  We investigate the $D_{s}^{+} \rightarrow K^{+} K^{-} \pi^{+}$ decay
theoretically with the final state interactions, which is based on the chiral
unitary approach and takes into account the external and internal $W$-emission
mechanisms at the quark level. Only considering three resonances contributions,
the $f_0(980)$ in $S$-wave, the $\bar {K}^{*}(892)^{0}$ and $\phi(1020)$ in
$P$-wave, one can make a good description of the recent experimental data from
BESIII Collaboration, where the contribution from $S$-wave is found to be
small. Besides, we also make a calculation of the corresponding branching
fractions, which are consistent with the results of BESIII Collaboration and
Particle Data Group.
