  We report on a systematic study of temporal Kerr cavity soliton dynamics in
the presence of pulsed or amplitude modulated driving fields. In stark contrast
to the more extensively studied case of phase modulations, we find that Kerr
cavity solitons are not always attracted to maxima or minima of driving field
amplitude inhomogeneities. Instead, we find that the solitons are attracted to
temporal positions associated with specific driving field values that depend
only on the cavity detuning. We describe our findings in light of a spontaneous
symmetry breaking instability that physically ensues from a competition between
coherent driving and nonlinear propagation effects. In addition to identifying
a new type of Kerr cavity soliton behaviour, our results provide valuable
insights to practical cavity configurations employing pulsed or amplitude
modulated driving fields.
