  We report on a non-linear scattering effect that challenges the notion of
topological protection for wave packets propagating in chiral edge modes.
Specifically, in a Floquet topological system close to resonant driving and
with a non-linear potential, we demonstrate how a wave packet propagating in a
chiral edge mode may be irreversibly deflected by scattering off a localized
wave-packet, or pass the collision region virtually unaffected in an
approximately linear fashion. An experimentally accessible knob to tune between
those two scenarios is provided by the relative phase between the involved
wave-packets. This genuinely non-linear interference phenomenon is in stark
contrast to linear scattering off a static impurity, which cannot destroy a
topological edge state. Besides corroborating our findings with numerically
exact simulations, we propose two physical platforms where our predictions may
be verified with state of the art experimental techniques: First, a coupled
waveguide setting where non-linearity has been engineered via an
intensity-dependent optical index. Second, a Bose-Einstein condensate of cold
atoms in an optical Honeycomb lattice governed by a non-linear Gross-Pitaevskii
equation that effectively accounts for many-body interactions.
