  The $\bar{K} + N \to K + \Xi$ reaction is studied for center-of-momentum
energies ranging from threshold to 3 GeV in an effective Lagrangian approach
that includes the hyperon $s$- and $u$-channel contributions as well as a
phenomenological contact amplitude. The latter accounts for the rescattering
term in the scattering equation and possible short-range dynamics not included
explicitly in the model. Existing data are well reproduced and three
above-the-threshold resonances were found to be required to describe the data,
namely, the $\Lambda(1890)$, $\Sigma(2030)$, and $\Sigma(2250)$. For the latter
resonance we have assumed the spin-parity of $J^P=5/2^-$ and a mass of 2265
MeV. The $\Sigma(2030)$ resonance is crucial in achieving a good reproduction
of not only the measured total and differential cross sections, but also the
recoil polarization asymmetry. More precise data are required before a more
definitive statement can be made about the other two resonances, in particular,
about the $\Sigma(2250)$ resonance that is introduced to describe a small bump
structure observed in the total cross section of $K^- + p \to K^+ + \Xi^-$. The
present analysis also reveals a peculiar behavior of the total cross section
data in the threshold energy region in $K^- + p \to K^+ + \Xi^-$, where the
$P$- and $D$-waves dominate instead of the usual $S$-wave. Predictions for the
target-recoil asymmetries of the $\bar{K} + N \to K + \Xi$ reaction are also
presented.
