Bright and dark solitary waves in a one-dimensional spin-polarized gas of fermionic atoms with p -wave interactions in a hard-wall trap

We elucidate the physics underlying the fact that both bright and dark solitary waves can arise in a one-dimensional spin-polarized gas of fermionic atoms with attractive three-dimensional p -wave interactions in a hard-wall trap. This is possible since the one-dimensional fermion system can be mapped to a system of bosons described by the Lieb-Linger model with either repulsive or attractive δ -function interactions which can support solitary waves.