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In this paper we elucidate the physics underlying the fact that both brightand dark solitary waves can arise in a one-dimensional spin-polarized gas offermionic atoms with attractive three-dimensional p-wave interactions in ahard-wall trap. This is possible since the one-dimensional fermion system canbe mapped to a system of bosons described by the Lieb-Liniger model with eitherrepulsive or attractive delta-function interactions which can support solitarywaves.

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