  The inclusion of strong coupling to states of projectile and target nuclei
for 115.9 MeV \nuc{16}{O} scattering from \nuc{12}{C} leads to an S-matrix
which, when subject to $S_{L} \rightarrow V(r) $ inversion, yields highly
undulatory local potentials. Previous work has shown that explicitly
$L$-dependent non-undulatory potentials are equivalent to undulatory
$L$-independent potentials with the same S-matrix. Here we show that
$L$-independent equivalents for certain simple model $L$-dependent potentials
exhibit undulatory features qualitatively similar to those arising from channel
coupling for 115.9 MeV \nuc{16}{O} scattering from \nuc{12}{C}. We discuss the
relevance to the question of $L$-dependence as a generic property of
nucleus-nucleus interactions.
