[en] We construct explicit multisoliton complex solutions for multicomponent Bose–Einstein condensate systems with time- and spatial-coordinate-dependent atomic potentials and interactions. The exact solutions are used to analyze the important solitary matter wave properties such as the profiles of temporal and spatial multimode beams as well as focusing effects. Results demonstrate that soliton complexes can be controlled nonlinearly during the interaction by modulating the external potentials and nonlinearities. - Highlights: • An algebraic approach is proposed for the dynamics of multicomponent BECs. • External potentials and nonlinearities are time and space-dependent. • Analytical solutions are constructed. • Multisoliton complexes are predicted