Formations of n-order two-soliton bound states in Bose-Einstein condensates with spatiotemporally modulated nonlinearities

The formations of n-order two-soliton bound states (TSBSs) in the Bose-Einstein condensates with spatiotemporally modulated nonlinearities are studied. Exact analytical expressions of the n-order TSBSs are derived by means of the similarity transformations. Further, the numerical simulations are carried out, consistent with the analytical results very well. The stability analysis shows that the solutions can be stable. Our results indicate that the attractive spatiotemporal inhomogeneous nonlinearities can support n-order TSBSs, which has the potential applications to the generation of matter-wave bright solitons in harmonic traps.