Two dark solitons are considered in a two-component Bose-Einstein condensate with an external magnetic trap, and effects of the trap potential on their dynamics are investigated by the numerical simulation. The results show that the dark solitons attract,
Based on the weakly coupled mode theory, the modulation properties of three-waveguide system are analyzed in general. We examine the modulation behavior for two cases that a voltage is applied on the beam-launched waveguide or non-beam-launched waveguide.