  We employ an isospin dependent version of the QMD transport model to study
the influence of the isospin dependent part of the nuclear matter equation of
state and in-medium nucleon-nucleon cross-sections on the dynamics of heavy-ion
collisions at intermediate energies. We find that the extraction of useful
information on the isospin-dependent part of the equation of state of nuclear
matter from proton or neutron elliptic flows is obstructed by their sensitivity
to model parameters and in-medium values of nucleon-nucleon cross-sections.
Opposite to that, neutron-proton elliptic flow difference shows little
dependence on those variables while its dependence on the isospin asymmetric
EoS is enhanced. Comparison with experimental neutron-hydrogen FOPI-LAND data
excludes the extreme super-soft scenarios for the high density dependence of
asy-EoS. Existing neutron-proton elliptic flow difference experimental data are
poised with uncertainties and cannot constrain the asy-EoS any further.
