Matter-Wave Solitons in Two-Component Bose-Einstein Condensates with Tunable Interactions and Time Varying Potential

We present three families of exact matter-wave soliton solutions for an effective one-dimension two-component Bose-Einstein condensates (BECs) with tunable interactions, harmonic potential and gain or loss term.We investigate the dynamics of bright-bright solitons, bright-dark solitons
and dark-dark solitons for the time-dependent expulsive harmonic trap potential,periodically modulated harmonic trap potential, and kinklike modulated harmonic trap potential.Through the Feshbach resonance, these dynamics can be realized in experiments by suitable control of time-dependent trap parameters, atomic interactions, and interaction with thermal cloud.