LAUSR

The gain or loss effect on the dynamics of the matter-wave solitons in three-component Bose–Einstein condensates with time-modulated interactions trapped in parabolic external potentials are investigated analytically. Some exact matter-wave soliton solutions to the three-coupled Gross–Pitaevskii equation describing the three-component Bose–Einstein condensates are constructed by similarity transformation. The dynamical properties of the matter-wave solitons are analyzed graphically, and the effects of the gain or loss parameter and the frequency of the external potentials on the matter-wave solitons are explored. It is shown that the gain coefficient makes the atom condensate to absorb energy from the background, while the loss coefficient brings about the collapse of the condensate.