A free-standing ferroelectric film subjected to a rotating electric in-plane field has previously been investigated under a polarizing microscope [1]. Depending on the strength and rotation frequency of the external field, various kinds of pattern formation were observed, e.g. ring systems which can shrink or grow. This contribution provides a theoretical examination of the effect. It is based on the usual Landau theory [2]. In particular, it is shown that the ring systems observed can be described as inversion walls, which exhibit soliton-like behavior(1). The analytical results are supported by numerical simulations. As a result, a qualitative and, to some extend, also a quantitative understanding of the complex behavior of ferroelectric liquid crystals in the case of inhomogeneously aligned smectic layers has been achieved.