Bakhram Umarov

Asymptotic soliton train solutions of Kaup-Boussinesq equations

Asymptotic soliton trains arising from a ‘large and smooth’ enough initial pulse are investigated by the use of the quasiclassical quantization method for the case of Kaup–Boussinesq shallow water equations. The parameter varying along the soliton train is determined by the Bohr–Sommerfeld quantization rule which generalizes the usual rule to the case of ‘two potentials’ h0(x) and u0(x) representing initial distributions of height and velocity, respectively. The influence of the initial velocity u0(x) on the asymptotic stage of the evolution is determined. Excellent agreement of numerical solutions of the Kaup–Boussinesq equations with predictions of the asymptotic theory is found.

Generation of three-qubit entangled W state by nonlinear optical state truncation

We propose an alternative scheme to generate the W state via optical state truncation using quantum scissors. In particular, these states may be generated through three-mode optical state truncation in a Kerr nonlinear coupler. The more general three-qubit state may also be produced if the system is driven by external classical fields.

Soliton interaction and switching in a coupler with third order dispersion and Raman effect

The interaction and switching of optical solitons in a nonlinear directional coupler are investigated analytically and numerically. The influence of the coupling-coefficient dispersion, the third order dispersion and the Raman effect in fibers on these processes are reported. Coupled soliton states are found, and their stability is checked numerically. Switching characteristics of solitons in directional couplers are studied.

Autosoliton in Ablowitz-Ladik chain with linear damping and nonlinear amplification

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.

Resonance phenomena in interaction of a spatial soliton with the modulated interface of two nonlinear media

The dynamics of a spatial soliton interacting with a periodically modulated interface of two nonlinear media is considered. Nonlinear resonances between the surface wave oscillations and periodic modulation of the interface are analysed. The estimation of the critical modulation amplitude that destroys the nonlinear surface wave is obtained. The results of numerical simulations of adiabatic equations for soliton parameters are consistent with analytical estimations.

Dispersion-managed solitons in a periodically and randomly inhomogeneous birefringent optical fiber

The propagation of dispersion-managed vector solitons in optical fibers with periodic and random birefringence is studied. With the help of a variational approach, the equations that describe the evolution of pulse parameters are derived. Numerical modeling is performed for variational equations and for fully coupled periodic and stochastic nonlinear Schrodinger equations. It is shown that variational equations can be effectively used to describe the averaged dynamics of dispersion-managed vector solitons with stochastic perturbations. It is shown, analytically and numerically, that dispersion-managed (DM) solitons have the same resistance to random birefringence as do ordinary solitons. The dependence of the mean decay length of a DM vector soliton on the strength of random birefringence and on the energy of the initial pulse is found.

Squeezing in multi-mode nonlinear optical state truncation

In this Letter, we show that multi-mode qubit states produced via nonlinear optical state truncation driven by classical external pumpings exhibit squeezing condition. We restrict our discussions to the two- and three-mode cases.

CHAOS IN THE PARAMETRICALLY DRIVEN SINE-GORDON SYSTEM

Abstract The appearance of chaos in the parametrically driven sine-Gordon equation is studied analytically. The chaotic behavior of breathers under the action of the periodic parametrical perturbations is found.

On asymptotic solutions of integrable wave equations

Asymptotic ‘soliton train’ solutions of integrable wave equations described by inverse scattering transform method with second-order scalar eigenvalue problem are considered. It is shown that if asymptotic solution can be presented as a modulated one-phase nonlinear periodic wavetrain, then the corresponding Baker–Akhiezer function transforms into quasiclassical eigenfunction of the linear spectral problem in weak dispersion limit for initially smooth pulses. In this quasiclassical limit the corresponding eigenvalues can be calculated with the use of the Bohr–Sommerfeld quantization rule. The asymptotic distributions of solitons parameters obtained in this way specify the solution of the Whitham equations.  2001 Elsevier Science B.V. All rights reserved.

Stochastic breaking by ac-bias of a bifluxon state in coupled long Josephson junctions

Abstract The dynamics of fluxons in coupled long Josephson junctions is considered. The condition for stochastic breaking of a bound state of fluxons under the action of ac-current is analytically derived and tested by numerical simulations.