  The contribution of collective or reaction channels to a local optical model
potential, OMP, can be readily calculated as a dynamical polarization
potential, DPP. The resulting local DPPs commonly have undulatory (`wavy')
features, often including local regions of emissivity in the imaginary
component. We show here that this undularity arises from $l$-dependence of the
underlying formal non-local and $l$-dependent DPP. The $l$-independent proton
OMPs, that have the same $S$-matrix $S_{lj}$ as phenomenological $l$-dependent
potentials, exhibit undulations that are qualitatively similar to undulations
of local DPPs generated by channel coupling. The $l$-dependent phenomenological
potentials studied are the potentials that give the best existing fits to the
relevant elastic scattering data and the undulatory potentials presented here,
being $S$-matrix equivalent (i.e.\ having the same $S$-matrix, $S_{lj}$) give
exactly the same scattering. In addition, we present calculations strongly
suggesting that undularity (`waviness') is a generic property of
$l$-independent potentials that are $S$-matrix equivalent to $l$-dependent
potentials. Implications for the validity of folding models based on a local
density model are noted.
