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Akhmediev, N.

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  • Propagation dynamics of ultrashort pulses in nonlinear fiber couplers

    The nonlinear fiber coupler is considered as a Hamiltonian dynamical system with an infinite number of degrees of freedom, with the soliton states of the coupler being the singular points of this dynamical system. Numerical simulations show that arbitrary initial conditions give rise, asymptotically, to oscillations around some of the stable singular points and some amount of radiation. Examples of different initial conditions, including unstable soliton states and single pulses launched in o...

    Generation of a train of three-dimensional optical solitons in a self-focusing medium

    The problem of modulation instability of a self-focused beam in a homogeneous nonlinear medium with saturation and anomalous group-velocity dispersion is solved numerically. It is shown that the results of this instability is beam breakup into a periodic train of three-dimensional (3D) spatial solitary waves. It is also shown that other types of periodic initial conditions can produce a periodic train of 3D spatial solitary waves. Our numerical simulations show that 3D solitary waves are attr...

    Composite solitons and two-pulse generation in passively mode-locked lasers modeled by the complex quintic Swift-Hohenberg equation

    The complex quintic Swift-Hohenberg equation (CSHE) is a model for describing pulse generation in mode-locked lasers with fast saturable absorbers and a complicated spectral response. Using numerical simulations, we study the single- and two-soliton solutions of the (1 - 1)-dimensional complex quintic Swift-Hohenberg equations. We have found that several types of stationary and moving composite solitons of this equation are generally stable and have a wider range of existence than for those o...

    Multisoliton regime of pulse generation by lasers passively mode locked with a slow saturable absorber

    The multiphase regime of a solid-state laser with a slow saturable absorber is studied. Solutions to the propagation equations are derived and their range of existence are analyzed. Single-pulse solutions, called solitons, exist for a certain range parameters. With high enough pump power, two or more pulses may be generated sequentially. In the two-pulse case, the pulses can propagate independently if far apart or form a bound state if close. Two-types of bound states are identified for the s...

    Bifurcations from stationary to pulsating solitons in the cubic-quintic complex Ginzburg-Landau equation

    Stationary to pulsating soliton bifurcation analysis of the complex Ginzburg-Landau equation (CGLE) is presented. The analysis is based on a reduction from an infinite-dimensional dynamical dissipative system to a finite-dimensional model. Stationary solitons, with constant amplitude and width, are associated with fixed points in the model. For the first time, pulsating solitons are shown to be stable limit cycles in the finite-dimensional dynamical system. The boundaries between the two type...

    Strongly asymmetric soliton explosions

    Strongly asymmetric soliton explosions in dissipative systems modeled by the one-dimensional complex cubic-quintic Ginzburg-Landau equation was analyzed in numerical simulations. It was found that the explosions occured at one side of the soliton, in spite of the fact that the initial conditions and the equation itself were symmetric. It was also found that the side of the solitons where it occured alternates from one explosion to the next, so that the left and right-hand sides of the soliton...

    Dynamics of solitonlike pulse propagation in birefringent optical fibers

    Integrated Stokes parameters are used to describe solitonlike pulse propagation and its state of polarization in birefringent optical fibers. A qualitative analysis on the Poincaré sphere is developed to describe the evolution of the state of polarization of the soliton as a whole. Simple analytic equations describing the pulse evolution are derived in the approximation of the average profile. It is shown that two qualitatively different regimes of propagation are possible, depending on the m...

    Soliton as strange attractor: Nonlinear synchronization and chaos

    We show that dissipative solitons can have dynamics similar to that of a strange attractor in low-dimensional systems. Using a model of a passively mode-locked fiber laser as an example, we show that soliton pulsations with periods equal to several round-trips of the cavity can be chaotic, even though they are synchronized with the round-trip time. The chaotic part of this motion is quantified using a two-dimensional map and estimating the Lyapunov exponent. We found a specific route to chaot...

    Stability of the soliton states in a nonlinear fiber coupler

    A detailed study of the stability of the soliton states for a nonlinear fiber coupler is presented. It is shown that the stability of the symmetric soliton states is delimited by the point of bifurcation: symmetric states are stable starting from zero energy up to the point of bifurcation, and unstable beyond the point of bifurcation. Asymmetric A-type states are stable at points with positive slope in the energy dispersion curve, and unstable otherwise. B-type asymmetric states are always un...
  • Dissipative ring solitons with vorticity

    We study dissipative ring solitons with vorticity in the frame of the (2+1)-dimensional cubic-quintic complex Ginzburg-Landau equation. In dissipative media, radially symmetric ring structures with any vorticity m can be stable in a finite range of parameters. Beyond the region of stability, the solitons lose the radial symmetry but may remain stable, keeping the same value of the topological charge. We have found bifurcations into solitons with n-fold bending symmetry, with n independent on ...

    Transformations of continuously self-focusing and continuously self-defocusing dissipative solitons

    Dissipative media admit the existence of two types of stationary self-organized beams: continuously self-focused and continuously self-defocused. Each beam is stable inside of a certain region of its existence. Beyond these two regions, beams loose their stability, and new dynamical behaviors appear. We present several types of instabilities related to each beam configuration and give examples of beam dynamics in the areas adjacent to the two regions. We observed that, in one case beams loose...

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