Resonances in a trapped 3D Bose-Einstein condensate under periodically varying atomic scattering length

Nonlinear oscillations of a 3D radial symmetric Bose-Einstein condensate under periodic variation in time of the atomic scattering length have been studied analytically and numerically. The time-dependent variational approach is used for the analysis of the characteristics of nonlinear resonances in the oscillations of the condensate. The bistability in oscillations of the BEC width is invistigated. The dependence of the BEC collapse threshold on the drive amplitude and parameters of the condensate and trap is found. Predictions of the theory are confirmed by numerical simulations of the full Gross-Pitaevski equation.Comment: 17 pages, 10 figures, submitted to Journal of Physics

Symmetry breaking induced by random fluctuations for Bose-Einstein condensates in a double-well trap

This paper is devoted to the study of the dynamics of two weakly-coupled Bose-Einstein condensates confined in a double-well trap and perturbed by random external forces. Energy diffusion due to random forcing allows the system to visit symmetry-breaking states when the number of atoms exceeds a threshold value. The energy distribution evolves to a stationary distribution which depends on the initial state of the condensate only through the total number of atoms. This loss of memory of the initial conditions allows a simple and complete description of the stationary dynamics of the condensate which randomly visits symmetric and symmetry-breaking states.Comment: 12 pages, 6 figure

Generalized Neighbor-Interaction Models Induced by Nonlinear Lattices

It is shown that the tight-binding approximation of the nonlinear Schr\"odinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear and nonlinear, neighbor interactions. The obtained lattices present non-standard possibilities, among which we mention a quasi-linear regime, where the pulse dynamics obeys essentially the linear Schr{\"o}dinger equation. We analyze the properties of such models both in connection with their modulational stability, as well as in regard to the existence and stability of their localized solitary wave solutions

Risk management as a basis for integrated water cycle management in Kazakhstan

Integrated Water Cycle Management (IWCM) aims to bring together a diversity of social, environmental, technological and economic aspects to implement sustainable water and land management systems. This paper investigates the challenges and opportunities facing Kazakhstan as it its efforts to move towards a more sustainable approach to managing its finite and highly stressed water resources. The use of a strategic-level risk governance framework to support a multi-disciplinary Kazakh-EU consortium in working collabora-tively towards enhancing capacity and capability to address identified challenges is described. With a clear focus on addressing capacity building needs, a strong emphasis is placed on developing taught integrated water cycle management programmes through communi-cation, stakeholder engagement and policy development including appropriate tools for managing the water issues including hydraulic models, GIS-based systems and scenario developments. Conclusions on the benefits of implementing an EU-style Water Framework Directive for Central Asia based on a risk management approach in Kazakhstan are formulated

Pulse confinement in optical fibers with random dispersion

Short range correlated uniform noise in the dispersion coefficient, inherent in many types of optical fibers, broadens and eventually destroys all initially ultra-short pulses. However, under the constraint that the integral of the random component of the dispersion coefficient is set to zero, or pinned, periodically or quasi-periodically along the fiber, the nature of the pulse propagation changes dramatically. For the case that randomness is added to constant positive dispersion, the pinning restriction significantly reduces pulse broadening. If the randomness is added to piecewise constant periodic dispersion, the pinning may even provide probability distributions of pulse parameters that are numerically indistinguishable from the statistically steady case. The pinning method can be used to both manufacture better fibers and upgrade existing fiber links.Comment: 4 pages, 2 figure

Stable two-dimensional dispersion-managed soliton

The existence of a dispersion-managed soliton in two-dimensional nonlinear Schr\"odinger equation with periodically varying dispersion has been explored. The averaged equations for the soliton width and chirp are obtained which successfully describe the long time evolution of the soliton. The slow dynamics of the soliton around the fixed points for the width and chirp are investigated and the corresponding frequencies are calculated. Analytical predictions are confirmed by direct PDE and ODE simulations. Application to a Bose-Einstein condensate in optical lattice is discussed. The existence of a dispersion-managed matter-wave soliton in such system is shown.Comment: 4 pages, 3 figures, Submitted to Phys. Rev.