Nonautonomous vector matter waves in two-component Bose-Einstein condensates with combined time-dependent harmonic-lattice potential

We construct exact self-similar soliton solutions of three-dimensional coupled Gross-Pitaevskii equations for two-species Bose-Einstein condensates (BECs) in a combined time-dependent harmonic-lattice potential. Based on these solutions, we investigate the control and manipulation of solitary waves for three kinds of BECs with changing diffraction and nonlinearity coefficients; the solutions include Ma breathers and Peregrine and Akhmediev soliton solutions. Our results indicate that matter waves readily propagate in this system. It is shown that diffraction and lattice potential factors play important roles in the beam evolution characteristics, such as the peak, the phase offset, the linear phase, and the chirp.