Biomedical subjects

Nail Akhmediev

Publications and source records attributed to Nail Akhmediev.

10 recordsLinked to original sources

PubMed2006

Optical bullets and double bullet complexes in dissipative systems.

We show that optical light bullets can coexist with double bullet complexes in nonlinear dissipative systems. Coexistence occurs for a relatively large range of the system parameters, and is associated with either marginal stability or bistable existence of the two dissipative soliton species. In the case of marginal stability, spontaneous transformations of single bullets into double bullet complexes are observed. Among the bistable cases, we show how both clockwise and anticlockwise rotating double bullet complexes can be formed out of the phase-controlled interaction of two single bullets. The internal dynamics of pulsating double bullet complexes, with oscillations in both the spatial separation between the two bullets and the bullet shape in time domain is also detailed.

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PubMed2006

Dynamical models for dissipative localized waves of the complex Ginzburg-Landau equation.

Finite-dimensional dynamical models for solitons of the cubic-quintic complex Ginzburg-Landau equation (CGLE) are derived. The models describe the evolution of the pulse parameters, such as the maximum amplitude, pulse width, and chirp. A clear correspondence between attractors of the finite-dimensional dynamical systems and localized waves of the continuous dissipative system is demonstrated. It is shown that stationary solitons of the CGLE correspond to fixed points, while pulsating solitons are associated with stable limit cycles. The models show that a transformation from a stationary soliton to a pulsating soliton is the result of a Hopf bifurcation in the reduced dynamical system. The appearance of moving fronts (kinks) in the CGLE is related to the loss of stability of the limit cycles. Bifurcation boundaries and pulse behavior in the regions between the boundaries, for a wide range of system parameters, are found from analysis of the reduced dynamical models. We also provide a comparison between various models and their correspondence to the exact results.

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PubMed2006

Soliton collisions with shape change by intensity redistribution in mixed coupled nonlinear Schrödinger equations.

A different kind of shape changing (intensity redistribution) collision with potential application to signal amplification is identified in the integrable -coupled nonlinear Schrödinger (CNLS) equations with mixed signs of focusing- and defocusing-type nonlinearity coefficients. The corresponding soliton solutions for the N=2 case are obtained by using Hirota's bilinearization method. The distinguishing feature of the mixed sign CNLS equations is that the soliton solutions can both be singular and regular. Although the general soliton solution admits singularities we present parametric conditions for which nonsingular soliton propagation can occur. The multisoliton solutions and a generalization of the results to the multicomponent case with arbitrary N are also presented. An appealing feature of soliton collision in the present case is that all the components of a soliton can simultaneously enhance their amplitudes, which can lead to a different kind of amplification process without induced noise.

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PubMed2005

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 chaotic motion that occurs through the creation, increase, and overlap of "islands" of chaos rather than through multiplication of frequencies.

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PubMed2004

Bifurcations and multiple-period soliton pulsations in a passively mode-locked fiber laser.

We observed, numerically and experimentally, multiple-period pulsations of the soliton parameters in a passively mode-locked fiber laser. Pulsation periods can vary from a few to hundreds of round trips. Short and long period pulsations can appear in combination. The new periods in the soliton modulation appear at bifurcation points related to certain values of the cavity parameters.

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PubMed2004

Strongly asymmetric soliton explosions.

We have observed, in numerical simulations, strongly asymmetric soliton explosions in dissipative systems modeled by the one-dimensional complex cubic-quintic Ginzburg-Landau equation. The explosions occur at one side of the soliton, in spite of the fact that the initial conditions and the equation itself are symmetric. From one explosion to the next, the side of the soliton where it occurs alternates, so that the left- and right-hand sides of the soliton explode successively. We give explanations for this effect based on a linear stability analysis of the unstable soliton. We also describe the transition from the stationary soliton into the exploding one as a three-stage process of soliton cooling.

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PubMed2003

Quantized separations of phase-locked soliton pairs in fiber lasers.

We report the discovery of a quantization of the separation between phase-locked soliton pairs that is related to the radiation waves known as Kelly sidebands, in a passively mode-locked fiber ring laser. Our numerical simulations that predict this phenomenon have been confirmed by our experimental results.

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PubMed2002

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 of the complex quintic Ginzburg-Landau equation. We have also found that the CSHE has a wider variety of localized solutions. In particular, there are three types of stable soliton pairs with pi and pi/2 phase difference and three different fixed separations between the pulses. Different types of soliton pairs can be generated by changing the parameter corresponding to the nonlinear gain (epsilon).

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PubMed2002

Experimental evidence for soliton explosions.

We show, experimentally and numerically, that Ti:sapphire mode-locked lasers can operate in a regime in which they intermittently produce exploding solitons. This happens when the laser operates near a critical point. Explosions happen spontaneously, but external perturbations can trigger them. In stable operation, all explosions have similar features, but are not identical. The characteristics of the explosions depend on the intracavity dispersion.

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PubMed2000

Multi-soliton complexes.

In this paper we introduce the concept of multi-soliton complexes (MSC). A particular example of a MSC is an incoherent soliton in a multimode fiber or in a photorefractive crystal, but there are many examples in other areas of physics. We discuss a variety of profiles of MSCs, their unusual collisional properties, the possibility of a MSC on a background and some other interesting properties of MSCs. Some of their features are also shared by single solitons, but there are many differences between the properties of the two types. (c) 2000 American Institute of Physics.

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