Matter-wave solitons of Bose-Einstein condensates in a time-dependent complicated potential

We investigate the dynamics of matter-wave solitons in Bose-Einstein condensates with a time-dependent complicated potential, which is composed of a linear, a harmonic and a complex potential of arbitrary form. This system is characterized by the time dependence of all the parameters of the complicated potential. A unified transformation is derived and exact soliton solutions are obtained analytically. Our results show that the dynamical evolution of the solitons can be dramatically affected by the complicated potential; the collisions between two solitons are essentially elastic in the absence of complex potential. Moreover, it is found that the number of atoms in the soliton can be effectively controlled by a proper choice of the external complex potential.