Publications (396)793.26 Total impact

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ABSTRACT: We study the infinite integrable nonlinear Schrödinger equation hierarchy beyond the LakshmananPorsezianDaniel equation which is a particular (fourthorder) case of the hierarchy. In particular, we present the generalized Lax pair and generalized soliton solutions, plane wave solutions, Akhmediev breathers, KuznetsovMa breathers, periodic solutions, and rogue wave solutions for this infiniteorder hierarchy. We find that “even order” equations in the set affect phase and “stretching factors” in the solutions, while “oddorder” equations affect the velocities. Hence oddorder equation solutions can be real functions, while evenorder equation solutions are always complex.  [Show abstract] [Hide abstract]
ABSTRACT: We show, experimentally and numerically, that a modelocked 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 doubleminima loss spectrum and nonlinear gain to the switching dynamics.  [Show abstract] [Hide abstract]
ABSTRACT: Since the 1960s, the BenjaminFeir (or modulation) instability (MI) has been considered as the selfmodulation 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.  [Show abstract] [Hide abstract]
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.  [Show abstract] [Hide abstract]
ABSTRACT: We have found a strongly pulsating regime of dissipative solitons in the laser model described by the complex cubicquintic GinzburgLandau 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.  [Show abstract] [Hide abstract]
ABSTRACT: We find that the Hirota equation admits breathertosoliton conversion at special values of the solution eigenvalues. This occurs for the firstorder, 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 quasiperiodic oscillations along the direction of propagation. Various breather solutions are considered, including the particular case of secondorder breathers of the nonlinear Schrödinger equation. © 2015 The Author(s) Published by the Royal Society. All rights reserved. 
Article: Extreme amplitude spikes in a laser model described by the complex Ginzburg–Landau equation
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ABSTRACT: We have found new dissipative soliton in the laser model described by the complex cubicquintic GinzburgLandau 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 
Article: Spiny solitons and noiselike pulses
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ABSTRACT: We have found new dissipative solitons in the laser model described by the complex cubicquintic 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 crosscorrelation frequencyresolved optical gating diagram of the "spiny solitons." They have no analogs among the noiselike pulses studied previously in experiments.  [Show abstract] [Hide abstract]
ABSTRACT: We analyze the quintic integrable equation of the nonlinear Schrödinger hierarchy that includes fifthorder dispersion with matching higherorder 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.  [Show abstract] [Hide abstract]
ABSTRACT: We analyze the rogue wave spectra of the SasaSatsuma 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. 
Article: Breather solutions of the integrable quintic nonlinear Schrödinger equation and their interactions
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ABSTRACT: We present breather solutions of the quintic integrable equation of the Schrödinger hierarchy. This equation has terms describing fifthorder dispersion and matching nonlinear terms. Using a Darboux transformation, we derive firstorder and secondorder breather solutions. These include first and secondorder roguewave 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.  [Show abstract] [Hide abstract]
ABSTRACT: International Conference “Nonlinear Photonics2014” 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.  [Show abstract] [Hide abstract]
ABSTRACT: It seems to be selfevident 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 socalled short pulse equation. The latter applies to ultrashort solitons in transparent materials like fused silica that are relevant for optical fibers. 
Article: Hydrodynamics of periodic breathers
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ABSTRACT: We report the first experimental observation of periodic breathers in water waves. One of them is KuznetsovMa 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.  [Show abstract] [Hide abstract]
ABSTRACT: We review recent achievements in theory of ultrashort 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 subcycle solitons even for the most favorable dispersion profile.  [Show abstract] [Hide abstract]
ABSTRACT: We present the fifthorder equation of the nonlinear Schrödinger hierarchy. This integrable partial differential equation contains fifthorder 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 twosoliton collisions and the degenerate case of the twosoliton 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 flowon effects. Furthermore, we present a new structure, composed of coincident equalamplitude solitons, which cannot exist for the standard NLSE.  [Show abstract] [Hide abstract]
ABSTRACT: We study the properties of the chaotic wave fields generated in the frame of the SasaSatsuma equation (SSE). Modulation instability results in a chaotic pattern of smallscale filaments with a free parameterthe propagation constant k. The average velocity of the filaments is approximately given by the group velocity calculated from the dispersion relation for the planewave solution. Remarkably, our results reveal the reason for the skewed profile of the exact SSE roguewave 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. 
Conference Paper: Dissipative solitons with energy and matter flows
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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. 
Conference Paper: Exploding Solitons vs Rogue Waves in Laser Cavities
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ABSTRACT: Exploding solitons can be found in dissipative systems including laser cavities and reactiondiffusion systems. Certain choice of laser parameters allows us to obtain very high amplitudes during explosions. They can be considered as rogue waves.
Publication Stats
11k  Citations  
793.26  Total Impact Points  
Top Journals
Institutions

19922015

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


19951999

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


19901992

The University of Arizona
 Department of Materials Sciences and Engineering
Tucson, Arizona, United States


19891990

Russian Academy of Sciences
Moskva, Moscow, Russia
