A. Gammal

Stability of trapped Bose-Einstein condensates

In three-dimensional trapped Bose-Einstein condensate (BEC), described by the time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of initial conditions on stability using a Gaussian variational approach and exact numerical simulations. We also discuss the validity of the criterion for stability suggested by Vakhitov and Kolokolov. The maximum initial chirp (initial focusing defocusing of cloud) that can lead a stable condensate to collapse even before the number of atoms reaches its critical limit is obtained for several specific cases. When we consider two- and three-body nonlinear terms, with negative cubic and positive quintic terms, we have the conditions for the existence of two phases in the condensate. In this case, the magnitude of the oscillations between the two phases are studied considering sufficient large initial chirps. The occurrence of collapse in a BEC with repulsive two-body interaction is also shown to be possible.

Improved numerical approach for the time-independent Gross-Pitaevskii nonlinear Schrodinger equation

In the present work, we improve a numerical method, developed to solve the Gross-Pitaevkii nonlinear Schrödinger equation. A particular scaling is used in the equation, which permits us to evaluate the wave-function normalization after the numerical solution. We have a two-point boundary value problem, where the second point is taken at infinity. The differential equation is solved using the shooting method and Runge-Kutta integration method, requiring that the asymptotic constants, for the function and its derivative, be equal for large distances. In order to obtain fast convergence, the secant method is used.

Critical number of atoms for attractive Bose-Einstein condensates with cylindrically symmetrical traps

We calculated, within the Gross-Pitaevskii formalism, the critical number of atoms for Bose-Einstein condensates with two-body attractive interactions in cylindrical traps with different frequency ratios. In particular, by using the trap geometries considered by Roberts et al. [Phys. Rev. Lett. 86, 4211 (2001)], we show that the theoretical maximum critical numbers are given approximately by

Oblique Dark Solitons in Supersonic Flow of a Bose-Einstein Condensate

{N}_{c}{=0.55(l}_{0}/|a|).

Dissipationless shock waves in Bose-Einstein condensates with repulsive interaction between atoms

Our results also show that, by exchanging the frequencies

DYNAMICS OF BRIGHT MATTER WAVE SOLITONS IN A BOSE EINSTEIN CONDENSATE

{\ensuremath{\omega}}_{z}

Atomic Bose-Einstein condensation with three-body interactions and collective excitations

and

Localized modes of binary mixtures of Bose-Einstein condensates in nonlinear optical lattices

{\ensuremath{\omega}}_{\ensuremath{\rho}},

Autosolitons in trapped Bose-Einstein condensates with two- and three-body inelastic processes

the geometry with

Critical numbers of attractive Bose-Einstein condensed atoms in asymmetric traps

{\ensuremath{\omega}}_{\ensuremath{\rho}}l{\ensuremath{\omega}}_{z}