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We study the dynamics and pairwise interactions of dark soliton stripes inthe two-dimensional defocusing nonlinear Schr\"odinger equation. By employing avariational approach we reduce the dynamics for dark soliton stripes to a setof coupled one-dimensional "filament" equations of motion for the position andvelocity of the stripe. The method yields good qualitative agreement with thenumerical results as regards the transverse instability of the stripes. Wepropose a phenomenological amendment that also significantly improves thequantitative agreement of the method with the computations. Subsequently, themethod is extended for a pair of symmetric dark soliton stripes that includethe mutual interactions between the filaments. The reduced equations of motionare compared with a recently proposed adiabatic invariant method and itscorresponding findings and are found to provide a more adequate representationof the original full dynamics for a wide range of cases encompassingperturbations with long and short wavelengths, and combinations thereof.

Reduced dynamics for one and two dark soliton stripes in the defocusing nonlinear Schr\"odinger equation: a variational approach