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We study interactions between the dark solitons of the parametrically drivennonlinear Schr\"odinger equation, Eq.(\ref{NLS}). When the driving strength,$h$, is below $\sqrt{\gamma^2 +1/9}$, two well-separated N\'eel walls may repelor attract. They repel if their initial separation $2z(0)$ is larger than thedistance $2z_u$ between the constituents in the unstable stationary complex oftwo walls. They attract and annihilate if $2z(0)$ is smaller than $2z_u$. TwoN\'eel walls with $h$ lying between $\sqrt{\gamma^2 + 1/9}$ and a thresholddriving strength $h_{sn}$ attract for $2z(0)<2z_u$ and evolve into a stablestationary bound state for $2z(0)>2z_u$. Finally, the N\'eel walls with $h$greater than $h_{sn}$ attract and annihilate -- irrespective of their initialseparation. Two Bloch walls of opposite chiralities attract, while Bloch wallsof like chiralities repel -- except near the critical driving strength, wherethe difference between the like-handed and oppositely-handed walls becomesnegligible. In this limit, similarly-handed walls at large separations repelwhile those placed at shorter distances may start moving in the same directionor transmute into an oppositely-handed pair and attract. The collision of twoBloch walls or two nondissipative N\'eel walls typically produces a quiescentor moving breather.Comment: 46 pages, 23 figures. To appear in Phys Rev E. A reference adde

Interactions of parametrically driven dark solitons. I. Néel-Néel and Bloch-Bloch interactions