Collisionally Inhomogeneous Bose-Einstein Condensates

This dissertation studies solitary waves in collisionally inhomogeneous BoseEinstein condensates in a magnetic trap using a quasi-1D mean-field model. We introduce a model for Bose-Einstein condensate with spatially and temporally modulated nonlinearity. In terms of the spatially periodic nonlinear lattice, we study BECs in a lattice one of which minimum in a period either overlap with the minimum of magnetic trap (termed ‘aligned’) or is displaced by π 2 (termed ‘misaligned’). In BECs in an aligned and misaligned lattice, both bright solitons and dark solitons are identified. Stability analysis using the BdG equations shows that bright solitons with this spatial modulation are always stable, whereas dark solitons can be either stable or unstable. A further investigation of how their stability depends on physical parameters reveals that the aligned and misaligned lattices introduce different behaviours. Unstable dark solitons can have both real eigenvalues and a quadruplet of four eigenvalues in an aligned lattice. In contrast, unstable dark solitons in BECs in a misaligned lattice can have only real eigenvalues. We also investigate the temporal evolution of both bright solitons and dark solitons in a dynamical nonlinear lattice. After studying the response of bright solitons and dark solitons to the turning on of a nonlinear lattice, we can expect a stable transition if the turning on is slow. If the lattice is abruptly turned on, instability occurs.