  A minimal coupling quantum hydrodynamic model of spin-1/2 fermions at the
full spin polarization corresponding to a nonlinear Schrodinger equation is
considered. The nonlinearity is primarily caused by the Fermi pressure. It
provides an effective repulsion between fermions. However, there is the
additional contribution of the short-range interaction appearing in the third
order by the interaction radius. It leads to the modification of the pressure
contribution. Solitons are considered for the infinite medium with no
restriction on the amplitude of the wave. The Fermi pressure leads to the
soliton in form of the area of decreased concentration. However, the center of
solution corresponding to the area of minimal concentration has nonzero value
of concentration. Therefore, the grey soliton is found. Soliton exist if the
speed of its propagation is below the Fermi velocity.
