The transverse-momentum distributions of pions in the Au(1 GeV/nucleon
) + Au collisions are analyzed. The calculations are carried out withi
n relativistic mean-field one- and two-fluid models. The rapidity dist
ributions of the mean transverse momentum of pions are found to be fai
rly sensitive to the nuclear equation of state and, especially, to the
stopping power. It is shown that the collective flow of pions in the
reaction plane always correlates with the ''hot'' how of nucleons (i.e
. those emitted from hot regions of nuclear system), while not always
with the total nucleon how. This ''hot'' nucleon flow can be experimen
tally singled out by selecting nucleons with sufficiently high transve
rse momenta. We predict that the ''hot'' nucleon flow selected in this
way will always correlate with the pion flow. Available experimental
data on transverse-momentum spectra of pions are compared with calcula
tions employing various equations of state and stopping power.