  A recent experiment has detected collision-induced frequency shifts in bright
matter-wave solitons for the first time [Nat. Phys. 10, 918 (2014)]. Using a
particle model, we derive the frequency shift for two solitons in a harmonic
trap, and compare it to the results of the recent experiment and reported
theoretical approximation. We find regimes where the frequency shift is much
smaller than previously predicted, and propose experiments to test these
findings. We also predict that reducing the experimental trap frequency will
reveal for the first time soliton molecules or soliton bound states in a cold
atoms system. The dynamics of such bound states are found to be both highly
phase-dependent, and sensitive to the residual 3D nature of the experiment.
