Beating dark-dark solitons and Zitterbewegung in spin-orbit coupled Bose-Einstein condensates

We present families of beating dark-dark solitons in spin-orbit (SO) coupled Bose-Einstein condensates. These families consist of solitons residing simultaneously in the two bands of the energy spectrum. The soliton components are characterized by two different spatial and temporal scales, which are identified by a multiscale expansion method. The solitons are "beating" ones, as they perform density oscillations with a characteristic frequency, relevant to Zitterbewegung (ZB). We find that spin oscillations may occur, depending on the parity of each soliton branch, which consequently lead to ZB oscillations of the beating dark solitons. Analytical results are corroborated by numerical simulations, illustrating the robustness of the solitons.Comment: 6 pages, 3 figure

Crossover dark soliton dynamics in ultracold one-dimensional Bose gases

Ultracold confined one-dimensional atomic gases are predicted to support dark soliton solutions arising from a nonlinear Schr\"{o}dinger equation of suitable nonlinearity. In weakly-interacting (high density) gases, the nonlinearity is cubic, whereas an approximate model for describing the behaviour of strongly - interacting (low density) gases is one characterized by a quintic nonlinearity. We use an approximate analytical expression for the form of the nonlinearity in the intermediate regimes to show that, near the crossover between the two different regimes, the soliton is predicted and numerically confirmed to oscillate at a frequency of $\sqrt{2/3}\Omega$, where $\Omega$ is the harmonic trap frequency.Comment: To appear in Phys. Lett.

Matter-wave solitons of collisionally inhomogeneous condensates

We investigate the dynamics of matter-wave solitons in the presence of a spatially varying atomic scattering length and nonlinearity. The dynamics of bright and dark solitary waves is studied using the corresponding Gross-Pitaevskii equation. The numerical results are shown to be in very good agreement with the predictions of the effective equations of motion derived by adiabatic perturbation theory. The spatially dependent nonlinearity leads to a gravitational potential that allows to influence the motion of both fundamental as well as higher order solitons.Comment: 19 pages, 4 figure

On the Modulational Instability of the Nonlinear Schr\"odinger Equation with Dissipation

The modulational instability of spatially uniform states in the nonlinear Schr\"odinger equation is examined in the presence of higher-order dissipation. The study is motivated by results on the effects of three-body recombination in Bose-Einstein condensates, as well as by the important recent work of Segur et al. on the effects of linear damping in NLS settings. We show how the presence of even the weakest possible dissipation suppresses the instability on a longer time scale. However, on a shorter scale, the instability growth may take place, and a corresponding generalization of the MI criterion is developed. The analytical results are corroborated by numerical simulations. The method is valid for any power-law dissipation form, including the constant dissipation as a special case