  The main focus of the present work is to study quasi-one-dimensional
kink-antikink stripes embedded in the two-dimensional sine-Gordon equation.
Using variational techniques, we reduce the interaction dynamics between a kink
and an antikink stripe on their respective time and space dependent widths and
locations. The resulting reduced system of coupled equations is found to
accurately describe the width and undulation dynamics of a single kink stripe
as well as that of interacting ones. As an aside, we also discuss two related
topics: the computational identification of the kink center and its numerical
implications and alternative perturbative and multiple scales approaches to the
transverse direction induced dynamics for a single kink stripe in the
two-dimensional realm.
