[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.
Full-text · Article · Jan 2009 · Physica D Nonlinear Phenomena
[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.
No preview · Article · Oct 2007 · Quantum Electronics
[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.
Full-text · Article · Oct 2002 · Physics Letters A
[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. (C) 2000 MAIK "Nauka/Interperiodica".
Full-text · Article · May 2000 · Technical Physics
[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.
No preview · Article · Nov 1998 · Technical Physics Letters
[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.
Full-text · Article · Mar 1998 · Physica D Nonlinear Phenomena
[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.
Full-text · Article · May 1997 · Optics Communications
[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.
[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.
Full-text · Article · Mar 1993 · Physics Letters A
[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.
Full-text · Article · Nov 1992 · Physics Letters A
[Show abstract][Hide abstract] ABSTRACT: The problem of nonlinear Schrödinger soliton interaction with an oscillating impurity is considered. The regimes of soliton motion for the cases of periodic and random oscillations of the impurity near an equilibrium point are investigated. As shown in the first case there exist regions of parameters under which a soliton dynamics becomes chaotic. The comparison of statistic characteristics of chaos in the region of dynamic and standard stochasticity is carried out. The coefficient of the soliton diffusion is found.[Russian Text Ignored.]
No preview · Article · Oct 1991 · physica status solidi (b)
[Show abstract][Hide abstract] ABSTRACT: The investigations of the nonlinear dynamics of liquid crystals (LC) is of a big interest. To study the propagation of solitary orientational waves the exact integrable models [1–3] are widely used. So the evolution of a wave in LC in a shear flow  and under a magnetic field  is described by the sine-Gordon (SG) equation. Accounting the highest gradient terms in the free energy of nematic leads to the modified Korteveg-de Vries (mKdV) equation .
[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.
Full-text · Article · Dec 1990 · Physics Letters A
[Show abstract][Hide abstract] ABSTRACT: The soliton and breather dynamics in a nematic liquid crystal under the action of constant and time-varying magnetic fields are investigated. The two cases are considered: with highest gradient terms in the free energy and without them. The action of addition magnetic fields and dissipation are considered using the perturbation theory for solitons and breathers. A condition for chaotic oscillation of director is obtained. Absorption of the external alternating-field energy in the linear approximation is studied.
[Russian Text Ignored]
No preview · Article · Apr 1988 · physica status solidi (b)
[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.
No preview · Article · Mar 1988 · Russian Physics Journal