  We investigate the collisions of Majorana zero modes, which are presented as
inter-soliton collisional events in fermionic superfluids with spin-orbit
coupling. Our results demonstrate that, the zero energy splitting, induced by
the overlapping of inter-soliton Majorana wave-functions upon collision,
generates an effective repulsive force for Majorana states, which in turn
protected themselves against into bulk excitation. As a result, the collision
between solitons associated with Majorana zero modes appears to be repulsive
and elastic, as they do not penetrate each other but instead repel without
energy loss. As well, similar repulsive behavior is observed in collisions
between soliton-induced and defect-pinned Majorana zero modes. Our research
offers new insights into the features of Majorana fermions, and robustness in
the collisions of Majorana zero modes bodes well for the prospects of
topological quantum computation with a multitude of Majorana qubits.
