  The relativistic transport model, in which the nucleon effective mass is
connected to the scalar field while its energy is shifted by the vector
potential, is extended to include the kaon degree of freedom. We further take
into account the medium modification of the kaon mass due to the explicit
chiral symmetry breaking. Both the propagation of kaons in the mean-field
potential and the kaon-baryon elastic scattering are explicitly treated in our
study. We find that the attractive kaon scalar mean-field potential in the
dense matter leads to an enhanced kaon yield in heavy-ion collisions at
energies of about 1 GeV/nucleon. The final-state kaon-baryon scattering is seen
to affect significantly the kaon momentum spectra, leading to an enhanced yield
of kaons with large momenta or at large laboratory angles. With a soft nuclear
equation of state and including the attractive kaon scalar potential, the
calculated kaon energy spectra agree with the data from the heavy-ion
synchrotron at GSI.
