  Within the newly updated version of the ultrarelativistic quantum molecular
dynamics (UrQMD) model, the transverse-velocity dependence of the elliptic flow
of free nucleons from $^{197}$Au+$^{197}$Au collisions at the incident energy
400 MeV$/$nucleon is studied within different windows of the normalized c.m.
rapidity $y_0$. It is found that the elliptic flow difference
$v_{2}^{n}$-$v_{2}^{p}$ and ratio $v_{2}^{n}$/$v_{2}^{p}$ of neutrons versus
protons are sensitive to the density dependence of the symmetry energy,
especially the ratio $v_{2}^{n}$/$v_{2}^{p}$ at small transverse velocity in
the intermediate rapidity intervals $0.4<|y_0|<0.6$. By comparing either
transverse-momentum dependent or integrated FOPI/LAND elliptic flow data of
nucleons and hydrogen isotopes with calculations using various Skyrme
interactions, all exhibiting similar values of isoscalar incompressibility but
very different density dependences of the symmetry energy, a moderately soft to
linear symmetry energy is extracted, in good agreement with previous UrQMD or
T\"{u}bingen QMD model calculations but contrasting results obtained with
$\pi^-/\pi^+$ yield ratios available in the literature.
