  In this work, we study the ($S$, $P$ and $D$)-wave $K^+K^-$ contributions to
$B\to KKK$ decays in the perturbative QCD approach at leading order. Within the
two-meson wave functions describing the nonperturbative dynamics in the
kaon-pair for different waves, we calculate the branching fractions and the
direct $CP$ asymmetries of these decay modes in the corresponding resonance
regions. Most of our numerical results are well consistent with the current
measurements. We note that the narrow-width approximation is invalid in the
quasi-two-body decays $B\to Kf_0(980)\to KKK$. For other decays, under the
narrow-width approximation we can extract the branching fractions of the
corresponding two-body decays involving the intermediate resonant states, and
the related branching fractions agree with the current experimental data well.
Furthermore, we also predict the corresponding quasi-two-body decays $B\to
K\pi^+\pi^-$, which are expected to be measured in the ongoing LHCb and
Belle-II experiments.
