  Semi-inclusive triple differential multiplicity distributions of positively
charged kaons have been measured over a wide range in rapidity and transverse
mass for central collisions of $^{58}$Ni with $^{58}$Ni nuclei. The transverse
mass ($m_t$) spectra have been studied as a function of rapidity at a beam
energy 1.93 AGeV. The $m_t$ distributions of K^+ mesons are well described by a
single Boltzmann-type function. The spectral slopes are similar to that of the
protons indicating that rescattering plays a significant role in the
propagation of the kaon. Multiplicity densities have been obtained as a
function of rapidity by extrapolating the Boltzmann-type fits to the measured
distributions over the remaining phase space. The total K^+ meson yield has
been determined at beam energies of 1.06, 1.45, and 1.93 AGeV, and is presented
in comparison to existing data. The low total yield indicates that the K^+
meson can not be explained within a hadro-chemical equilibrium scenario,
therefore indicating that the yield does remain sensitive to effects related to
its production processes such as the equation of state of nuclear matter and/or
modifications to the K^+ dispersion relation.
