  This work investigates the collective motion of kaons in heavy ion reactions
at SIS energies (about 1-2 GeV/nucleon). A radial collective flow of $K^+$
mesons is predicted to exist in central Au + Au collisions, which manifests in
a characteristic "shoulder-arm" shape of the transverse mass spectrum of the
midrapidity $K^+$ mesons. The $K^+$ radial flow arises from the repulsive $K^+$
mean field in nuclear matter. In spite of a strong reabsorption and
rescattering the attractive $K^-$ mean field leads as well to a collective
radial flow of $K^-$ mesons. The $K^-$ radial flow, however, is different from
that of $K^+$ mesons and can be observed by a characteristic "concave"
structure of the transverse mass spectrum of the $K^-$ mesons emitted at
midrapidity. The kaon radial flows can therefore serve as a novel tool for the
investigation of kaon properties in dense nuclear matter.
