In this paper, solutions of the nonlinear Schrödinger equation with a parabolic and a periodic potential modelling the dynamics of Bose–Einstein condensates are considered. A Galërkin projection approach is applied to reduce the partial differential equation to a system of nonlinear ordinary...

We study the dynamics of solitons in Bose–Einstein condensates (BECs) loaded into an optical lattice (OL), which is combined with an external parabolic potential. Chiefly, the one-dimensional (1D) case is considered. First, we demonstrate analytically that, in the case of the repulsive BEC,...

We study the dynamics of atomic Bose–Einstein condensates (BECs), when the quadrupole mode is excited. Within the Thomas–Fermi approximation, we derive an exact first-order system of differential equations that describes the parameters of the BEC wave function. Using perturbation theory...

Motivated by the recent experimental progress on the collective modes of a Bose–Einstein condensate whose atomic scattering length is tuned via Feshbach resonances, we analyze by variational means the dynamics of Faraday waves in trapped Bose–Einstein condensates. These waves can be excited...

By employing a nonlinear three-mode model, we study the band structure of Bose–Einstein condensates in Fourier-Synthesized optical lattices, where the nonlinearity comes from the mean field treatment of interaction between atoms. In linear case, we present the band structure of the system. It...

We derive a general expression for interferencing intensity in two Bose–Einstein condensates with Josephson-like coupling when the two Bose–Einstein condensates are initially in arbitrary quantum pure states. The expression can be used to numerically calculate the intensity. As examples, we...

The dynamics of dissipative and coherent N-body systems, such as a Bose–Einstein condensate, which can be described by an extended Gross–Pitaevskii formalism, is investigated. In order to analyze chaotic and unstable regimes, two approaches are considered: a metric one, based on calculations...

We systematically investigate slowly moving matter-wave gap soliton propagation in weak random optical lattices. With the weak randomness, an effective-particle theory is constructed to show that the motion of a gap soliton is similar to a particle moving in random potentials. Based on the...

We present one-dimensional (1D) stability analysis of a recently proposed method to filter and control localized states of the Bose–Einstein condensate (BEC), based on novel trapping techniques that allow one to conceive methods to select a particular BEC shape by controlling and manipulating...