 If the BEC is repulsive, so that formula_30, then a possible solution of the Gross–Pitaevskii equation is,

where formula_32 is the value of the condensate wavefunction at formula_33, and formula_34 is the coherence length (a.k.a.the healing length, see below).This solution represents the dark soliton, since there is a deficit of condensate in a space of nonzero density.