[show abstract][hide abstract] ABSTRACT: We study modulational instability of matter-waves in Bose-Einstein condensates (BEC) under strong temporal nonlinearity-management. Both BEC in an optical lattice and homogeneous BEC are considered in the framework of the Gross-Pitaevskii equation, averaged over rapid time modulations. For a BEC in an optical lattice, it is shown that the loop formed on a dispersion curve undergoes transformation due to the nonlinearity-management. A critical strength for the nonlinearity-management strength is obtained that changes the character of instability of an attractive condensate. MI is shown to occur below(above) the threshold for the positive (negative) effective mass. The enhancement of number of atoms in the nonlinearity-managed gap soliton is revealed.
Physica D Nonlinear Phenomena 01/2009; 238:1345. · 1.67 Impact Factor
[show abstract][hide abstract] ABSTRACT: A variational method is used to study propagation of chirped optical pulses in media with periodic amplification. A nonlinear resonance and chaos in oscillations of the pulse duration are considered. A stochastic instability of evolution of the pulse duration and also pulse decay under the influence of periodic amplification are predicted. A calculation is reported of the stochastic pulse-decay length and a comparison is made with the results of a numerical simulation. The applications of the results to long-haul optical communication lines with amplifiers and to optical fibres with a periodically modulated core diameter are considered.
[show abstract][hide abstract] ABSTRACT: The existence of discrete autosolitons in a nonlinear lattice is studied. The Ablowitz–Ladik (AL) model with linear damping, nonlinear cubic amplification and quintic damping and complex second difference representing the discrete analog of the filter is investigated. The parameters of the autosoliton are calculated using the perturbation theory for the AL model. Analytical predictions are confirmed by numerical simulations of the AL model with nonconservative perturbations.
Physics Letters A 10/2002; 305:371. · 1.77 Impact Factor
[show abstract][hide abstract] ABSTRACT: The evolution of a randomly modulated sine-Gordon breather in a nonlinear medium is studied theoretically. The initial wave
field is affected by multiplicative noise. For breather amplitude and velocity, the probability distribution function is determined
by means of the inverse scattering transform and the method of cumulants. The distributions are shown to be non-Gaussian.
The mean and the most probable values of the breather amplitude and velocity are calculated.
[show abstract][hide abstract] ABSTRACT: Theoretical results are presented on the interaction of optical solitons in two coupled waveguides. Conditions under which coupled soliton states exist are established, and criteria for the decay of the coupled states are obtained. The numerical simulation of the dynamics of optical solitons in two tunnel-coupled waveguides is also discussed.
[show abstract][hide abstract] ABSTRACT: The evolution of a randomly modulated kink in the sine-Gordon equation is investigated. The distribution function for the kink velocity is found using the inverse scattering transform. It is shown that the distribution function has a non-Gaussian form. The most probable and the mean value of the kink velocity are calculated. It is shown that the asymmetry of distribution function grows when velocity increases. The mean energy of emission random waves is found. The waves with wavelength of the same order with the correlation length are shown to be excited more effectively in the system.
Physica D Nonlinear Phenomena 01/1998; 113(2):115-122. · 1.67 Impact Factor
[show abstract][hide abstract] ABSTRACT: Propagation of a chirped optical soliton in a fiber with randomly varying parameters is considered. The investigation is concerned with fibers with randomly modulated diameter of the core or random variations of the parameters of the amplifiers along a fiber communication line. The description of a soliton propagation process is based on the nonlinear Schrödinger equation with randomly varying parameter of nonlinearity. In the framework of the variational approach the decay law for long distance propagating solitons is derived. The results of analytical calculations are in good agreement with the performed numerical simulations.
[show abstract][hide abstract] ABSTRACT: The stability of solitary and nonlinear periodic orientational waves in nematic liquid crystals is studied. The parameter regions for the stability of nonlinear periodic waves of the modified Boussinesq equation are found.
Physics Letters A 03/1993; 174(s 5–6):403–406. · 1.77 Impact Factor
[show abstract][hide abstract] ABSTRACT: Nonlinear waves in systems with ferroelectric and ferromagnetic properties (segnetomagnets) are studied. The magnetic sub-system is assumed to have easy plane anisotropy. If the ferroelectric subsystem is homogeneous, then a magnetic soliton is described by the double sG equation. The interaction of ferroelectric and magnetic solitons is investigated. The parameters of coupled states of ferroelectric and magnetic solitons are calculated.
Physics Letters A 11/1992; 171:125. · 1.77 Impact Factor
[show abstract][hide abstract] ABSTRACT: It is shown that the dynamics of nematics under the action of a magnetic field is described by an equation that is a combination of the modified Korteweg-de Vries equation and the sine-Gordon equation. This equation may be integrated by the inverse scattering transform method. The evolution of a rectangular distribution is considered. The perturbation theory for this equation is constructed.
Physics Letters A 01/1990; 151:221. · 1.77 Impact Factor
[show abstract][hide abstract] ABSTRACT: We consider a one-dimensional model of displacive structural phase transitions with random temperature-type impurities. The modification to the central peak is calculated. It is shown that random-temperature impurities lead to a divergence in the central peak intensity. We find good agreement between our results and the experimental temperature dependence of the central peak.
[show abstract][hide abstract] ABSTRACT: Soliton dynamics is studied in a compressed ferromagnetic chain having anisotropy of the easy plane type. It is shown that there exists a soliton wave of lattice deformation which follows the magnetic soliton. Two models are considered for the connection between deformation and spins. The soliton renormalization constant is found. The effect of lattice anharmonicity is studied.