Compression of bright bound soliton trains in the Bose-Einstein condensates with exponentially time-dependent atomic scattering length in an expulsive parabolic potential

► Three types of two bright bound solitons with increasing coherence in Bose-Einstein condensates are investigated. ► Two methods are provided to improve the number of matter density peaks before the soliton collapse. ► Compression of three- and four-bright-bound-soliton trains is presented. ► Estimation of net binding forces gives an explanation for soliton interaction patterns.