  We present a study of the central exclusive production of the $K^{+} K^{-}$
pairs in proton-proton collisions at high energies. We consider diffractive
mechanisms including the $K^{+} K^{-}$ continuum, the dominant scalar
$f_{0}(980)$, $f_{0}(1500)$, $f_{0}(1710)$ and tensor $f_{2}(1270)$,
$f'_{2}(1525)$ resonances decaying into the $K^{+} K^{-}$ pairs. We include
also photoproduction mechanisms for the non-resonant (Drell-S\"{o}ding) and the
$\phi(1020)$ resonance contributions. The theoretical results are calculated
within the tensor-pomeron approach including both pomeron and reggeon
exchanges. Predictions for planned or current experiments at RHIC and LHC are
presented. We discuss the influence of the experimental cuts on the integrated
cross section and on various differential distributions for outgoing particles.
The distributions in two-kaon invariant mass, in a special `glueball filter
variable', as well as examples of angular distributions in the $K^{+}K^{-}$
rest frame are presented. We compare the $\phi(1020)$ and continuum
photoproduction contributions to the $f_{0}(980)$ and continuum diffractive
contributions and discuss whether the $\phi(1020)$ resonance could be extracted
experimentally. For the determination of some model parameters we also include
a discussion of $K$-nucleon scattering, in particular total cross sections, and
of $\phi(1020)$ photoproduction.

High Energy Physics - Phenomenology