spiny solitons" because they chaotically generate spikes of extreme amplitude and ultrashort duration.We have calculated the probability density function of these spikes that demonstrate their rogue wave nature. We have also calculated the average profiles, autocorrelation functions, average spectra, and cross-correlation frequency-resolved optical gating diagram of the "spiny solitons." They have no analogs among the noise-like pulses studied previously in experiments.
    No preview · Article · Jul 2015 · Journal of the Optical Society of America B
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    A Chowdury · D J Kedziora · A Ankiewicz · N Akhmediev
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    ABSTRACT: We analyze the quintic integrable equation of the nonlinear Schrödinger hierarchy that includes fifth-order dispersion with matching higher-order nonlinear terms. We show that a breather solution of this equation can be converted into a nonpulsating soliton solution on a background. We calculate the locus of the eigenvalues on the complex plane which convert breathers into solitons. This transformation does not have an analog in the standard nonlinear Schrödinger equation. We also study the interaction between the new type of solitons, as well as between breathers and these solitons.
    Full-text · Article · Mar 2015 · Physical Review E
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    ABSTRACT: We analyze the rogue wave spectra of the Sasa-Satsuma equation and their appearance in the spectra of chaotic wave fields produced through modulation instability. Chaotic wave fields occasionally produce high peaks that result in a wide triangular spectrum, which could be used for rogue wave detection.
    No preview · Article · Feb 2015 · Physica D Nonlinear Phenomena
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    A Chowdury · D J Kedziora · A Ankiewicz · N Akhmediev
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    ABSTRACT: We present breather solutions of the quintic integrable equation of the Schrödinger hierarchy. This equation has terms describing fifth-order dispersion and matching nonlinear terms. Using a Darboux transformation, we derive first-order and second-order breather solutions. These include first- and second-order rogue-wave solutions. To some extent, these solutions are analogous with the corresponding nonlinear Schrödinger equation (NLSE) solutions. However, the presence of a free parameter in the equation results in specific solutions that have no analogues in the NLSE case. We analyze new features of these solutions.
    Full-text · Article · Feb 2015 · Physical Review E
  • N. Akhmediev · Yaroslav Kartashov
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    ABSTRACT: International Conference “Nonlinear Photonics-2014” took place in Barcelona, Spain on July 27–31, 2014. It was a part of the “Advanced Photonics Congress” which is becoming a traditional notable event in the world of photonics. The current focus issue of Optics Express contains contributions from the participants of the Conference and the Congress. The articles in this focus issue by no means represent the total number of the congress contributions (around 400). However, it demonstrates wide range of topics covered at the event. The next conference of this series is to be held in 2016 in Australia, which is the home of many researchers working in the field of photonics in general and nonlinear photonics in particular.
    No preview · Article · Jan 2015 · Optics Express
  • Sh. Amiranashvili · U. Bandelow · N. Akhmediev
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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.
    No preview · Article · Dec 2014 · Optics Express
  • A Chabchoub · B Kibler · J M Dudley · N Akhmediev
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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.
    No preview · Article · Oct 2014 · Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences
  • Shalva Amiranashvili · Uwe Bandelow · Nail Akhmediev
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    ABSTRACT: We review recent achievements in theory of ultra-short optical pulses propagating in nonlinear fibers. The following problem is especially emphasized: what is the shortest duration (the highest peak power) of an optical soliton and which physical phenomenon is responsible for breakdown of too short pulses. We argue that there is an universal mechanism that destroys sub-cycle solitons even for the most favorable dispersion profile.
    No preview · Article · Oct 2014
  • A Chowdury · D J Kedziora · A Ankiewicz · N Akhmediev
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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.
    No preview · Article · Sep 2014 · Physical Review E
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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.
    No preview · Article · Sep 2014 · Physical Review E
  • Nail Akhmediev · Jose M. Soto-Crespo · Helmut 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.
    No preview · Conference Paper · Jul 2014
  • Wonkeun Chang · Nail Akhmediev
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    ABSTRACT: Exploding solitons can be found in dissipative systems including laser cavities and reaction-diffusion systems. Certain choice of laser parameters allows us to obtain very high amplitudes during explosions. They can be considered as rogue waves.
    No preview · Conference Paper · Jul 2014

Publication Stats

11k Citations
793.26 Total Impact Points


  • 1992-2015
    • Australian National University
      • Research School of Physics & Engineering
      Canberra, Australian Capital Territory, Australia
    • Moscow Technological Institute
      Moskva, Moscow, Russia
    • Research Institute of Physical Problems F.V. Lukin
      Moskva, Moscow, Russia
  • 2013
    • University of Bayreuth
      Bayreuth, Bavaria, Germany
    • Imperial College London
      Londinium, England, United Kingdom
  • 1999
    • University of Rochester
      • Institute of Optics
      Rochester, New York, United States
  • 1995-1999
    • University of Canberra
      Canberra, Australian Capital Territory, Australia
  • 1998
    • AT&T Labs
      Austin, Texas, United States
  • 1997
    • Polytechnic University of Catalonia
      • Department of Signal Theory and Communications (TSC)
      Barcino, Catalonia, Spain
  • 1990-1992
    • The University of Arizona
      • Department of Materials Sciences and Engineering
      Tucson, Arizona, United States
  • 1989-1990
    • Russian Academy of Sciences
      Moskva, Moscow, Russia