  We study the antikaon potential at finite momentum for proton and neutron
nuclear matter. Our approach is based on the momentum dependence of the real
part of the total $K^-N$ scattering amplitude, which is fixed in free space by
experimental data, using the dispersion relation approach. We decompose the
contributions to the scattering amplitude from different processes and consider
the $\Lambda$(1405) and $\Sigma$(1385) to be dissolved in nuclear matter at
density $\rho_0$. Within this approach the $K^-$ potential is found to be
attractive up to high kaon momenta. Our result is in line with the data on the
antikaon potential evaluated from the analysis of kaonic atoms (low momenta),
heavy-ion (interdmediate momenta) and proton-nucleus (high momenta) collisions.
