  In 2017, the BESIII Collaboration announced the observation of a charged
charmonium-like structure in the $\psi(3686)\pi^\pm$ invariant mass spectrum of
the $e^+ e^- \to \psi(3686) \pi^+ \pi^-$ process at different energy points,
which enables us to perform a precise study of this process based on the
initial single pion emission (ISPE) mechanism. In this work, we perform a
combined fit to the experimental data of the cross section of $e^+ e^- \to
\psi(3686) \pi^+ \pi^-$, and the corresponding $\psi(3686)\pi^\pm$ and dipion
invariant mass spectra. Our result shows that the observed charged
charmonium-like structure in $e^+ e^- \to \psi(3686) \pi^+ \pi^-$ can be well
reproduced based on the ISPE mechanism, and that the corresponding dipion
invariant mass spectrum and cross section can be depicted with the same
parameters. In fact, it provides strong evidence that the ISPE mechanism can be
an underlying mechanism resulting in such novel a phenomenon.
