Using a relativistic transport model, we study the azimuthal momentum asymmetry of kaons with fixed transverse momentum, i.e., the differential flow, in heavy-ion collisions at beam momentum of 6 GeV/c per nucleon, available from the Alternating Gradient Synchrotron ͑AGS͒ at the Brookhaven National Laboratory ͑BNL͒. We find that in the absence of kaon potential the kaon differential flow is positive and increases with transverse momentum as that of nucleons. The repulsive kaon potential as predicted by theoretical models, however, reduces the kaon differential flow, changing it to negative for kaons with low transverse momenta. Cancellation between the negative differential flow at low momenta and the positive one at high momenta is then responsible for the experimentally observed nearly vanishing in-plane transverse flow of kaons in heavyion experiments. ͓S0556-2813͑99͒02109-3͔ PACS number͑s͒: 25.75. Ld, 13.75.Jz, 21.65.ϩf Since the work of Kaplan and Nelson ͓1͔ on the possibility of a kaon condensation in the core of neutron stars, there have been many theoretical studies of kaon properties in dense matter ͓2͔. It is now generally agreed that a kaon has a weak repulsive potential in nuclear matter while an antikaon has instead a strong attractive one. The latter is responsible for the existence of the kaon condensation that was originally proposed in Ref. ͓1͔. Brown and Bethe ͓3͔ have further argued that because of the softening of the nuclear equation of state due to the kaon condensation, the maximum mass of neutron stars would decrease, hence allowing for the existence of mini black holes.Since a hot dense matter can be created in the initial stage of high energy heavy ion collisions, a unique opportunity thus exists for studying the kaon in-medium properties ͓4-7͔. Indeed, Li et al. ͓8͔ have shown that it is possible to extract the information on kaon potential or dispersion relation in dense matter from the kaon collective flow in heavy ion collisions. Specifically, they have found, based on the relativistic transport model, that the repulsive kaon potential in nuclear medium would reduce its flow relative to that of nucleons, while the flow of antikaons would be similar to that of nucleons due to their attractive potential ͓9͔. Since then, many theoretical studies ͓10-14͔ have been carried out, and all have reached the same conclusion. These theoretical studies have stimulated a number of experiments at both GSI and AGS. All experiments have shown that kaons have very small, if not zero, flow, i.e., both the kaon average in-plane transverse momentum as a function of rapidity and its slope at midrapidity are consistent with zero within the experimental error bars ͓15͔. For example, both the FOPI and KAOS Collaborations at SIS/GSI ͓16-18͔ have found a negligible flow for K ϩ in collisions of NiϩNi at E beam /Aϭ1.93 GeV and AuϩAu at 1 GeV, respectively. Several collaborations at the AGS/BNL have also carried out the flow analysis for K ϩ , K Ϫ , and K s 0 in AuϩAu collisions at beam energies from 2 to 12...