  We study the dynamics and pairwise interactions of dark soliton stripes in
the two-dimensional defocusing nonlinear Schr\"odinger equation. By employing a
variational approach we reduce the dynamics for dark soliton stripes to a set
of coupled one-dimensional "filament" equations of motion for the position and
velocity of the stripe. The method yields good qualitative agreement with the
numerical results as regards the transverse instability of the stripes. We
propose a phenomenological amendment that also significantly improves the
quantitative agreement of the method with the computations. Subsequently, the
method is extended for a pair of symmetric dark soliton stripes that include
the mutual interactions between the filaments. The reduced equations of motion
are compared with a recently proposed adiabatic invariant method and its
corresponding findings and are found to provide a more adequate representation
of the original full dynamics for a wide range of cases encompassing
perturbations with long and short wavelengths, and combinations thereof.
