  Based on recent experimental results, we give field-theoretic description of
$U(1)$ defects localized on the domain lines on thin films. We describe
topology of our model and solve this model in the adiabatic approximation. It
turns out that such a model naturally provides periodic structure observed in
experiment. The effective theory turns out to be the sine-Gordon model, but
unlike the previous theoretical considerations we argue that in this case it is
favorable for sine-Gordon kinks to merge into one defect with a uniform
winding. We consider a system of adjacent domain lines and anti-lines and
explain the experimental fact that the appearance of defects on a domain line
prevents defect creation on the adjacent anti-lines. We also quantize the model
and investigate possible effects of finite transverse dimension of the film.
