F. G. Bass

Dynamics of solitons under random perturbations

Abstract The dynamics of solitons is investigated in media with randomly inhomogeneous and fluctuating parameters. Some exact results of the theory of nonlinear stochastic waves are given. An analysis is made of various approximate approaches, e.g. of the mean field method and the Born approximation. Special attention is paid to the perturbation technique based on the inverse scattering transform and to the construction of the most adequate stochastic perturbation theory for solitons. The described formalism is used to investigate the evolution of nonlinear wave (soliton) parameters, and the statistical characteristics of radiation generated by solitons in fluctuating media are analysed also. The same approach makes it possible to take into account the simultaneous effect of random and regular (e.g., friction) perturbations on the dynamics of solitons. Examples are given of situations arising when one describes nonlinear waves in real physical systems.

Propagation of nonlinear incoherent pulses in single-mode optical fibers

Abstract Propagation of incoherent nonlinear picosecond pulses in a single-mode optical fiber is considered within the framework of the nonlinear Schrodinger equation. Statistical characteristics of a non-soliton wave packet induced by a random input pulse are obtained with the help of the inverse scattering technique. The probability of a soliton creation from the random pulse is found. Mean soliton amplitude and velocity changings caused by small fluctuations of the soliton-like input pulse are calculated. The influence of dissipative losses on the obtained results is discussed.

On stochastic dynamics of solitons in inhomogeneous optical fibers

Abstract Stochastic dynamics of a soliton in a long optical fiber is analysed within the framework of the nonlinear Schrodinger equation. It is shown that in the case of periodic perturbations describing, e.g. sound propagation along a fiber, adiabatic dynamics of a soliton may be stochastic, and the condition for this stochastic motion is obtained. In the case of random perturbations we obtain the solution of the associated Fokker-Plank equation for the random soliton parameters and calculate the mean soliton intensity. Taking into account the radiative losses we also derive the law of radiative damping of an optical soliton in the fiber with random inhomogeneities.

On multistability of nonlinear fiber interferometer with recirculating delay line

Abstract We investigate an optical fiber device based on the scheme proposed by Backman [A.B. Backman, J. Lightware Technol. 7 (1989) 151] with a nonlinear fiber. The possibility of multistable regimes has been stated. Advantages and differences between such a scheme and a linear one studied earlier are discussed.

Excitation of excitons in semi-infinite solids with a nonrelativistic electron beam

The instability of an infinite thin electron beam propagating in vacuum over the surface of an isotropic nongyrotropic crystal is investigated. The possibilities of exciting additional longitudinal waves and polarization waves are analyzed. The dispersion laws of exciton-beam coupled waves are obtained. It is demonstrated that the interaction of the beam with the additional bulk longitudinal wave and the surface polarization wave leads to the appearance of the absolute instability.

Nonlinear beam waves in inhomogeneous media

Nonlinear potential space charge waves, caused by particle beam propagation in statistically inhomogeneous resistive media, are considered. Variations of wave parameters caused by the fluctuation are obtained. Complete analogy with the corresponding linear case is stated. All calculations are carried out in the hydrodynamic approximation.

Dynamic integrals of Hamiltonian systems with mixing

Abstract The main qualitative properties of the mixing motion are generalized in the following hypothesis: in the nonintegrable case adiabatic integrals of motion are Holder class functions in the resonance phase. We show that this hypothesis allows one to connect characters of chaotic motion and is a new way of comprehension of mixing phenomena. The type of this function may be exactly determined from natural or numerical experiments.

Space-charge waves in a randomly inhomogeneous medium

The propagation and amplification of space-charge waves generated in the transmission of charged-particle beams through randomly inhomogeneous and time-varying media and also in beams with fluctuating parameters are investigated. We consider potential waves generated in the motion of a cold nonrelativistic beam of charged particles in a medium with a fluctuating dielectric constant. The nature of the propagation of electromagnetic waves in a statistical medium is determined both by the space scale and by the intensity of the dielectric constant fluctuations. Here we consider the cases of one-dimensional dielectric constant fluctuations of arbitrary intensity and small space scale, smooth three-dimensional large-scale fluctuations, and three-dimensional fluctuations of arbitrary scale and small intensity.