Using high-resolution cosmological N-body simulations, we study how the den
sity profiles of dark matter halos are affected by the filtering of the den
sity power spectrum below a given scale length and by the introduction of a
thermal velocity dispersion. In the warm dark matter (WDM) scenario, both
the free-streaming scale, R-f, and the velocity dispersion, v(th)(w), are d
etermined by the mass, m(W), of the WDM particle. We found that v(th)(w) is
too small to affect the density profiles of WDM halos. Down to the resolut
ion attained in our simulations (similar to0.01 virial radii), there is not
any significant difference in the density profiles and concentrations of h
alos obtained in simulations with and without the inclusion of v(th)(w). Re
solved soft cores appear only when we artificially increase the thermal vel
ocity dispersion to a value that is much higher than v(th)(w). We show that
the size of soft cores in a monolithic collapse is related to the tangenti
al velocity dispersion. The density profiles of the studied halos with mass
es down to similar to0.01 the filtering mass M-f can be described by the Na
varro-Frenk-White shape; soft cores are not formed. Nevertheless, the conce
ntrations of these halos are lower than those of the CDM counterparts and a
re approximately independent of mass. The cosmogony of halos with masses le
ss than or similar to M-f is not hierarchical: they form through monolithic
collapse and by fragmentation of larger structures. The formation epoch of
these halos is slightly later than that of halos with masses approximate t
o M-f. The lower concentrations of WDM halos with respect to their CDM coun
terparts can be accounted for by their late formation epoch. Overall, our r
esults point to a series of advantages of a WDM model over the CDM one. In
addition to solving the substructure problem, a WDM model with R-f similar
to 0.16 Mpc (m(W) approximate to 0.75 keV; flat cosmology with Omega (Lambd
a) = h = 0.7) also predicts concentrations, a Tully-Fisher relation, and fo
rmation epochs for small halos, which seems to be in better agreement with
observations than CDM predictions.